Jon Davis | Western Michigan University (original) (raw)
Papers by Jon Davis
International Journal of Educational Research, 2014
Introduction and background Researchers from around the world have recently been turning their fo... more Introduction and background Researchers from around the world have recently been turning their focus on what we refer to as proof-related constructs
Mathematics Teaching in the Middle School, Sep 1, 2006
Engaging in meaningful problems outside of school rarely involves only mathematics knowledge. Oft... more Engaging in meaningful problems outside of school rarely involves only mathematics knowledge. Oftentimes, multiple subject areas are involved when solving problems that professionals routinely encounter outside of school. unfortunately, middle and secondary students often experience subject areas as isolated islands within the ocean of their experiences. Efforts to bring the closely related subject areas of mathematics and science together have been promoted in documents by NCTM (1989, 2000) and the American Association for the Advancement of Science (1989).
The Middle Grades Research Journal, 2014
Across the United States, K-12 schools and postsecondary institutions are rushing to address a ne... more Across the United States, K-12 schools and postsecondary institutions are rushing to address a need for individuals trained in seience, technology, engineering, and mathematics (STEM). Moreover, instead of considering these as four separate content areas, an inte- grated view of STEM (e.g., Capraro, Capraro, & Morgan, 2013) considers these content areas as a whole that is indeed greater than the sum of its parts. The student goals associated with integrated STEM include the following: STEM literacy, 21st century competencies, STEM workforce readiness, interest and engagement, and ability to make connections among STEM disciplines (Honey, Pearson, & Schweingruber, 2014).The National Research Council (2011) recently identified five key educational system elements that cut across content areas to help promote STEM education. These key elements are as follows: "a coherent set of standards and curriculum," "teachers with high capacity to teach in their discipline," &q...
International Journal of Educational Research, 2018
We report findings on teachers' noticing of features in the teacher resources of mathematics curr... more We report findings on teachers' noticing of features in the teacher resources of mathematics curriculum programs. Based on prior analysis, we selected teachers using one of two curriculum types: delivery mechanism or thinking device. The participating teachers and the curriculum programs aimed to align with the Common Core Standards for Mathematics, and thus, they ostensibly held a common aim for instruction. We analyzed 147 lesson planning interviews with 20 middle school mathematics teachers. We found that teachers attended to similar features of teacher resources; however, patterns for interpreting and planning decisions varied based on teachers' orientations and curriculum type. 1. Introduction and purpose The widespread adoption of the Common Core State Standards for Mathematics (CCSSM) (Common Core State Standards Initiative, 2010) in the United States has influenced education at all levels from state-level policy to curriculum design to classroom teaching and learning. The CCSSM was intended to provide more focus and coherence for teachers and students (Schmidt & Houang, 2012; Woolard, 2013). Consistent with this aim, the CCSSM requires a shift from past states' standards to more rigorous content (Porter, McMaken, Hwang, & Yang, 2011), and potentially more ambitious forms of practice with more demanding curriculum programs (National Council of Teachers of Mathematics, 2014; Tran, Reys, Teuscher, Dingman, & Kasmer, 2016). In the United States, the CCSSM were initially adopted by 45 states plus the District of Columbia. As of 2018, among the 45 states who adopted the CCSSM or a modified version (the modifications usually entail additions), 11 states have withdrawn (Academic Benchmarks, 2018). Among these 11 states, in most cases their standards continue to reflect the CCSSM. Thus, despite a rollback in some states, the CCSSM or slightly modified versions continue as the predominant standards in the U.S. Thus, at the time of our study, the CCSSMadopting states shared a relatively common articulation of content and the progression of content across the grades. This set of common goals and policy for curriculum standards provided an opportune time to consider how districts and teachers interpret curriculum materials that share the aim of (ostensibly) alignment with the CCSSM. The purpose of this study was to investigate how middle school mathematics teachers use curriculum resources to plan lessons in the context of CCSSM. More specifically, the extent to which teachers' orientations and the type of curriculum materials interact with what teachers notice in curriculum. U.S. teachers historically have relied heavily on district-adopted mathematics textbooks (Grouws, Smith, & Sztajn, 2004), and yet types of curriculum materials and teachers' use of materials can vary substantially with implications
Journal of Mathematics Teacher Education, 2017
