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## Mathematics Education Theses and Dissertations

Theses/dissertations from 2024 2024.

New Mathematics Teachers' Goals, Orientations, and Resources that Influence Implementation of Principles Learned in Brigham Young University's Teacher Preparation Program , Caroline S. Gneiting

## Theses/Dissertations from 2023 2023

Impact of Applying Visual Design Principles to Boardwork in a Mathematics Classroom , Jennifer Rose Canizales

Practicing Mathematics Teachers' Perspectives of Public Records in Their Classrooms , Sini Nicole White Graff

Parents' Perceptions of the Importance of Teaching Mathematics: A Q-Study , Ashlynn M. Holley

Engagement in Secondary Mathematics Group Work: A Student Perspective , Rachel H. Jorgenson

## Theses/Dissertations from 2022 2022

Understanding College Students' Use of Written Feedback in Mathematics , Erin Loraine Carroll

Identity Work to Teach Mathematics for Social Justice , Navy B. Dixon

Developing a Quantitative Understanding of U-Substitution in First-Semester Calculus , Leilani Camille Heaton Fonbuena

The Perception of At-Risk Students on Caring Student-Teacher Relationships and Its Impact on Their Productive Disposition , Brittany Hopper

Variational and Covariational Reasoning of Students with Disabilities , Lauren Rigby

Structural Reasoning with Rational Expressions , Dana Steinhorst

Student-Created Learning Objects for Mathematics Renewable Assignments: The Potential Value They Bring to the Broader Community , Webster Wong

## Theses/Dissertations from 2021 2021

Emotional Geographies of Beginning and Veteran Reformed Teachers in Mentor/Mentee Relationships , Emily Joan Adams

You Do Math Like a Girl: How Women Reason Mathematically Outside of Formal and School Mathematics Contexts , Katelyn C. Pyfer

Developing the Definite Integral and Accumulation Function Through Adding Up Pieces: A Hypothetical Learning Trajectory , Brinley Nichole Stevens

## Theses/Dissertations from 2020 2020

Mathematical Identities of Students with Mathematics Learning Dis/abilities , Emma Lynn Holdaway

Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures , Porter Peterson Nielsen

Student Use of Mathematical Content Knowledge During Proof Production , Chelsey Lynn Van de Merwe

## Theses/Dissertations from 2019 2019

Making Sense of the Equal Sign in Middle School Mathematics , Chelsea Lynn Dickson

Developing Understanding of the Chain Rule, Implicit Differentiation, and Related Rates: Towards a Hypothetical Learning Trajectory Rooted in Nested Multivariation , Haley Paige Jeppson

Secondary Preservice Mathematics Teachers' Curricular Reasoning , Kimber Anne Mathis

“Don’t Say Gay. We Say Dumb or Stupid”: Queering ProspectiveMathematics Teachers’ Discussions , Amy Saunders Ross

Aspects of Engaging Problem Contexts From Students' Perspectives , Tamara Kay Stark

## Theses/Dissertations from 2018 2018

Addressing Pre-Service Teachers' Misconceptions About Confidence Intervals , Kiya Lynn Eliason

How Teacher Questions Affect the Development of a Potential Hybrid Space in a Classroom with Latina/o Students , Casandra Helen Job

Teacher Graphing Practices for Linear Functions in a Covariation-Based College Algebra Classroom , Konda Jo Luckau

Principles of Productivity Revealed from Secondary Mathematics Teachers' Discussions Around the Productiveness of Teacher Moves in Response to Teachable Moments , Kylie Victoria Palsky

## Theses/Dissertations from 2017 2017

Curriculum Decisions and Reasoning of Middle School Teachers , Anand Mikel Bernard

Teacher Response to Instances of Student Thinking During Whole Class Discussion , Rachel Marie Bernard

Kyozaikenkyu: An In-Depth Look into Japanese Educators' Daily Planning Practices , Matthew David Melville

Analysis of Differential Equations Applications from the Coordination Class Perspective , Omar Antonio Naranjo Mayorga

## Theses/Dissertations from 2016 2016

The Principles of Effective Teaching Student Teachershave the Opportunity to Learn in an AlternativeStudent Teaching Structure , Danielle Rose Divis

Insight into Student Conceptions of Proof , Steven Daniel Lauzon

## Theses/Dissertations from 2015 2015

Teacher Participation and Motivation inProfessional Development , Krystal A. Hill

Student Evaluation of Mathematical Explanations in anInquiry-Based Mathematics Classroom , Ashley Burgess Hulet

English Learners' Participation in Mathematical Discourse , Lindsay Marie Merrill

Mathematical Interactions between Teachers and Students in the Finnish Mathematics Classroom , Paula Jeffery Prestwich

Parents and the Common Core State Standards for Mathematics , Rebecca Anne Roberts

Examining the Effects of College Algebra on Students' Mathematical Dispositions , Kevin Lee Watson

Problems Faced by Reform Oriented Novice Mathematics Teachers Utilizing a Traditional Curriculum , Tyler Joseph Winiecke

Academic and Peer Status in the Mathematical Life Stories of Students , Carol Ann Wise

## Theses/Dissertations from 2014 2014

The Effect of Students' Mathematical Beliefs on Knowledge Transfer , Kristen Adams

Language Use in Mathematics Textbooks Written in English and Spanish , Kailie Ann Bertoch

Teachers' Curricular Reasoning and MKT in the Context of Algebra and Statistics , Kolby J. Gadd

Mathematical Telling in the Context of Teacher Interventions with Collaborative Groups , Brandon Kyle Singleton

An Investigation of How Preservice Teachers Design Mathematical Tasks , Elizabeth Karen Zwahlen

## Theses/Dissertations from 2013 2013

Student Understanding of Limit and Continuity at a Point: A Look into Four Potentially Problematic Conceptions , Miriam Lynne Amatangelo

Exploring the Mathematical Knowledge for Teaching of Japanese Teachers , Ratu Jared R. T. Bukarau

Comparing Two Different Student Teaching Structures by Analyzing Conversations Between Student Teachers and Their Cooperating Teachers , Niccole Suzette Franc

Professional Development as a Community of Practice and Its Associated Influence on the Induction of a Beginning Mathematics Teacher , Savannah O. Steele

Types of Questions that Comprise a Teacher's Questioning Discourse in a Conceptually-Oriented Classroom , Keilani Stolk

## Theses/Dissertations from 2012 2012

Student Teachers' Interactive Decisions with Respect to Student Mathematics Thinking , Jonathan J. Call

Manipulatives and the Growth of Mathematical Understanding , Stacie Joyce Gibbons

Learning Within a Computer-Assisted Instructional Environment: Effects on Multiplication Math Fact Mastery and Self-Efficacy in Elementary-Age Students , Loraine Jones Hanson

Mathematics Teacher Time Allocation , Ashley Martin Jones

## Theses/Dissertations from 2011 2011

How Student Positioning Can Lead to Failure in Inquiry-based Classrooms , Kelly Beatrice Campbell

Teachers' Decisions to Use Student Input During Class Discussion , Heather Taylor Toponce

A Conceptual Framework for Student Understanding of Logarithms , Heather Rebecca Ambler Williams

## Theses/Dissertations from 2010 2010

Growth in Students' Conceptions of Mathematical Induction , John David Gruver

Contextualized Motivation Theory (CMT): Intellectual Passion, Mathematical Need, Social Responsibility, and Personal Agency in Learning Mathematics , Janelle Marie Hart

Thinking on the Brink: Facilitating Student Teachers' Learning Through In-the-Moment Interjections , Travis L. Lemon

Understanding Teachers' Change Towards a Reform-Oriented Mathematics Classroom , Linnae Denise Williams

## Theses/Dissertations from 2009 2009

A Comparison of Mathematical Discourse in Online and Face-to-Face Environments , Shawn D. Broderick

The Influence of Risk Taking on Student Creation of Mathematical Meaning: Contextual Risk Theory , Erin Nicole Houghtaling

Uncovering Transformative Experiences: A Case Study of the Transformations Made by one Teacher in a Mathematics Professional Development Program , Rachelle Myler Orsak

## Theses/Dissertations from 2008 2008

Student Teacher Knowledge and Its Impact on Task Design , Tenille Cannon

How Eighth-Grade Students Estimate with Fractions , Audrey Linford Hanks

Similar but Different: The Complexities of Students' Mathematical Identities , Diane Skillicorn Hill

Choose Your Words: Refining What Counts as Mathematical Discourse in Students' Negotiation of Meaning for Rate of Change of Volume , Christine Johnson

Mathematics Student Teaching in Japan: A Multi-Case Study , Allison Turley Shwalb

## Theses/Dissertations from 2007 2007

Applying Toulmin's Argumentation Framework to Explanations in a Reform Oriented Mathematics Class , Jennifer Alder Brinkerhoff

What Are Some of the Common Traits in the Thought Processes of Undergraduate Students Capable of Creating Proof? , Karen Malina Duff

Probing for Reasons: Presentations, Questions, Phases , Kellyn Nicole Farlow

One Problem, Two Contexts , Danielle L. Gigger

The Main Challenges that a Teacher-in-Transition Faces When Teaching a High School Geometry Class , Greg Brough Henry