Eight middle school mathematics teachers' perceptions and uses of curriculum materials and the Co... more Eight middle school mathematics teachers' perceptions and uses of curriculum materials and the Common Core State Standards for Mathematics (CCSSM) were investigated. Adapting a noticing framework and models of dialogic instruction and direct instruction, teachers' noticing practices with curriculum materials and the CCSSM when planning, enacting, and reflecting on lessons were examined. Teachers who were committed to implementing the CCSSM and who were using one of two substantively different curriculum programs were purposefully selected. Data sources included multiple forms of interviews and classroom observations. The teaching evidenced three distinct noticing patterns. These patterns indicated that teachers' curriculum materials were associated with how teachers perceived and enacted the CCSSM. Teaching with a curriculum program that was designed as a thinking device prioritized the Standards for Mathematical Practice of CCSSM evidenced noticing that was consistent with dialogic instruction. Teaching with a curriculum program that was designed as a delivery mechanism prioritized the Content Standards of CCSSM and evidenced noticing consistent with direct instruction. Findings indicated that the designated curriculum and contributed to differing interpretations of CCSSM and served as a lens for noticing. However, a dialogic curriculum program was not sufficient to support dialogic approaches in practice. One pattern showed teachers planning dialogic lessons, but the lesson enactments were not consistent with teachers' plans, with evidence that the teachers were not aware that their practices differed from dialogic approaches. Implications for research and practice are discussed.
International Journal of Educational Research, 2018
This contribution to curriculum ergonomics focuses on teachers' perceptions of problem solving an... more This contribution to curriculum ergonomics focuses on teachers' perceptions of problem solving and rigor in the Common Core State Standards for Mathematics, the curricular aims and objectives component of the official curriculum in the U.S. Our analyses involve 89 middle school mathematics teachers (MSMTs) using two different types of district-adopted textbooks: thinking device (TD) and delivery mechanism (DM). We found that MSMTs' perceptions of problem solving and rigor in the Common Core varied by textbook type. Consequently, while this paper examines teachers' perceptions of curricular aims and objectives, it was apparent that another component of the official curriculum, teachers' district-adopted textbooks, played a strong role in influencing these perceptions. The implications of these results are discussed.
Journal for Research in Mathematics Education, Mar 1, 2008
This study extends our understanding of the relationship between the use of Standards based middl... more This study extends our understanding of the relationship between the use of Standards based middle grades curricula and the learning of traditional mathematics topics as measured by two widely used standardized tests, the SAT-9 and the New Standards Mathematics Reference Exam. Sixteen hundred middle grades students in 43 classrooms from five districts with varying demographic profiles participated. These districts had participated in a Local Systemic Change (LSC) project supported by NSF. Students had used either the Connected Mathematics Project (CMP) or the MATH Thematics (STEM) program for three years. Achievement related information was accumulated and used to detect patterns and to estimate their magnitude on the Open Ended, Problem Solving and Procedures subtests of the SAT-9. Hierarchical Linear Modeling (HLM) was used to analyze subtest results following methods described by Raudenbush and Bryk (2002). HLM permitted us to model variation in mathematics proficiency by controlling for other factors such as student prior achievement and classroom ethnic composition. It also allowed us to examine student and classroom patterns of achievement simultaneously. Student and classroom level predictive models were developed and fitted to predict student scores for various subgroups and to compare the predicted values against national Normal Curve Equivalence (NCE) means. A group of "value added" students were tested on three separate occasions over a two-year period of time to permit examination of achievement trends and achievement gaps among the various subpopulations. In the within classrooms HLM analysis, students' socioeconomic status (SES) and prior mathematics knowledge were significant predictors of achievement. A number of different factors such as SES, prior knowledge, concentrations of Asian students, percent special education and school district were significant predictors of between classroom variation. Students' performance on the Open Ended and Problem Solving subtests were above national means, despite the fact that many began below this level. Their progress on the Procedures subtest was less stellar with districts ending below national means. This is perhaps not surprising since these curricula do not focus on paper and pencil calculation to the same extent as more traditional curricula. Results suggest that Standards based students do learn traditional mathematics topics, at least those topics assessed by the two tests used. This study continues to raise the question "What mathematics is most valued and what type of a curriculum is most likely to provide it?
The Mathematics Enthusiast, 2014
As educational systems around the world attempt to reform their mathematics programs to increase ... more As educational systems around the world attempt to reform their mathematics programs to increase students' opportunities to engage in processes central to the practice of mathematics such as proof, it is important to understand how this mathematical act is portrayed in national curriculum documents that drive that change. This study examined the presence of reasoningand-proving (RP) in Ireland's national reform-oriented secondary syllabi for junior cycle (ages 12-15) and senior cycle (ages 15-18) students. The analyses reveal that there were no differences among direct and indirect RP learning outcomes within each syllabus, but statistically significant differences did exist across syllabi in these categories. Students were provided with statistically different opportunities to engage in pattern identification, conjecture formulation, and argument construction in both syllabi. There were significantly fewer opportunities to engage in conjecture formulation for junior cycle students and significantly more opportunities to construct arguments for senior cycle students. There were no instances of proof as falsification across both syllabi, but students were given similar opportunities to experience proof as explanation, verification, and generation of new knowledge. Across both syllabi there were statistically significantly more RP learning outcomes that were divorced from content than those that were connected to content. The results as well as the implications of these results for the design of national curriculum documents are discussed.
Irish Mathematical Society Bulletin, 2013
This study examined student tasks in the area of complex number operations in six Irish secondary... more This study examined student tasks in the area of complex number operations in six Irish secondary mathematics textbooks and a Project Maths teaching and learning plan for reasoningand-proving (RP) opportunities. At the ordinary level, 9.1% of 1274 student tasks were coded as RP. At the higher level, 13.3% of 1373 tasks were coded as RP. The majority of argument opportunities in ordinary level materials were the lowest form of argument-proofwriting exercises. At the higher level, the majority of argument opportunities were within argument-specific or argument-general categories. Less than 2% of the tasks at the ordinary or higher level involved pattern identification or conjecture development. Students were not asked to test conjectures, construct counterexamples, develop proof subcomponents, or formulate RP objects in any of the seven sets of materials. Only one RP task appearing across all seven sets of materials involved the use of technology. The implication of these results as well as how textbook materials could be redesigned using the RP framework are discussed. 2010 Mathematics Subject Classification. 97C99.
This study examined the college mathematics placement exam results of 1,277 students learning fro... more This study examined the college mathematics placement exam results of 1,277 students learning from nine secondary mathematics curricula and two Advanced Placement (AP) mathematics programs in 25 different high schools in the United States. The results suggest that students learning from several traditional mathematics programs and AP Calculus significantly outperformed students learning from the reform-oriented mathematics program, Core-Plus Mathematics Project, on algebra manipulation and calculus readiness questions. Prior mathematics achievement, course completion, and gender also significantly influenced mathematics placement scores. Students cross a number of divides as part of their schooling in different countries around the world. The divide between secondary and postsecondary education, which the majority of students in the United States encounter at some point on their educational journeys, is one of the most difficult for students to cross for several reasons. First, post...
R E Source, Nov 20, 2014
This study investigated how a group of 10 prospective secondary mathematics teachers (PST) read, ... more This study investigated how a group of 10 prospective secondary mathematics teachers (PST) read, evaluated, and adapted a textbook lesson involving the symbolic manipulation capabilities of computer algebra systems (CAS-S). PST read the entire lesson and tended to focus on the organizing question at the beginning of the student lesson and the CAS-S sections of the lesson. PST frequently evaluated the lesson with respect to the teacher and whether lesson elements would promote student understanding. Only one PST evaluated the lesson with respect to the student and how they student might interpret lesson elements. There were five categories of curricular adaptations exhibited by PST: following, additive, mix, reductive, and adaptive. In general, the adaptations made to the lesson by PST were positive. CAS-S based elements were occasionally removed by PST but typically due to non-technology based reasons such as problem redundancy. Several positive adaptations were made by PST to CAS-S based elements such as asking students to make predictions before using CAS-S and understanding the hidden procedures used by the technology.