Discovering the Derivative Can Be "Invigorating:" Mark's Journey to Understanding Instantaneous Velocity , Charity Ann Gardner Hyer

## Theses/Dissertations from 2006 2006

How a Master Teacher Uses Questioning Within a Mathematical Discourse Community , Omel Angel Contreras

Determining High School Geometry Students' Geometric Understanding Using van Hiele Levels: Is There a Difference Between Standards-based Curriculum Students and NonStandards-based Curriculum Students? , Rebekah Loraine Genz

The Nature and Frequency of Mathematical Discussion During Lesson Study That Implemented the CMI Framework , Andrew Ray Glaze

Second Graders' Solution Strategies and Understanding of a Combination Problem , Tiffany Marie Hessing

What Does It Mean To Preservice Mathematics Teachers To Anticipate Student Responses? , Matthew M. Webb

## Theses/Dissertations from 2005 2005

Fraction Multiplication and Division Image Change in Pre-Service Elementary Teachers , Jennifer J. Cluff

An Examination of the Role of Writing in Mathematics Instruction , Amy Jeppsen

## Theses/Dissertations from 2004 2004

Reasoning About Motion: A Case Study , Tiffini Lynn Glaze

## Theses/Dissertations from 2003 2003

An Analysis of the Influence of Lesson Study on Preservice Secondary Mathematics Teachers' View of Self-As Mathematics Expert , Julie Stafford

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- Published: 11 March 2019

## Enhancing achievement and interest in mathematics learning through Math-Island

- Charles Y. C. Yeh ORCID: orcid.org/0000-0003-4581-6575 1 ,
- Hercy N. H. Cheng 2 ,
- Zhi-Hong Chen 3 ,
- Calvin C. Y. Liao 4 &
- Tak-Wai Chan 5

Research and Practice in Technology Enhanced Learning volume 14 , Article number: 5 ( 2019 ) Cite this article

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Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many students may then continue to fall behind the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning mathematics. In fact, students in Taiwan generally have lower interest in learning mathematics compared to many other regions/countries. Thus, how to enhance students’ mathematics achievement and interest are two major problems, especially for those low-achieving students. This paper describes how we designed a game-based learning environment, called Math-Island , by incorporating the mechanisms of a construction management game into the knowledge map of the elementary mathematics curriculum. We also report an experiment conducted with 215 elementary students for 2 years, from grade 2 to grade 3. In this experiment, in addition to teacher-led instruction in the classroom, students were directed to learn with Math-Island by using their own tablets at school and at home. As a result of this experiment, we found that there is an increase in students’ mathematics achievement, especially in the calculation and word problems. Moreover, the achievements of low-achieving students in the experimental school outperformed the low-achieving students in the control school (a control group in another school) in word problems. Moreover, both the low-achieving students and the high-achieving students in the experimental school maintained a rather high level of interest in mathematics and in the system.

## Introduction

Mathematics has been regarded as a fundamental subject because arithmetic and logical reasoning are the basis of science and technology. For this reason, educational authorities emphasize students’ proficiency in computational skills and problem-solving. Recently, the results of the Program for International Student Assessment (PISA) and the Trends in Mathematics and Science Study (TIMSS) in 2015 (OECD 2016 ; Mullis et al. 2016 ) revealed a challenge for Taiwan. Although Taiwanese students had higher average performance in mathematics literacy compared to students in other countries, there was still a significant percentage of low-achieving students in Taiwan. Additionally, most Taiwanese students show low levels of interest and confidence in learning mathematics (Lee 2012 ).

The existence of a significant percentage of low-achieving students is probably due to teacher-led instruction, which still dominates mathematics classrooms in most Asian countries. It should be noted that students in every classroom possess different abilities and hence demonstrate different achievements. Unfortunately, in teacher-led instruction, all the students are required to learn from the teacher in the same way at the same pace (Hwang et al. 2012 ). Low-achieving students, without sufficient time, are forced to receive knowledge passively. Barr and Tagg ( 1995 ) pointed out that it is urgent for low-achieving students to have more opportunities to learn mathematics at their own pace. Researchers suggested one-to-one technology (Chan et al. 2006 ) through which every student is equipped with a device to learn in school or at home seamlessly. Furthermore, they can receive immediate feedback from Math-Island, which supports their individualized learning actively and productively. Thus, this may provide more opportunities for helping low-achieving students improve their achievement.

The low-interest problem for almost all students in Taiwan is usually accompanied by low motivation (Krapp 1999 ). Furthermore, students with continuously low performance in mathematics may eventually lose their interest and refuse to learn further (Schraw et al. 2001 ). This is a severe problem. To motivate students to learn, researchers design educational games to provide enjoyable and engaging learning experiences (Kiili and Ketamo 2007 ). Some of these researchers found that game-based learning may facilitate students’ learning in terms of motivation and learning effects (Liu and Chu 2010 ), spatial abilities and attention (Barlett et al. 2009 ), situated learning, and problem-solving (Li and Tsai 2013 ). Given these positive results, we hope that our educational game can enhance and sustain the student’s interest in learning mathematics.

In fact, many researchers who endeavored to develop educational games for learning mathematics have shown that their games could facilitate mathematics performance, enjoyment, and self-efficacy (Ku et al. 2014 ; McLaren et al. 2017 ). Although some of the studies were conducted for as many as 4 months (e.g., Hanus and Fox 2015 ), one may still criticize them for the possibility that the students’ interest could be a novelty effect—meaning their interest will decrease as the feeling of novelty diminishes over time (Koivisto and Hamari 2014 ). Due to the limitations of either experimental time or sample sizes, most studies could not effectively exclude the novelty effect of games, unless they were conducted in a natural setting for a long time.

In this study, we collaborated with an experimental elementary school for more than 2 years. The mathematics teachers in the school adopted our online educational game, Math-Island . The students used their own tablet PCs to learn mathematics from the game in class or at home at their own pace. In particular, low-achieving students might have a chance to catch up with the other students and start to feel interested in learning mathematics. Most importantly, because the online educational game was a part of the mathematics curriculum, the students could treat the game as their ordinary learning materials like textbooks. In this paper, we reported a 2-year study, in which 215 second graders in the school adopted the Math-Island game in their daily routine. More specifically, the purpose of this paper was to investigate the effect of the game on students’ mathematics achievement. Additionally, we were also concerned about how well the low-achieving students learned, whether they were interested in mathematics and the game, and how their interest in mathematics compared with that of high-achieving students. In such a long-term study with a large sample size, it was expected that the novelty effect would be considerably reduced, allowing us to evaluate the effect of the educational game on students’ achievement and interest.

The paper is organized as follows. In the “ Related works ” section, we review related studies on computer-supported mathematics learning and educational games. In the “ Design ” section, the game mechanism and the system design are presented. In the “ Method ” section, we describe the research method and the procedures of this study. In the “ Results ” section, the research results about students’ achievement and interest are presented. In the “ Discussion on some features of this study ” section, we discuss the long-term study, knowledge map design, and the two game mechanisms. Finally, the summary of the current situation and potential future work is described in the “ Conclusion and future work ” section.

## Related works

Computer-supported mathematics learning.

The mathematics curriculum in elementary schools basically includes conceptual understanding, procedural fluency, and strategic competence in terms of mathematical proficiency (see Kilpatrick et al. 2001 ). First, conceptual understanding refers to students’ comprehension of mathematical concepts and the relationships between concepts. Researchers have designed various computer-based scaffolds and feedback to build students’ concepts and clarify potential misconceptions. For example, for guiding students’ discovery of the patterns of concepts, Yang et al. ( 2012 ) adopted an inductive discovery learning approach to design online learning materials in which students were provided with similar examples with a critical attribute of the concept varied. McLaren et al. ( 2017 ) provided students with prompts to correct their common misconceptions about decimals. They conducted a study with the game adopted as a replacement for seven lessons of regular mathematics classes. Their results showed that the educational game could facilitate better learning performance and enjoyment than a conventional instructional approach.

Second, procedural fluency refers to the skill in carrying out calculations correctly and efficiently. For improving procedural fluency, students need to have knowledge of calculation rules (e.g., place values) and practice the procedure without mistakes. Researchers developed various digital games to overcome the boredom of practice. For example, Chen et al. ( 2012a , 2012b ) designed a Cross Number Puzzle game for practicing arithmetic expressions. In the game, students could individually or collaboratively solve a puzzle, which involved extensive calculation. Their study showed that the low-ability students in the collaborative condition made the most improvement in calculation skills. Ku et al. ( 2014 ) developed mini-games to train students’ mental calculation ability. They showed that the mini-games could not only improve students’ calculation performance but also increase their confidence in mathematics.

Third, strategic competence refers to mathematical problem-solving ability, in particular, word problem-solving in elementary education. Some researchers developed multilevel computer-based scaffolds to help students translate word problems to equations step by step (e.g., González-Calero et al. 2014 ), while other researchers noticed the problem of over-scaffolding. Specifically, students could be too scaffolded and have little space to develop their abilities. To avoid this situation, many researchers proposed allowing students to seek help during word problem-solving (Chase and Abrahamson 2015 ; Roll et al. 2014 ). For example, Cheng et al. ( 2015 ) designed a Scaffolding Seeking system to encourage elementary students to solve word problems by themselves by expressing their thinking first, instead of receiving and potentially abusing scaffolds.