practice. Thirty percent of the teachers planned lessons from unit/chapter materials to become fa... more practice. Thirty percent of the teachers planned lessons from unit/chapter materials to become familiar with the mathematical content of the lesson, the presentation of the mathematics in the materials, and the context in which the lesson was couched. Thirty-two percent of the teachers went beyond becoming familiar with the content, presentation, and context to make decisions for student learning, for example, potential student questions, possible misunderstandings, anticipation of various solution strategies, accommodation of various ability levels, or conceptual development within a unit. One MiC teacher planned lessons that emphasized higher order thinking, depth of knowledge, and/or understanding. For example, the teacher planned questions that engaged students in interpreting a solution in terms of the problem context, exploring connections among equivalent representations of numbers, or summarizing the mathematics in a series of lessons. Planning forms of instruction that promote classroom discourse for the purpose of the lesson varied among all teachers in Districts 1-4. Forty-two percent of the teachers anticipated using whole-class discussion and small-group or pair work. Although these teachers planned for such lesson formats, the focus was primarily on completing tasks rather than on facilitating or encouraging substantive conversation of mathematics concepts. Twenty-eight percent planned for students' participation and collaboration for during instruction, but these still were not the primary focus of the lesson plan. Twenty-five percent of the teachers rarely planned students' discourse in the classroom as part of the lesson. Instead, instruction focused on factual information or presentation of algorithms and procedures. One MiC teacher planned forms of instruction that promoted substantive conversation. The teacher planned classroom activities that encouraged students to participate in discussion, evaluate other's ideas, interpret their own ideas in terms of comments from others, and build substantive conversation. Similarly, planned student activities that promoted discussion, problem solving, and reflection on the content of the lesson varied among the teachers. Forty-seven percent of the teachers included investigation of problems and discussion of answers and solution strategies (whether during small-group work or whole-class discussions) in lesson plans. Twenty-five percent of the teachers included investigation of problems and discussion of answers and solution strategies as important elements in lesson plans, although questions or activities that encouraged students to reflect on or summarize lessons were rarely included. Twenty-one percent of the teachers rarely planned investigation of problems and discussion of mathematical ideas for the lessons. Emphasis, instead, was placed on practicing routine calculations, and little discussion among students was anticipated. For two MiC teachers, investigation of problems and discussion of answers and solution strategies were dominant in lesson plans. Mathematical Interaction during Instruction Six subcategories characterized the mathematical interaction during instruction: lesson presentation and development; nature of mathematical inquiry during instruction; interactive decisions during instruction; nature of students' explanations; elicitation of multiple strategies; and lesson reflection, summary, or closure. With respect to lesson presentation and development, the results for the 35 teachers in Districts 1 and 2 revealed differences by grade level, type of curriculum taught, and by district. By grade level, more fifth-and seventh-grade teachers taught mathematics for conceptual understanding than sixth-grade teachers (7 of 13 fifth-grade teachers compared to 2 of 12 sixth-grade and 4 of 10 seventh-grade teachers). Only one teacher, a fifth-grade teacher, emphasized conceptual understanding with active participation by students with teacher support. Lesson presentations set the stage for students to explore the mathematical content of the lesson on their own. Student solutions and generalizations were later presented and compared during discussions orchestrated by the teacher. Nine teachers (one sixth grade) emphasized conceptual understanding with active participation by students and teacher. Lesson presentations featured a conceptual basis for the mathematical content, and the mathematical work was shared by students and teacher. The greatest number of teachers, however, demonstrated procedures and 11 strategies for students to use. Five of the 13 fifth-grade teachers, 7 of 12 sixth-grade teachers, and 4 of 10 seventh-grade teachers presented and emphasized particular procedures or strategies. An additional pattern of variation was found when the levels of lesson presentation were reviewed by curriculum taught. Twelve of the 24 teachers using MiC either attempted to teach for or clearly emphasized conceptual understanding in contrast to only 1 of the 11 teachers using conventional curricula. On the other hand, 8 of the 11 teachers using conventional curricula presented particular procedures or strategies in class in comparison to 8 of the 24 MiC teachers. When these results were reviewed by district, however, differences became apparent for teachers using MiC. In District 2, 7 of the 12 MiC teachers either attempted to teach for or clearly emphasized conceptual understanding in comparison to 5 of the 12 MiC teachers in District 1. Also, both teachers using MiC and teachers using conventional curricula were less likely to teach particular procedures in District 2 than in District 1. Teachers also varied in the nature of inquiry during instruction. Differences were noted by grade level and type of curriculum taught. Nine of 13 fifth-grade teachers, in comparison to 5 of 12 sixth-grade and 3 of 10 seventh-grade teachers, emphasized conceptual understanding, relationships among mathematical ideas, or linking procedural and conceptual knowledge. Also, more sixth-grade teachers (3 of 12 in comparison to 2 of 13 fifth-grade and 2 of 10 seventh-grade teachers) provided limited attention to conceptual understanding. The nature of inquiry for 4 of 12 sixthgrade and 5 of 10 seventh-grade teachers, in comparison to 2 of 13 fifth-grade teachers, was limited to lower order thinking. Lessons did not promote conceptual understanding, connections among mathematical ideas, and connections between mathematics and students' lives. Teachers' interactive decisions also varied among the 35 teachers in Districts 1 and 2. Differences were revealed by grade level, by curriculum taught, and by district. By grade level, more fifth-grade teachers made interactive decisions that were aligned with teaching mathematics for understanding than did sixth-and seventh-grade teachers (5 of 13 compared to no sixth-grade teachers and 2 of 10 seventh-grade teachers). In contrast, more sixth-grade teachers made interactive decisions that were least aligned with teaching for understanding (7 of 12 compared to 3 of 13 fifth-grade teachers and 4 of 10 seventh-grade teachers). An additional pattern of variation was found when reviewed by curriculum taught. Fourteen of the 24 MiC teachers made interactive decisions that supported teaching mathematics for understanding in contrast to one of the teachers using conventional curricula. On the other hand, 8 of the 11 teachers using conventional curricula made interactive decisions least aligned with teaching for understanding compared to 6 of the 24 MiC teachers. Differences by district were also apparent for teachers using MiC. In District 2, 8 of the 12 MiC teachers made interactive decisions that were aligned with teaching mathematics for understanding in comparison to 5 of the 12 MiC teachers in District 1. Students' explanations in most classes were focused on procedures or students' responses were limited to answers only. By curriculum, significant differences in students' explanations were evident among ratings in each district in favor of teachers using MiC. Nonetheless, the results suggest that encouragement of students' explanations in classes in which MiC and conventional curricula are used needs further attention. Multiple strategies were generally not elicited from students during instruction. By curriculum, multiple strategies were elicited more frequently during MiC lessons than in lessons using conventional curricula. Few opportunities, if any, were provided for reflection on or summary of lesson content. Nine teachers provided some opportunities each week for students to reflect on the mathematics or summarize what they had learned in a lesson or in a series of lessons. Only three teachers frequently provided such opportunities for students. 12 Classroom Assessment Practice Three subcategories of Instruction characterized classroom assessment practice: evidence sought during classroom assessment; purpose and coherence of feedback given in response to classroom assessment; and content of feedback provided in response to classroom assessment. In Districts 1 and 2, 57% of the 35 study teachers (11 of the 24 MiC teachers and 9 of the 11 teachers using conventional curricula) sought evidence of procedural competence based on student homework and classwork during their assessment practice. Five teachers (all MiC) sought student explanations in addition to procedural competence and answers. However, these explanations were often void of mathematical substance and were used to generate some form of communication rather than assess student understanding. Three teachers (2 MiC) were somewhat effective at eliciting student responses and orchestrating substantive whole-class discussions. However, the overriding focus of their classroom practice was to use correct answers and procedures as evidence of student learning. Six teachers (5 MiC) viewed student explanations as evidence of student learning. The teachers sought both process...
Digital Experiences in Mathematics Education
Research suggests that tasks that use technology as a reorganizer (technology is used to produce ... more Research suggests that tasks that use technology as a reorganizer (technology is used to produce dynamic representations) are linked with the development of students' conceptual knowledge, yet many secondary mathematics textbooks in the USA predominantly include tasks that use technology as an amplifier (technology is used to produce static images). Thus, if teachers wish to incorporate tasks that use technology as a reorganizer, they must locate these resources elsewhere or construct them themselves. This study took place in a technology, pedagogy, content course where each prospective teacher (PT) engaged in at least one component of an ideation, rehearsal/ refinement, enactment, and reflection intervention, where they were asked to adapt traditional textbook lessons to promote students' rich conceptual understandings of function transformations via technology as reorganizer tasks. A total of 15 PTs agreed to participate, 8 seeking a grade K-8 certification and 7 seeking a grade 6-12 certification. On the initial lesson plan involving linear function transformations, the majority of PTs (13 out of 15) used technology as an amplifier, but on the final lesson plan involving absolute value function transformations, 13 PTs used technology as a reorganizer. There were also increases in the incidence of lesson elements that promoted moderate or rich forms of conceptual knowledge between the initial and final lesson plans. We discuss the implications of these results and introduce readers to dynamic conceptual components as manipulable bridges between different mathematical representations that hold the potential to develop students' richer forms of conceptual knowledge.