## Digital educational games for mathematics learning

Because mathematics is an abstract subject, elementary students easily lose interest in it, especially low-achieving students. Some researchers tailored educational games for learning a specific set of mathematical knowledge (e.g., the Decimal Points game; McLaren et al. 2017 ), so that students could be motivated to learn mathematics. However, if our purpose was to support a complete mathematics curriculum for elementary schools, it seemed impractical to design various educational games for all kinds of knowledge. A feasible approach is to adopt a gamified content structure to reorganize all learning materials. For example, inspired by the design of most role-playing games, Chen et al. ( 2012a , 2012b ) proposed a three-tiered framework of game-based learning—a game world, quests, and learning materials—for supporting elementary students’ enjoyment and goal setting in mathematics learning. Furthermore, while a game world may facilitate students’ exploration and participation, quests are the containers of learning materials with specific goals and rewards. In the game world, students receive quests from nonplayer virtual characters, who may enhance social commitments. To complete the quests, students have to make efforts to undertake learning materials. Today, quests have been widely adopted in the design of educational games (e.g., Azevedo et al. 2012 ; Hwang et al. 2015 ).

However, in educational games with quests, students still play the role of receivers rather than active learners. To facilitate elementary students’ initiative, Lao et al. ( 2017 ) designed digital learning contracts, which required students to set weekly learning goals at the beginning of a week and checked whether they achieved the goals at the end of the week. More specifically, when setting weekly goals, students had to decide on the quantity of learning materials that they wanted to undertake in the coming week. Furthermore, they also had to decide the average correctness of the tests that followed the learning materials. To help them set reasonable and feasible goals, the system provided statistics from the past 4 weeks. As a result, the students may reflect on how well they learned and then make appropriate decisions. After setting goals, students are provided with a series of learning materials for attempting to accomplish those goals. At the end of the week, they may reflect on whether they achieved their learning goals in the contracts. In a sense, learning contracts may not only strengthen the sense of commitment but also empower students to take more control of their learning.

In textbooks or classrooms, learning is usually predefined as a specific sequence, which students must follow to learn. Nevertheless, the structure of knowledge is not linear, but a network. If we could reorganize these learning materials according to the structure of knowledge, students could explore knowledge and discover the relationships among different pieces of knowledge when learning (Davenport and Prusak 2000 ). Knowledge mapping has the advantage of providing students concrete content through explicit knowledge graphics (Ebener et al. 2006 ). Previous studies have shown that the incorporation of knowledge structures into educational games could effectively enhance students’ achievement without affecting their motivation and self-efficacy (Chu et al. 2015 ). For this reason, this study attempted to visualize the structure of knowledge in an educational game. In other words, a knowledge map was visualized and gamified so that students could make decisions to construct their own knowledge map in games.

To enhance students’ mathematics achievement and interests, we designed the Math-Island online game by incorporating a gamified knowledge map of the elementary mathematics curriculum. More specifically, we adopt the mechanisms of a construction management game , in which every student owns a virtual island (a city) and plays the role of the mayor. The goal of the game is to build their cities on the islands by learning mathematics.

## System architecture

The Math-Island game is a Web application, supporting cross-device interactions among students, teachers, and the mathematics content structure. The system architecture of the Math-Island is shown in Fig. 1 . The pedagogical knowledge and learning materials are stored in the module of digital learning content, organized by a mathematical knowledge map. The students’ portfolios about interactions and works are stored in the portfolio database and the status database. When a student chooses a goal concept in the knowledge map, the corresponding digital learning content is arranged and delivered to his/her browser. Besides, when the student is learning in the Math-Island, the feedback module provides immediate feedback (e.g., hints or scaffolded solutions) for guidance and grants rewards for encouragement. The learning results can also be shared with other classmates by the interaction module. In addition to students, their teachers can also access the databases for the students’ learning information. Furthermore, the information consists of the students’ status (e.g., learning performance or virtual achievement in the game) and processes (e.g., their personal learning logs). In the Math-Island, it is expected that students can manage their learning and monitor the learning results by the construction management mechanism. In the meantime, teachers can also trace students’ learning logs, diagnose their weaknesses from portfolio analysis, and assign students with specific tasks to improve their mathematics learning.

The system architecture of Math-Island

- Knowledge map

To increase students’ mathematics achievement, the Math-Island game targets the complete mathematics curriculum of elementary schools in Taiwan, which mainly contains the four domains: numerical operation , quantity and measure , geometry , and statistics and probability (Ministry of Education of R.O.C. 2003 ). Furthermore, every domain consists of several subdomains with corresponding concepts. For instance, the domain of numerical operation contains four subdomains: numbers, addition, and subtraction for the first and second graders. In the subdomain of subtraction, there are a series of concepts, including the meaning of subtraction, one-digit subtraction, and two-digit subtraction. These concepts should be learned consecutively. In the Math-Island system, the curriculum is restructured as a knowledge map, so that they may preview the whole structure of knowledge, recall what they have learned, and realize what they will learn.

More specifically, the Math-Island system uses the representational metaphor of an “island,” where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. As shown in Fig. 2 , for example, in an area of numeral operation in Math-Island, there are many roads, such as an addition road and a subtraction road. On the addition road, the first building should be the meaning of addition, followed by the buildings of one-digit addition and then two-digit addition. Students can choose these buildings to learn mathematical concepts. In each building, the system provides a series of learning tasks for learning the specific concept. Currently, Math-Island provides elementary students with more than 1300 learning tasks from the first grade to the sixth grade, with more than 25,000 questions in the tasks.

The knowledge map

In Math-Island, a learning task is an interactive page turner, including video clips and interactive exercises for conceptual understanding, calculation, and word problem-solving. In each task, the learning procedure mainly consists of three steps: watching demonstrations, practicing examples, and getting rewards. First, students learn a mathematical concept by watching videos, in which a human tutor demonstrates examples, explains the rationale, and provides instructions. Second, students follow the instructions to answer a series of questions related to the examples in the videos. When answering questions, students are provided with immediate feedback. Furthermore, if students input wrong answers, the system provides multilevel hints so that they could figure out solutions by themselves. Finally, after completing learning tasks, students receive virtual money according to their accuracy rates in the tasks. The virtual money is used to purchase unique buildings to develop their islands in the game.

## Game mechanisms

In the Math-Island game, there are two game mechanisms: construction and sightseeing (as shown in Fig. 3 ). The former is designed to help students manage their learning process, whereas the latter is designed to facilitate social interaction, which may further motivate students to better develop their cities. By doing so, the Math-Island can be regarded as one’s learning portfolio, which is a complete record that purposely collects information about one’s learning processes and outcomes (Arter and Spandel 2005 ). Furthermore, learning portfolios are a valuable research tool for gaining an understanding about personal accomplishments (Birgin and Baki 2007 ), because learning portfolios can display one’s learning process, attitude, and growth after learning (Lin and Tsai 2001 ). The appearance of the island reflects what students have learned and have not learned from the knowledge map. When students observe their learning status in an interesting way, they may be concerned about their learning status with the enhanced awareness of their learning portfolios. By keeping all activity processes, students can reflect on their efforts, growth, and achievements. In a sense, with the game mechanisms, the knowledge map can be regarded as a manipulatable open learner model, which not only represents students’ learning status but also invites students to improve it (Vélez et al. 2009 ).

Two game mechanisms for Math-Island

First, the construction mechanism allows students to plan and manage their cities by constructing and upgrading buildings. To do so, they have to decide which buildings they want to construct or upgrade. Then, they are required to complete corresponding learning tasks in the building to determine which levels of buildings they can construct. As shown in Fig. 4 , the levels of buildings depend on the completeness of a certain concept, compared with the thresholds. For example, when students complete one third of the learning tasks, the first level of a building is constructed. Later, when they complete two thirds of the tasks, the building is upgraded to the second level. After completing all the tasks in a building, they also complete the final level and are allowed to construct the next building on the road. Conversely, if students failed the lowest level of the threshold, they might need to watch the video and/or do the learning tasks again. By doing so, students can make their plans to construct the buildings at their own pace. When students manage their cities, they actually attempt to improve their learning status. In other words, the construction mechanism offers an alternative way to guide students to regulate their learning efforts.

Screenshots of construction and sightseeing mechanisms in Math-Island

Second, the sightseeing mechanism provides students with a social stage to show other students how well their Math-Islands have been built. This mechanism is implemented as a public space, where other students play the role of tourists who visit Math-Island. In other words, this sightseeing mechanism harnesses social interaction to improve individual learning. As shown in Fig. 4 , because students can construct different areas or roads, their islands may have different appearances. When students visit a well-developed Math-Island, they might have a positive impression, which may facilitate their self-reflection. Accordingly, they may be willing to expend more effort to improve their island. On the other hand, the student who owns the island may also be encouraged to develop their island better. Furthermore, when students see that they have a completely constructed building on a road, they may perceive that they are good at these concepts. Conversely, if their buildings are small, the students may realize their weaknesses or difficulties in these concepts. Accordingly, they may be willing to make more effort for improvement. On the other hand, the student who owns the island may also be encouraged to develop their island better. In a word, the visualization may play the role of stimulators, so that students may be motivated to improve their learning status.