We describe two metaphors that we hope can be used to better understand the contemporary mathemat... more We describe two metaphors that we hope can be used to better understand the contemporary mathematics curriculum context in U.S. middle schools, to see how this new context is both similar to and different from prior curriculum contexts. We explain the role and positioning of middle school mathematics curriculum materials over the last century or more and build from learning theory to develop the metaphors. The first metaphor, curriculum as delivery mechanism, builds from technical rational or scientific discourses and encompasses perspectives that are so pervasive they are often unstated and unquestioned. The second metaphor, curriculum as epistemic device, posits that role of curriculum is to provoke interactions that generate understanding. In this metaphor, the role of tasks in curriculum materials is to provoke and progressively refine student thinking, individually and collectively.
International Journal of Educational Research, 2018
We conceptualize curriculum ergonomics as a field that studies the interactions between users and... more We conceptualize curriculum ergonomics as a field that studies the interactions between users and curriculum materials. We identify five themes that a curriculum ergonomics lens brings into sharper focus: (1) teachers' relationships with and capacity to use curriculum resources; (2) alignment between design intentions and patterns of curriculum use; (3) ways in which curriculum resources influence instruction; (4) ways in which curriculum features are purposefully designed to achieve an educative purpose; and (5) the dissolution of boundaries between design and use. We first summarize the literature in curriculum ergonomics and then show how key themes from that literature inform the discussion of curriculum ergonomics.
We analyzed 52 middle school mathematics lessons from multiple states and curriculum contexts to ... more We analyzed 52 middle school mathematics lessons from multiple states and curriculum contexts to understand how teachers were enacting the CCSSM. The teachers stated that all of the lessons were CCSSM-aligned. We categorized curriculum materials according to two approaches, with one approach associated with curriculum programs funded by NSF and the other representing curriculum programs commercially produced, typically from a large publisher. We analyzed the nature of mathematical activity and level of interactions in the lessons. We found significant differences across curriculum approaches in the mathematical activity categories related to cognitive demand and in the level of interaction. The implications are that curriculum programs strongly mediated the enactment of the CCSSM.
ZDM – Mathematics Education, 2021
Background: The rates of overweight and obese adults in the United Arab Emirates (UAE) have incre... more Background: The rates of overweight and obese adults in the United Arab Emirates (UAE) have increased dramatically in recent decades. Several anthropometric measurements are used to assess body weight status. Some anthropometric measurements might not be convenient to use in certain communities and settings. The objective of this study was to assess the agreement of four anthropometric measurements and indices of weight status and to investigate their associations with cardiometabolic risks. Methods: The study design was a cross-section population-based study. Adults living in the Northern Emirates were surveyed. Fasting blood samples, blood pressure readings and anthropometric measurements were also collected. Results: A total of 3531 subjects were included in this study. The prevalence of obesity/overweight was 66.4% based on body mass index (BMI), 61.7% based on waist circumference (WC), 64.6% based on waist-hip ratio (WHR) and 71% based on neck circumference (NC). There were moderate agreements between BMI and WC and between WC and WHR, with kappa (k) ranging from 0.41 to 0.60. NC showed poor agreement with BMI, WC and WHR, with k ranging from 0 to 0.2. Overweight and obesity based on BMI, WC and WHR were significantly associated with cardiometabolic risks. Conclusion: Overall, there was a moderate to a poor agreement between BMI, WC, WHR and NC. Particularly, NC showed poor agreement with BMI, WC and WHR. BMI and WC showed better performance for identifying cardiometabolic risks than WHR and NC.
Mathematical Thinking and Learning, 2020
This study investigates the effects of a technology methods course containing a unique collaborat... more This study investigates the effects of a technology methods course containing a unique collaborative design experience on prospective elementary and secondary mathematics teachers’ technological beliefs, computer algebra system (CAS) beliefs, and technological pedagogical content knowledge (TPACK). Overall gain scores on all three instruments were statistically significant. Moreover, gender and level (elementary vs. secondary) were statistically significant predictors of TPACK gain scores. However, the influence of level on TPACK gain score was different for female prospective teachers (PTs) than male PTs. Even in the case of low gain scores PTs displayed beliefs that were aligned with productive uses of technology in the classroom. PTs showed greater gains on knowledge subdomains associated with technological knowledge than on technology free subdomains (e.g., pedagogical content knowledge).
International Journal of Research in Education and Science
This article may be used for research, teaching, and private study purposes. Any substantial or s... more This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.
International Journal of Educational Research, 2014
Introduction and background Researchers from around the world have recently been turning their fo... more Introduction and background Researchers from around the world have recently been turning their focus on what we refer to as proof-related constructs
Mathematics Teaching in the Middle School, Sep 1, 2006
Engaging in meaningful problems outside of school rarely involves only mathematics knowledge. Oft... more Engaging in meaningful problems outside of school rarely involves only mathematics knowledge. Oftentimes, multiple subject areas are involved when solving problems that professionals routinely encounter outside of school. unfortunately, middle and secondary students often experience subject areas as isolated islands within the ocean of their experiences. Efforts to bring the closely related subject areas of mathematics and science together have been promoted in documents by NCTM (1989, 2000) and the American Association for the Advancement of Science (1989).
The Middle Grades Research Journal, 2014
Across the United States, K-12 schools and postsecondary institutions are rushing to address a ne... more Across the United States, K-12 schools and postsecondary institutions are rushing to address a need for individuals trained in seience, technology, engineering, and mathematics (STEM). Moreover, instead of considering these as four separate content areas, an inte- grated view of STEM (e.g., Capraro, Capraro, & Morgan, 2013) considers these content areas as a whole that is indeed greater than the sum of its parts. The student goals associated with integrated STEM include the following: STEM literacy, 21st century competencies, STEM workforce readiness, interest and engagement, and ability to make connections among STEM disciplines (Honey, Pearson, & Schweingruber, 2014).The National Research Council (2011) recently identified five key educational system elements that cut across content areas to help promote STEM education. These key elements are as follows: "a coherent set of standards and curriculum," "teachers with high capacity to teach in their discipline," &q...
International Journal of Educational Research, 2018
We report findings on teachers' noticing of features in the teacher resources of mathematics curr... more We report findings on teachers' noticing of features in the teacher resources of mathematics curriculum programs. Based on prior analysis, we selected teachers using one of two curriculum types: delivery mechanism or thinking device. The participating teachers and the curriculum programs aimed to align with the Common Core Standards for Mathematics, and thus, they ostensibly held a common aim for instruction. We analyzed 147 lesson planning interviews with 20 middle school mathematics teachers. We found that teachers attended to similar features of teacher resources; however, patterns for interpreting and planning decisions varied based on teachers' orientations and curriculum type. 1. Introduction and purpose The widespread adoption of the Common Core State Standards for Mathematics (CCSSM) (Common Core State Standards Initiative, 2010) in the United States has influenced education at all levels from state-level policy to curriculum design to classroom teaching and learning. The CCSSM was intended to provide more focus and coherence for teachers and students (Schmidt & Houang, 2012; Woolard, 2013). Consistent with this aim, the CCSSM requires a shift from past states' standards to more rigorous content (Porter, McMaken, Hwang, & Yang, 2011), and potentially more ambitious forms of practice with more demanding curriculum programs (National Council of Teachers of Mathematics, 2014; Tran, Reys, Teuscher, Dingman, & Kasmer, 2016). In the United States, the CCSSM were initially adopted by 45 states plus the District of Columbia. As of 2018, among the 45 states who adopted the CCSSM or a modified version (the modifications usually entail additions), 11 states have withdrawn (Academic Benchmarks, 2018). Among these 11 states, in most cases their standards continue to reflect the CCSSM. Thus, despite a rollback in some states, the CCSSM or slightly modified versions continue as the predominant standards in the U.S. Thus, at the time of our study, the CCSSMadopting