This paper reported a 2-year study in which the Math-Island system was adopted in an elementary school. The study addressed the following two research questions: (1) Did the Math-Island system facilitate students’ mathematics achievement in terms of conceptual understanding, calculating, and word problem-solving? In particular, how was the mathematics achievement of the low-achieving students? (2) What was students’ levels of interest in mathematics and the system, particularly that of low-achieving students?

## Participants

The study, conducted from June 2013 to June 2015, included 215 second graders (98 females and 117 males), whose average age was 8 years old, in an elementary school located in a suburban region of a northern city in Taiwan. The school had collaborated with our research team for more than 2 years and was thus chosen as an experimental school for this study. In this school, approximately one third of the students came from families with a low or middle level of socioeconomic status. It was expected that the lessons learned from this study could be applicable to other schools with similar student populations in the future. The parents were supportive of this program and willing to provide personal tablets for their children (Liao et al. 2017 ). By doing so, the students in the experimental school were able to use their tablets to access the Math-Island system as a learning tool at both school and home. To compare the students’ mathematics achievement with a baseline, this study also included 125 second graders (63 females and 62 males) from another school with similar socioeconomic backgrounds in the same region of the city as a control school. The students in the control school received only conventional mathematics instruction without using the Math-Island system during the 2-year period.

Before the first semester, a 3-week training workshop was conducted to familiarize the students with the basic operation of tablets and the Math-Island system. By doing so, it was ensured that all participants had similar prerequisite skills. The procedure of this study was illustrated in Table 1 . At the beginning of the first semester, a mathematics achievement assessment was conducted as a pretest in both the experimental and the control school to examine the students’ initial mathematics ability as second graders. From June 2013 to June 2015, while the students in the control school learned mathematics in a conventional way, the students in the experimental school learned mathematics not only in mathematics classes but also through the Math-Island system. Although the teachers in the experimental school mainly adopted lectures in mathematics classes, they used the Math-Island system as learning materials at school and for homework. At the same time, they allowed the students to explore the knowledge map at their own pace. During the 2 years, every student completed 286.78 learning tasks on average, and each task took them 8.86 min. Given that there were 344 tasks for the second and third graders, the students could finish 83.37% of tasks according to the standard progress. The data also showed that the average correctness rate of the students was 85.75%. At the end of the second year, another mathematics achievement assessment was administered as a posttest in both schools to evaluate students’ mathematics ability as third graders. Additionally, an interest questionnaire was employed in the experimental school to collect the students’ perceptions of mathematics and the Math-Island system. To understand the teachers’ opinions of how they feel about the students using the system, interviews with the teachers in the experimental school were also conducted.

## Data collection

Mathematics achievement assessment.

To evaluate the students’ mathematics ability, this study adopted a standardized achievement assessment of mathematics ability (Lin et al. 2009 ), which was developed from a random sample of elementary students from different counties in Taiwan to serve as a norm with appropriate reliability (the internal consistency was 0.85, and the test-retest reliability was 0.86) and validity (the correlation by domain experts in content validity was 0.92, and the concurrent validity was 0.75). As a pretest, the assessment of the second graders consisted of 50 items, including conceptual understanding (23 items), calculating (18 items), and word problem-solving (9 items). As a posttest, the assessment of the third graders consisted of 60 items, including conceptual understanding (18 items), calculating (27 items), and word problem-solving (15 items). The scores of the test ranged from 0 to 50 points. Because some students were absent during the test, this study obtained 209 valid tests from the experimental school and 125 tests from the control school.

## Interest questionnaire

The interest questionnaire comprised two parts: students’ interest in mathematics and the Math-Island system. Regarding the first part, this study adopted items from a mathematics questionnaire of PISA and TIMSS 2012 (OECD 2013 ; Mullis et al. 2012 ), the reliability of which was sound. This part included three dimensions: attitude (14 items, Cronbach’s alpha = .83), initiative (17 items, Cronbach’s alpha = .82), and confidence (14 items Cronbach’s alpha = .72). Furthermore, the dimension of attitude was used to assess the tendency of students’ view on mathematics. For example, a sample item of attitudes was “I am interested in learning mathematics.” The dimension of initiatives was used to assess how students were willing to learn mathematics actively. A sample item of initiatives was “I keep studying until I understand mathematics materials.” The dimension of confidences was used to assess students’ perceived mathematics abilities. A sample item was “I am confident about calculating whole numbers such as 3 + 5 × 4.” These items were translated to Chinese for this study. Regarding the second part, this study adopted self-made items to assess students’ motivations for using the Math-Island system. This part included two dimensions: attraction (8 items) and satisfaction (5 items). The dimension of attraction was used to assess how well the system could attract students’ attention. A sample item was “I feel Math-island is very appealing to me.” The dimension of satisfaction was used to assess how the students felt after using the system. A sample item was “I felt that upgrading the buildings in my Math-Island brought me much happiness.” These items were assessed according to a 4-point Likert scale, ranging from “strongly disagreed (1),” “disagreed (2),” “agreed (3),” and “strongly agreed (4)” in this questionnaire. Due to the absences of several students on the day the questionnaire was administered, there were only 207 valid questionnaires in this study.

## Teacher interview

This study also included teachers’ perspectives on how the students used the Math-Island system to learn mathematics in the experimental school. This part of the study adopted semistructured interviews of eight teachers, which comprised the following three main questions: (a) Do you have any notable stories about students using the Math-Island system? (b) Regarding Math-Island, what are your teaching experiences that can be shared with other teachers? (c) Do you have any suggestions for the Math-Island system? The interview was recorded and transcribed verbatim. The transcripts were coded and categorized according to the five dimensions of the questionnaire (i.e., the attitude, initiative, and confidence about mathematics, as well as the attraction and satisfaction with the system) as additional evidence of the students’ interest in the experimental school.

## Data analysis

For the first research question, this study conducted a multivariate analysis of variance (MANOVA) with the schools as a between-subject variable and the students’ scores (conceptual understanding, calculating, and word problem-solving) in the pre/posttests as dependent variables. Moreover, this study also conducted a MANOVA to compare the low-achieving students from both schools. In addition, the tests were also carried out to compare achievements with the norm (Lin et al. 2009 ). For the second research question, several z tests were used to examine how the interests of the low-achieving students were distributed compared with the whole sample. Teachers’ interviews were also adopted to support the results of the questionnaire.

## Mathematics achievement

To examine the homogeneity of the students in both schools in the first year, the MANOVA of the pretest was conducted. The results, as shown in Table 2 , indicated that there were no significant differences in their initial mathematics achievements in terms of conceptual understanding, calculating, and word problem-solving (Wilks’ λ = 0.982, F (3330) = 2.034, p > 0.05). In other words, the students of both schools had similar mathematics abilities at the time of the first mathematics achievement assessment and could be fairly compared.

At the end of the fourth grade, the students of both schools received the posttest, the results of which were examined by a MANOVA. As shown in Table 3 , the effect of the posttest on students’ mathematics achievement was significant (Wilks’ λ = 0.946, p < 0.05). The results suggested that the students who used Math-Island for 2 years had better mathematics abilities than those who did not. The analysis further revealed that the univariate effects on calculating and word problem-solving were significant, but the effect on conceptual understanding was insignificant. The results indicated that the students in the experimental school outperformed their counterparts in terms of the procedure and application of arithmetic. The reason may be that the system provided students with more opportunities to do calculation exercises and word problems, and the students were more willing to do these exercises in a game-based environment. Furthermore, they were engaged in solving various exercises with the support of immediate feedback until they passed the requirements of every building in their Math-Island. However, the students learned mathematical concepts mainly by watching videos in the system, which provided only demonstrations like lectures in conventional classrooms. For this reason, the effect of the system on conceptual understanding was similar to that of teachers’ conventional instruction.

Furthermore, to examine the differences between the low-achieving students in both schools, another MANOVA was also conducted on the pretest and the posttest. The pretest results indicated that there were no significant differences in their initial mathematics achievement in terms of conceptual understanding, calculating, and word problem-solving (Wilks’ λ = 0.943, F (3110) = 2.210, p > 0.05).

The MANOVA analysis of the posttest is shown in Table 4 . The results showed that the effect of the system on the mathematics achievement of low-achieving students was significant (Wilks’ λ = 0.934, p < 0.05). The analysis further revealed that only the univariate effect on word problem-solving was significant. The results suggested that the low-achieving students who used Math-Island for 2 years had better word problem-solving ability than those students in the control school, but the effect on conceptual understanding and procedural fluency was insignificant. The results indicated that the Math-Island system could effectively enhance low-achieving students’ ability to solve word problems.

Because the mathematics achievement assessment was a standardized achievement assessment (Lin et al. 2009 ), the research team did a further analysis of the assessments by comparing the results with the norm. In the pretest, the average score of the control school was the percentile rank of a score (PR) 55, but their average score surprisingly decreased to PR 34 in the posttest. The results confirmed the fact that conventional mathematics teaching in Taiwan might result in an M-shape distribution, suggesting that low-achieving students required additional learning resources. Conversely, the average score of the experimental school was PR 48 in the pretest, and their score slightly decreased to PR 44 in the posttest. Overall, both PR values were decreasing, because the mathematics curriculum became more and more difficult from the second grade to the fourth grade. However, it should be noted that the experimental school has been less affected, resulting in a significant difference compared with the control school (see Table 5 ). Notably, the average score of word problem-solving in the posttest of the experimental school was PR 64, which was significantly higher than the nationwide norm ( z = 20.8, p < .05). The results were consistent with the univariate effect of the MANOVA on word problem-solving, suggesting that the Math-Island system could help students learn to complete word problems better. This may be because the learning tasks in Math-Island provided students with adequate explanations for various types of word problems and provided feedback for exercises.

To examine whether the low-achieving students had low levels of interest in mathematics and the Math-Island system, the study adopted z tests on the data of the interest questionnaire. Table 5 shows the descriptive statistics and the results of the z tests. Regarding the interest in mathematics, the analysis showed that the interest of the low-achieving students was similar to that of the whole sample in terms of attitude, initiative, and confidence. The results were different from previous studies asserting that low-achieving students tended to have lower levels of interest in mathematics (Al-Zoubi and Younes 2015 ). The reason was perhaps that the low-achieving students were comparably motivated to learn mathematics in the Math-Island system. As a result, a teacher ( #T-301 ) said, “some students would like to go to Math-Island after school, and a handful of students could even complete up to forty tasks (in a day),” implying that the students had a positive attitude and initiative related to learning mathematics.

Another teacher ( T-312 ) also indicated “some students who were frustrated with math could regain confidence when receiving the feedback for correct answers in the basic tasks. Thanks to this, they would not feel high-pressure when moving on to current lessons.” In a sense, the immediate feedback provided the low-achieving students with sufficient support and may encourage them to persistently learn mathematics. Furthermore, by learning individually after class, they could effectively prepare themselves for future learning. The results suggested that the system could serve as a scaffolding on conventional instruction for low-achieving students. The students could benefit from such a blended learning environment and, thus, build confidence in mathematics by learning at their own paces.

The low-achieving students as a whole were also attracted to the system and felt satisfaction from it. Teacher ( #T-307 ) said that, “There was a hyperactive and mischievous student in my class. However, when he was alone, he would go on to Math-Island, concentrating on the tasks quietly. He gradually came to enjoy learning mathematics. It seemed that Math-Island was more attractive to them than a lecture by a teacher. I believed that students could be encouraged, thus improve their ability and learn happily.” Another teacher ( #T-304 ) further pointed out that, “For students, they did not only feel like they were learning mathematics because of the game-based user interface. Conversely, they enjoyed the contentment when completing a task, as if they were going aboard to join a competition.” In teachers’ opinions, such a game-based learning environment did not disturb their instruction. Instead, the system could help the teachers attract students’ attention and motivate them to learn mathematics actively because of its appealing game and joyful learning tasks. Furthermore, continuously overcoming the tasks might bring students a sense of achievement and satisfaction.

## Discussion on some features of this study

In addition to the enhancement of achievement and interest, we noticed that there are some features in this study and our design worth some discussion.

## The advantages of building a long-term study

Owing to the limitations of deployment time and sample sizes, it is hard for most researchers to conduct a longitudinal study. Fortunately, we had a chance to maintain a long-term collaboration with an experimental school for more than 2 years. From this experiment, we notice that there are two advantages to conducting a long-term study.

## Obtaining substantial evidence from the game-based learning environment

The research environment was a natural setting, which could not be entirely controlled and manipulated like most experiments in laboratories. However, this study could provide long-term evidence to investigate how students learned in a game-based learning environment with their tablets. It should be noted that we did not aim to replace teachers in classrooms with the Math-Island game. Instead, we attempted to establish an ordinary learning scenario, in which the teachers and students regarded the game as one of the learning resources. For example, teachers may help low-achieving students to improve their understanding of a specific concept in the Math-Island system. When students are learning mathematics in the Math-Island game, teachers may take the game as a formative assessment and locate students’ difficulties in mathematics.

## Supporting teachers’ instructions and facilitating students’ learning

The long-term study not only proved the effectiveness of Math-Island but also offered researchers an opportunity to determine teachers’ roles in such a computer-supported learning environment. For example, teachers may encounter difficulties in dealing with the progress of both high- and low-achieving students. How do they take care of all students with different abilities at the same time? Future teachers may require more teaching strategies in such a self-directed learning environment. Digital technology has an advantage in helping teachers manage students’ learning portfolios. For example, the system can keep track of all the learning activities. Furthermore, the system should provide teachers with monitoring functions so that they know the average status of their class’s and individuals’ learning progress. Even so, it is still a challenge for researchers to develop a well-designed visualization tool to support teachers’ understanding of students’ learning conditions and their choice of appropriate teaching strategies.

## Incorporating a gamified knowledge map of the elementary mathematics curriculum

Providing choices of learning paths.

Math-Island uses a representational metaphor of an “island,” where a virtual city is located and represents the knowledge map. Furthermore, the island comprises areas, roads, and buildings, which are the embodiments of domains, subdomains, and concepts in the curriculum, respectively. Because the gamified knowledge map provides students with multiple virtual roads to learn in the system, every student may take different routes. For instance, some students may be more interested in geometry, while others may be confident in exploring the rules of arithmetic. In this study, we noticed that the low-achieving students needed more time to work on basic tasks, while high-achieving students easily passed those tasks and moved on to the next ones. As a result, some of the high-achieving students had already started to learn the materials for the next grade level. This was possibly because high-achieving students were able to respond well to challenging assignments (Singh 2011 ). Therefore, we should provide high-achieving students with more complex tasks to maintain their interest. For example, Math-Island should provide some authentic mathematical problems as advanced exercises.

## Visualizing the learning portfolio

In this study, we demonstrated a long-term example of incorporating a gamified knowledge map in an elementary mathematical curriculum. In the Math-Island game, the curriculum is visualized as a knowledge map instead of a linear sequence, as in textbooks. By doing so, students are enabled to explore relationships in the mathematics curriculum represented by the knowledge map; that is, the structure of the different roads on Math-Island. Furthermore, before learning, students may preview what will be learned, and after learning, students may also reflect on how well they learned. Unlike traditional lectures or textbooks, in which students could only follow a predefined order to learn knowledge without thinking why they have to learn it, the knowledge map allows students to understand the structure of knowledge and plan how to achieve advanced knowledge. Although the order of knowledge still remains the same, students take primary control of their learning. In a sense, the knowledge map may liberate elementary students from passive learning.

## Adopting the mechanisms of a construction management game

This 2-year study showed that the adaptation of two game mechanisms, construction and sightseeing, into the elementary mathematical curriculum could effectively improve students’ learning achievement. The reason may be that students likely developed interests in using Math-Island to learn mathematics actively, regardless of whether they are high- and low-achieving students.

## Gaining a sense of achievement and ownership through the construction mechanism

Regardless of the construction mechanism, Math-Island allows students to plan and manage their cities by constructing and upgrading buildings. Math-Island took the advantages of construction management games to facilitate elementary students’ active participation in their mathematical learning. Furthermore, students may manage their knowledge by planning and constructing of buildings on their virtual islands. Like most construction management games, students set goals and make decisions so that they may accumulate their assets. These assets are not only external rewards but also visible achievements, which may bring a sense of ownership and confidence. In other words, the system gamified the process of self-directed learning.

## Demonstrating learning result to peers through the sightseeing mechanism

As for the sightseeing mechanism, in conventional instruction, elementary students usually lack the self-control to learn knowledge actively (Duckworth et al. 2014 ) or require a social stage to show other students, resulting in low achievement and motivation. On the other hand, although previous researchers have already proposed various self-regulated learning strategies (such as Taub et al. 2014 ), it is still hard for children to keep adopting specific learning strategies for a long time. For these reasons, this study uses the sightseeing mechanism to engage elementary students in a social stage to show other students how well their Math-Islands have been built. For example, in Math-Island, although the students think that they construct buildings in their islands, they plan the development of their knowledge maps. After learning, they may also reflect on their progress by observing the appearance of the buildings.

In brief, owing to the construction mechanism, the students are allowed to choose a place and build their unique islands by learning concepts. During the process, students have to do the learning task, get feedback, and get rewards, which are the three major functions of the construction functions. In the sightseeing mechanism, students’ unique islands (learning result) can be shared and visited by other classmates. The student’s Math-Island thus serves as a stage for showing off their learning results. The two mechanisms offer an incentive model connected to the game mechanism’s forming a positive cycle: the more the students learn, the more unique islands they can build, with more visitors.

## Conclusion and future work

This study reported the results of a 2-year experiment with the Math-Island system, in which a knowledge map with extensive mathematics content was provided to support the complete elementary mathematics curriculum. Each road in Math-Island represents a mathematical topic, such as addition. There are many buildings on each road, with each building representing a unit of the mathematics curriculum. Students may learn about the concept and practice it in each building while being provided with feedback by the system. In addition, the construction management online game mechanism is designed to enhance and sustain students’ interest in learning mathematics. The aim of this study was not only to examine whether the Math-Island system could improve students’ achievements but also to investigate how much the low-achieving students would be interested in learning mathematics after using the system for 2 years.

As for enhancing achievement, the result indicated that the Math-Island system could effectively improve the students’ ability to calculate expressions and solve word problems. In particular, the low-achieving students outperformed those of the norm in terms of word problem-solving. For enhancing interest, we found that both the low-achieving and the high-achieving students in the experimental school, when using the Math-Island system, maintained a rather high level of interest in learning mathematics and using the system. The results of this study indicated some possibility that elementary students could be able to learn mathematics in a self-directed learning fashion (Nilson 2014 ; Chen et al. 2012a , b ) under the Math-Island environment. This possibility is worthy of future exploration. For example, by analyzing student data, we can investigate how to support students in conducting self-directed learning. Additionally, because we have already collected a considerable amount of student data, we are currently employing machine learning techniques to improve feedback to the students. Finally, to provide students appropriate challenges, the diversity, quantity, and difficulty of content may need to be increased in the Math-Island system.

## Abbreviations

Program for International Student Assessment

The percentile rank of a score

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## Acknowledgements

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: The authors would like to thank the Ministry of Science and Technology of the Republic of China, Taiwan, for financial support (MOST 106-2511-S-008-003-MY3), and Research Center for Science and Technology forLearning, National Central University, Taiwan.

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## Contributions

CYCY contributed to the study design, data acquisition and analysis, mainly drafted the manuscript and execution project. HNHC was involved in data acquisition, revision of the manuscript and data analysis.ZHC was contributed to the study idea and drafted the manuscript. CCYL of this research was involved in data acquisition and revision of the manuscript. TWC was project manager and revision of the manuscript. All authors read and approved the final manuscript.

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Charles Y.C. Yeh is currently an PhD student in Graduate Institute of Network Learning Technology at National Central University. The research interests include one-to-one learning environments and game-based learning.

Hercy N. H. Cheng is currently an associate professor and researcher in National Engineering Research Center for E-Learning at Central China Normal University, China. His research interests include one-to-one learning environments and game-based learning.

Zhi-Hong Chen is an associate professor in Graduate Institute of Information and Computer Education at National Taiwan Normal University. His research interests focus on learning technology and interactive stories, technology intensive language learning and game-based learning.

Calvin C. Y. Liao is currently an Assistant Professor and Dean’s Special Assistant in College of Nursing at National Taipei University of Nursing and Health Sciences in Taiwan. His research focuses on computer-based language learning for primary schools. His current research interests include a game-based learning environment and smart technology for caregiving & wellbeing.

Tak-Wai Chan is Chair Professor of the Graduate Institute of Network Learning Technology at National Central University in Taiwan. He has worked on various areas of digital technology supported learning, including artificial intelligence in education, computer supported collaborative learning, digital classrooms, online learning communities, mobile and ubiquitous learning, digital game based learning, and, most recently, technology supported mathematics and language arts learning.

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Yeh, C.Y.C., Cheng, H.N.H., Chen, ZH. et al. Enhancing achievement and interest in mathematics learning through Math-Island. RPTEL 14 , 5 (2019). https://doi.org/10.1186/s41039-019-0100-9

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## Intervention Strategies Utilized by Elementary Mathematics Teachers and Their Perceived Effectiveness in Enhancing Learners' Performance

2022, Psychology and Education: A Multidisciplinary Journal

This study aimed to determine the intervention strategies used by elementary Mathematics teachers and their effectiveness in enhancing learners' performance. Employing a descriptive-correlational research design, the study described the demographic profile of the respondents and the intervention strategies utilized by the teachers and their effectiveness in terms of fundamental, computational and word problem-solving skills. It also determined the significant difference in the intervention strategies utilized by the teachers when grouped according to their demographic profile and the significant relationship between the intervention strategies and their extent of effectiveness in enhancing their learner's performance. Findings revealed that the teachers strongly agreed that they used Repetition in helping their pupils learn better. A significant difference was also noted in the use of Repetition and Timed-testing as intervention strategies specifically in terms of sex. Meanwhile, Male and female teachers differ in their use of two strategies although there was no significant difference in all other strategies under study. Moreover, the teachers did not exhibit any significant difference on the perceived level of effectiveness of the intervention strategies based on the selected demographic profile. Also, significant relationship between the intervention strategies and their perceived level of effectiveness in enhancing learners' performance was evident in the study. Finally, the study concluded that teachers perceived the intervention strategies as effective in enhancing their learners' performance.

## Related Papers

Psychology and Education: A Multidisciplinary Journal

Psychology and Education

This study aimed to determine the learning difficulties of the Grade I pupils identified by the Multi-Factored Assessment Tool (MFAT) and the interventions employed by the teachers as basis for managing intervention model. The respondents of this study are the Grade I teachers in the Division of Quezon who were chosen through purposive sampling. A questionnaire was used to gather the data needed. A descriptive study design was employed. Specifically, this study attempted to answer the following questions: 1.) What are the learning difficulties of the Grade I pupils identified by the Multi-Factored Assessment Tool (MFAT) in Cognitive Domain (Literacy and Numeracy), Communication Domain, and Social Domain? 2.) What interventions did the Grade I teachers employ to address the learning difficulties of the Grade I pupils in Cognitive Domain (Literacy and Numeracy), Communication Domain, and Social Domain? 3.) What are the effective interventions employed in addressing the learner's difficulties in Cognitive Domain (Literacy and Numeracy), Communication Domain, and Social Domain? 4.) What intervention model could be proposed to address learner's difficulties in Cognitive Domain (Literacy and Numeracy), Communication Domain, and Social Domain? Based on the findings of the study, it has been found out that the learning difficulties of the Grade I pupils identified by the Multi-Factored Assessment Tool (MFAT) were: "difficulty in recognizing and reading pre-primer sight words, primer sight words, and basic Filipino words", "difficulty in identifying time by the hour", "difficulty in telling stories to peer/class and teacher coherently with uninterrupted flow of sounds, words, syllables, and phrases", and "difficulty in participating in group activities and role plays", and that the interventions employed by the teachers in addressing the learning difficulties of the Grade I pupils were "Marungko Reading Intervention Strategy", "It's Hour Time", "Who Am I?", and "It's Play Time Intervention Strategy" which were generally very effective. Furthermore, it has been found that all of the interventions employed by the Grade I teachers were very effective in addressing the learning difficulties of the Grade I pupils in cognitive domain (literacy and numeracy), communication domain, and social domain.

Psychology and Education , JUNIE BIASON

This developmental research aimed to assess the learning competencies in mathematics as basis for contextualized instructional material development. The respondents of the study were the 250 Grade VI learners in the District of Lemery, Lemery, Iloilo, who were chosen using the stratified random sampling. The researcher-made instrument was used to gather data. The instrument is a 45-item multiple choice test which was validated and reliability tested. This study employed mean and percentage in data analysis. The results of the study revealed that topics under whole numbers was in "approaching to mastery" level, number relations was in "developing" level, fractions was in "frustration" level, decimals was in "developing" level, ratio, proportion, and percent was in "approaching to mastery" level, geometry was in "developing" level, patterns and algebra was in "developing" level, topics related to measurement was in "frustration" level, statistics and probability was in "developing" level. It was further found out that the least mastered competency was in the topic related to fraction. It was concluded that learners performed best in the topics related to whole numbers and underperformed in the topics related to fractions and measurement. Contextualized instructional material was developed to improve the performance of the learners on the topics which they found difficult. The evaluation of developed instructional material revealed "exemplary" in terms of content, quality, usability, instructional design, and in overall. It was further recommended that learners, teachers and school administrator should collaborate with each other to address the problem in mastering the learning competencies in mathematics.

Psychology and Education , Cyril Cabello , Lovella S. Calmerin

Quasi-experimental research with pretest and posttest design was conducted to investigate the effectiveness of the Strategic Instructional Material (SIM)-based teaching in ameliorating the mastery level of fourth grade learners of Camanjac Elementary School. Two groups were created, namely: a) control group and b) the experimental group. There were 12 learners in each group and the second group were exposed to SIM-based teaching and the other won't. Study findings disclosed that majority of both groups had very low scores in the pretest, and the latter group had great increase in their scores while the former group had a very slight change in the scores of their posttest. Additionally, both groups showed a considerable mean improvement from the pretest to the posttest, demonstrating the critical role that SIM play in the teaching-learning process. The experimental group acquired higher mean gain than the controlled group and had a Very High perception towards the use of SIM in the teaching of Fundamental Operations in Mathematics. The study concluded that SIMbased teaching is an effective intervention in improving the mastery level of students in the concepts of Fundamental Operations in Math. Furthermore, the researchers recommend the use of SIM for remediation where all teachers put more of an emphasis on the teaching and learning process and by incorporating interventions that the students enjoy. School administrators should concentrate on remediation programs and instructional intervention plans to avoid problems with fundamental mathematical abilities in children and constructing SIMs not only on least mastered skills but also on all skills covered by the lesson.

Mark John A. Belleza , Psychology and Education

Numeracy skills are important mathematical skills that include a variety of capabilities to understand and analyze numerical information, to make the right conclusions and decisions, and apply in daily life the concepts and ideas of mathematics. This one group pretest-posttest experimental design aimed to ascertain the effectiveness of enhanced mathematics learning kit with parental involvement at homes on the learners' numeracy level using purposive sampling technique amid the COVID-19 pandemic. The data were obtained using the Regional Unified Numeracy Test (RUNT). Mean and standard deviation followed by Wilcoxon Signed-Rank Test were utilized for data analysis. Level of significance was set at 0.05 alpha level. The data showed that the numeracy skills of learners was low prior to the intervention. After the exposure to the enhanced mathematics learning kit with parental involvement at homes, results showed a considerable increase of numeracy skills from low level before the intervention to high level after the intervention. The findings also revealed a significant difference between the pretest and posttest means scores of the non-numerate learners. Thus, an enhanced mathematics learning kit with parental involvement at homes can be used as effective intervention in improving the numeracy skills of the nonnumerate learners, especially this new normal. Therefore, it is recommended that teachers should actively involve the parents and strengthen their capacity as learning facilitators of their children's self-learning modules in mathematics. Further, activities in the self-learning modules should be enhanced based on the cognitive level of the learners to develop their skills and higher understanding especially in teaching and learning Mathematics amid the pandemic times.

Psychology and Education , Belen C. Gabriel , Mary Hope Kadusale

The recent health crisis experienced by all nations in the world created detrimental change in the countenance of educational sector especially in the new mode of delivering the instructions as measure in containing the virus and as well as continuing education. In the works of literature, little to no attention was given to the formulation of the most essential learning competencies (MELCs) as strategic measure for modular learning. This paves the way to probe the lived experiences of the teachers pertaining to the compromised competencies under MELCs. Anchoring to the Sociocultural Theory of Cognitive Development by Vgotsky, this study utilized Interpretative Phenomenological Research Design with Interpretative Phenomenological Analysis (IPA) popularized by Moustakas and modified by Van Kaam as approach to analyzed the transcripts. Using purposive sampling, there were 7 informants participated the study. They are all qualified according to the inclusion criteria set by the study. The study generated three themes which are: The Compromised, The Cut-short, and The Champion. These themes elaborated the lived experiences of the teachers using the Most Essential Learning Competencies forwarded to the students. It is recommended that the learning support should be magnified in the new learning modality. Hence, the Most Essential Learning Competencies will be not be compromised.

Psychology and Education , Cyril Cabello

There is myriad of strategies that can be employed in the classroom. One of these is the Cooperative Learning. Because cooperative learning is a common strategy, it will just be used in different topics without considering its effectiveness in a particular topic. Thus, little attention is given to test how effective this strategy is. This study endeavored to assess if cooperative learning can make the discussion of pie chart an engaging one. The study used Quasi-Experimental research design in fulfilling its objectives. The respondents are grade 6 learners studying at Langin Elementary School in Ronda, Cebu, Philippines. There are 30 respondents in total in both control (15) and experimental (15). The experimental group garnered the mean of 11.47 and the control group mean with 9 in the pretest. While in the posttest, the experimental group garnered 19.33 and the control group landed on 17.60. With the 0.05 significance level, the results between the pretest and posttest of the two groups were found to be significant (p-value= 0.00). This is a realization that strategies can possibly constitute a significant difference. In this study, both the traditional way of teaching the topic and the one that is being introduced marked significantly. Thus, it is recommended to have this strategy tested in different topics in Mathematics and other subjects wherein the findings of this study can be verified.

This study which utilized the research and development design aimed to develop instructional module in enhancing the study and thinking skills of learners and to validate their functionality, relevance, and acceptability. It was conducted in December, 2019 in the Schools Division of Iloilo. The respondents of this study are the 177 senior high school and hybrid English teachers, 30 teachervalidators and 5 experts. The data were gathered using the researcher-made needs analysis survey, and the evaluation tools for functionality and relevance and an adopted instrument for the acceptability. The development of learning modules underwent four phases: (1) document and needs analysis; (2) the development of modules; (3) the evaluation by teacher-validators and expertevaluators; and (4) finalization and reproduction of modules in their final form. Results show that the teacher-validators perceive the instructional module as highly functional and highly relevant while the experts evaluated the instruments as excellent in all areas of the modules such as the objectives, instruction, learning activities, physical aspects and evaluation measures.

Psychology and Education , Rosalie Q. Daligdig , Richa P. Buaya , Catherine P . Tapales

Academe has always been working on innovating diverse strategic instructions employed in the classroom to effectively transfer knowledge and achieve curriculum objectives. Academic intervention is vital in developing new and existing skills, thus motivating learners’ competence in this contemporary milieu. In the literature, little to no attention is given to improving classroom discussion using differentiated instructions. This study aimed to evaluate the efficiency of differentiated instruction as a method of teaching weather patterns and seasons of the Philippines to students among grade 6 learners at Moalboal Central Elementary School, Moalboal, Cebu, Philippines. This study utilized a quasi-experimental research design participated by 30 respondents in total for both experimental and controlled groups. A T-test was used as a statistical tool to analyze the degree of difference. In the pretest, the results showed that both groups' mean (11) were equal. The posttest showed a difference of three points from the controlled group's mean (10) to the experimental group's mean (13). Based on the data gathered, the conventional method displayed no significant difference (p-value 0.42), whereas the utilization of differentiated instruction implied that there is a significant difference (p-value 0.00) as a result. Hence, the intervention suggested can make a difference in elevating the students' learning experience. It is recommended to have this strategy employed in different topics to verify its effectiveness in improving classroom discussion.

Psychology and Education , Cyril Cabello , Jankien N. Ugbamen , Elmer L. Acruz

In our technologically advanced generation, using video as instructional support is the modern way to give high-quality instruction. Numerous studies have looked at how video education affects students' academic ability, but none have particularly looked at the scientific idea of the Convergent Plate Boundary. This study evaluates how well the video instruction enriched the Convergent Plate Boundary discussion. The study used a mixed method to triangulate the quantitative and qualitative information collected from the respondents who were Grade 10 students at Balao National High School in Balao, Barili, Cebu, Philippines. The t-test was used to analyze the data for the 30 students in the experimental and control groups. The controlled group has a p-value of 0.014 and the experimental group has a p-value of 0.00072. The findings showed a significant difference between the pretest and posttest of both the controlled and experimental groups. Three themes that describe the students' interactions with instructional videos were developed from their real-world experiences: perceived usability, usefulness of instructional videos, and enjoyment. With this, video instruction is a strategy driven by technology that can change the behavior of the students and improve their academic performance as well. This study recommends that: (1) schools should begin using instructional videos to teach and master various disciplines, especially science; (2) schools should use instructional videos to improve students' attitudes toward science and other subjects; (3) teachers should receive training on how to design, develop, and use instructional videos to foster learning; and (4) the benefits of using instructional videos in teaching.

Fanny Mae G Mobida , Lorievic V. Carmelotes , Psychology and Education

Since the pandemic started, XUGS has continued the mission of education through online learning. They utilized the MS Teams platform as a medium for teaching and learning. The teachers observed the delay of pupils' submission and as a result, this study focuses on the intervention through locking of MS Teams Assessment to improve the promptness of the pupils' submission of Math quizzes. The objective of this study is to determine the number of pupils who submitted in a specific time range, duration and their quizzes scores. More so, it also seeks the perceptions from pupils, parents, and teachers about the intervention. It revealed that this intervention is very effective in improving promptness of pupils' submission in which 80% of the population of pupils submitted their quizzes in less than 30 minutes, given the 10-15 items with one hour allotted time. This result is consistent from Quizzes 1, 2, and 3. Also, the intervention gained positive feedback from pupils, parents, and teachers. Based on the perspective of pupils, 80% Agree; and 100% of teachers Strongly Agree that the locking of MS Teams is very effective in improving the promptness of pupils' submission. And 95% of the parents perceive their son/daughter is practicing time management at home because they have deadlines set by the teacher in the MS Teams. These findings support the idea that this intervention should be continued in this new mode of learning, in which schools use learning management systems like MS Teams to improve the promptness of students' submissions by locking them in.

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## Examining the Impact of Modified P3 Task Taxonomy-Enriched Educational Robotics PD Program on Teachers’ STEM Content Knowledge

- Published: 26 June 2024

## Cite this article

- Salih Cepni ORCID: orcid.org/0000-0003-2343-8796 1 ,
- Mirac Aydin ORCID: orcid.org/0000-0001-9616-5341 2 ,
- Kubra Ada Yildiz ORCID: orcid.org/0000-0001-6243-9703 3 ,
- Salih Birisci ORCID: orcid.org/0000-0001-7131-5112 4 ,
- Cem Ozkan ORCID: orcid.org/0000-0003-4865-7098 5 &
- Cemal Yalabuk ORCID: orcid.org/0009-0005-6952-4798 6

The importance of integrating effective teaching strategies in Professional Development (PD) programs for Educational Robotics (ER)-based Science Technology Engineering and Mathematics (STEM) education is increasingly recognized. However, we need to add to the growing body of studies on comprehensive instructional approaches for teaching robotics to educators within PD STEM environments. This study investigates the effects of the modified P3 task taxonomy enriched ER-based STEM PD course on science, mathematics, and computer science teachers’ STEM knowledge. The taxonomy denotes a strategy utilized to teach high school students ER. Twenty in-service teachers participated in the study, attended a 24-hour PD program in which they were taught how to use Arduino robotics kits, were assigned three tasks, and were engaged in creating lesson plans incorporating ER into their regular teaching practices. The one-group pre and post-test experimental design was adopted in the study. The instruments included a science, robotics, and mathematics content knowledge test administered before and after the PD program. Moreover, the variations in mean scores for both the pre-test and post-test, pertaining to knowledge in science, mathematics, and robotics, were demonstrated. Using a paired-sample t-test, we found that the P3 task taxonomy scaffolded PD program had statistically significant impacts with large effect sizes in robotics (2.08), science (1.49), and mathematics (0.92). These results hold important implications, suggesting that the P3 task taxonomy offers a new approach beyond learning by design, the 5E model, and project-based learning for scaffolding PD in ER settings.

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## Acknowledgements

This study has been funded by Bursa Uludag University in Turkey under the grant number SOA-2022-1121.

## Author information

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Department of Mathematics and Science Education, Faculty of Education, Bursa Uludağ University, Nilufer, Bursa, Türkiye

Salih Cepni

Department of Mathematics and Science Education, Fatih Faculty of Education, Trabzon University, Sogutlu, Trabzon, Türkiye

Mirac Aydin

Mathematics Education Doctorate Program, Institute of Educational Sciences, Bursa Uludağ University, Nilufer, Bursa, Türkiye

Kubra Ada Yildiz

Department of Computer Education and Instructional Technologies, Faculty of Education, Bursa Uludağ University, Nilufer, Bursa, Türkiye

Salih Birisci

İletim Engineering Limited Company, Bursa, Türkiye

Computer Education and Instructional Technology Master Program, Faculty of Education, Bursa Uludağ University, Nilufer, Bursa, Türkiye

Cemal Yalabuk

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Slope graphs representing changes in both mean scores and individual scores, along with frequencies for each question in science, robotics, and mathematics knowledge.

Changes in mean scores for each question on the science content knowledge test

Changes in scores/levels for each question on the science content knowledge test for Task 1

Changes in scores/levels for each question on the science content knowledge test for Task 2

Changes in scores/levels for each question on the science content knowledge test for Task 3

Changes in scores/levels for each question on the robotic content knowledge test for Task 1

Changes in scores/levels for each question on the robotic content knowledge test for Task 2

Changes in scores/levels for each question on the robotic content knowledge test for Task 3

Changes in scores/levels for each question on the mathematics content knowledge test for Task 1

Changes in scores/levels for each question on the mathematics content knowledge test for Task 2

Changes in scores/levels for each question on the robotic mathematics knowledge test for Task 3

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## About this article

Cepni, S., Aydin, M., Ada Yildiz, K. et al. Examining the Impact of Modified P3 Task Taxonomy-Enriched Educational Robotics PD Program on Teachers’ STEM Content Knowledge. Int J of Sci and Math Educ (2024). https://doi.org/10.1007/s10763-024-10475-1

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Received : 30 October 2023

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Published : 26 June 2024

DOI : https://doi.org/10.1007/s10763-024-10475-1

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determined teaching strategies applied by the teachers in teaching mathematics; and (iii) analysed the influence of learning styles and teaching strategies on the academic performance in mathematics. 1.1 Theoretical framework According to Samadi (2011), studies about the learning styles started in the 1950s and

Microsoft Word - ED504828.doc. INCREASING STUDENT LEARNING IN MATHEMATICS WITH THE USE OF. COLLABORATIVE TEACHING STRATEGIES. Jenna Di Fatta, B.A. Sarah Garcia, B. S. Stephanie Gorman, B. S. An Action Research Proposal Submitted to the Graduate Faculty of the School of.

HAVE APPROVED THIS THESIS Teaching Strategies to Promote Understanding of Mathematics through ... classroom when teaching math. Not only do teachers have many options on learning theories that they can use but also throughout the years many different classrooms standards. With all these standards it can be difficult for teachers to discover the ...

mathematics (Wilson, Fernandez and Hadaway, 2011). The main goal in teaching mathematical problem-solving is for the students to develop a generic ability in solving real-life problems and to apply mathematics in real life situations. It can also be used, as a teaching method, for a deeper understanding of concepts.

Teaching Mathematics: Strategies for Improved Mathematical Perform ance. International Journal . of Social Sciences and Educational Studies, 10 (3), 146-150.

able to recognize that math anxiety is real, and be aware of strategies to reduce mathematics anxiety with our students (Stuart, 2000). Mathematics anxiety can be characterized by math

math performance, as well as their self-reported self-efficacy in math, happiness in class, and behavior in class. In addition, I estimate the relationship between domains of teaching practice captured by two observation instruments and the set of student outcomes. Finally, I examine the predictive validity of teacher effect estimates on

This article identifies and describes the teaching strategies used by mathematic teachers in implementing tasks. The context of this study was the classroom of three mathematic teachers at ...

Mathematics (DEBT-M) program, as well as my many years as a mathematics teacher and supervisor, I have found high-quality diversity training to be essential in helping teachers close mathematics opportunity gaps and improve outcomes for students. Unfortunately, high-quality diversity training is not universally available.

mathematics curriculum standards to concentrate on mathematics content and numerical reasoning (NCTM, 2000, 2015). This development inspired the change in the focus of education curriculum to teaching pedagogy. More emphasis was placed on teacher instruction of mathematics content, instead of the content alone. Student goals were

teaching mathematics subjects was one of the methods used in teaching the subject (Yavuz & Erbay, 2015), and mathematics teachers have considered the shifting of emphasis from teaching problem-solving to teaching through problem-solving (Taplin, n.d.). It is believed that important mathematics concepts and procedures

This paper explores the teaching strategies for mathematical problem-solving in a secondary school in Johor, Malaysia. It involves a qualitative study in which a semi-structured interview was conducted with mathematics teachers. Data were analyzed using a six-step thematic analysis. The results can be viewed from three contexts of findings ...

how to implement various teaching and learning approaches was limited. They relied heavily on conducting experiments and recording results. Key words: Teaching strategies; mathematics; Grade 6; probability; teaching and learning approaches; essential aspects.

Theses/Dissertations from 2020. Mathematical Identities of Students with Mathematics Learning Dis/abilities, Emma Lynn Holdaway. Teachers' Mathematical Meanings: Decisions for Teaching Geometric Reflections and Orientation of Figures, Porter Peterson Nielsen. Student Use of Mathematical Content Knowledge During Proof Production, Chelsey Lynn ...

herwise, it will be a failure of teacher and teaching [6]. 4. DiscussionThese findings clearly demonstrate that mathematics teachers mainly preferred techniques requiring less preparation and effort, such as "Question and Answer" and "Demonstration."Techniques requiring greater preparation and.

Computer-supported mathematics learning. The mathematics curriculum in elementary schools basically includes conceptual understanding, procedural fluency, and strategic competence in terms of mathematical proficiency (see Kilpatrick et al. 2001).First, conceptual understanding refers to students' comprehension of mathematical concepts and the relationships between concepts.

There are 6 out of the 10 strategies that are considered to be very effective such. as showing an application, visual presentation, presenting a challenge, using the. inductive method, using the ...

on their math paper; sometimes my job as a math teacher and tutor feels like part counselor, part instructor. I hear peoples' spontaneous confessions of math anxiety when I tell them I am entering the math teaching profession, the most common response being "oh, you are going to be a math teacher? I was horrible at math. Just thinking about it

Modern Educational Methods and Strategies in Teaching Mathematics: Changing Thoughts By Yousef Methkal Abd Algani and Jamal Eshan . This book first published 2023 . Cambridge Scholars Publishing . Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK . British Library Cataloguing in Publication Data .

oaquin, Cleo ude A. "Students' Academic Performance in Mathematics as Influenced by Teaching and Learning Styles Unpublished Master of Arts in Teaching (Mathematics) Thesis, Filamer Christian University Roxas City, October, 2013. bstract A teacher should be aware of the kinds of learners she is handling so she can suit her teaching ...

Noel A. Sabando The literature cited that the intervention strategies in teaching Mathematics is to enhance the elementary pupils' fundamental, computational, and word problem-solving skills using visualization, guess and check, find a pattern, work backward, repetition, timed testing, and math games during the pre-pandemic time.

Email address: [email protected]. The Study of Teaching Effective Strategies on Student's Math. Achievements. Mohammad-Hassan Behzadi, Farhad Hosseinzadeh Lotfi, Nasrin Mahboudi 1*. (1 ...

mathematics teaching approaches on students' performance with the intent to identify effective approaches that can improve performance in mathematics. The results of a random-effects meta-analysis showed that mathematics teaching approaches have an overall large significant effect ( 1.39 ) on students' performance. Specifically, the

The importance of integrating effective teaching strategies in Professional Development (PD) programs for Educational Robotics (ER)-based Science Technology Engineering and Mathematics (STEM) education is increasingly recognized. However, we need to add to the growing body of studies on comprehensive instructional approaches for teaching robotics to educators within PD STEM environments. This ...