states shared a relatively common articulation of content and the progression of content across the grades. This set of common goals and policy for curriculum standards provided an opportune time to consider how districts and teachers interpret curriculum materials that share the aim of (ostensibly) alignment with the CCSSM. The purpose of this study was to investigate how middle school mathematics teachers use curriculum resources to plan lessons in the context of CCSSM. More specifically, the extent to which teachers' orientations and the type of curriculum materials interact with what teachers notice in curriculum. U.S. teachers historically have relied heavily on district-adopted mathematics textbooks (Grouws, Smith, & Sztajn, 2004), and yet types of curriculum materials and teachers' use of materials can vary substantially with implications
Journal of Mathematics Teacher Education, 2017
Eight middle school mathematics teachers' perceptions and uses of curriculum materials and the Co... more Eight middle school mathematics teachers' perceptions and uses of curriculum materials and the Common Core State Standards for Mathematics (CCSSM) were investigated. Adapting a noticing framework and models of dialogic instruction and direct instruction, teachers' noticing practices with curriculum materials and the CCSSM when planning, enacting, and reflecting on lessons were examined. Teachers who were committed to implementing the CCSSM and who were using one of two substantively different curriculum programs were purposefully selected. Data sources included multiple forms of interviews and classroom observations. The teaching evidenced three distinct noticing patterns. These patterns indicated that teachers' curriculum materials were associated with how teachers perceived and enacted the CCSSM. Teaching with a curriculum program that was designed as a thinking device prioritized the Standards for Mathematical Practice of CCSSM evidenced noticing that was consistent with dialogic instruction. Teaching with a curriculum program that was designed as a delivery mechanism prioritized the Content Standards of CCSSM and evidenced noticing consistent with direct instruction. Findings indicated that the designated curriculum and contributed to differing interpretations of CCSSM and served as a lens for noticing. However, a dialogic curriculum program was not sufficient to support dialogic approaches in practice. One pattern showed teachers planning dialogic lessons, but the lesson enactments were not consistent with teachers' plans, with evidence that the teachers were not aware that their practices differed from dialogic approaches. Implications for research and practice are discussed.
International Journal of Educational Research, 2018
This contribution to curriculum ergonomics focuses on teachers' perceptions of problem solving an... more This contribution to curriculum ergonomics focuses on teachers' perceptions of problem solving and rigor in the Common Core State Standards for Mathematics, the curricular aims and objectives component of the official curriculum in the U.S. Our analyses involve 89 middle school mathematics teachers (MSMTs) using two different types of district-adopted textbooks: thinking device (TD) and delivery mechanism (DM). We found that MSMTs' perceptions of problem solving and rigor in the Common Core varied by textbook type. Consequently, while this paper examines teachers' perceptions of curricular aims and objectives, it was apparent that another component of the official curriculum, teachers' district-adopted textbooks, played a strong role in influencing these perceptions. The implications of these results are discussed.
Journal for Research in Mathematics Education, Mar 1, 2008
This study extends our understanding of the relationship between the use of Standards based middl... more This study extends our understanding of the relationship between the use of Standards based middle grades curricula and the learning of traditional mathematics topics as measured by two widely used standardized tests, the SAT-9 and the New Standards Mathematics Reference Exam. Sixteen hundred middle grades students in 43 classrooms from five districts with varying demographic profiles participated. These districts had participated in a Local Systemic Change (LSC) project supported by NSF. Students had used either the Connected Mathematics Project (CMP) or the MATH Thematics (STEM) program for three years. Achievement related information was accumulated and used to detect patterns and to estimate their magnitude on the Open Ended, Problem Solving and Procedures subtests of the SAT-9. Hierarchical Linear Modeling (HLM) was used to analyze subtest results following methods described by Raudenbush and Bryk (2002). HLM permitted us to model variation in mathematics proficiency by controlling for other factors such as student prior achievement and classroom ethnic composition. It also allowed us to examine student and classroom patterns of achievement simultaneously. Student and classroom level predictive models were developed and fitted to predict student scores for various subgroups and to compare the predicted values against national Normal Curve Equivalence (NCE) means. A group of "value added" students were tested on three separate occasions over a two-year period of time to permit examination of achievement trends and achievement gaps among the various subpopulations. In the within classrooms HLM analysis, students' socioeconomic status (SES) and prior mathematics knowledge were significant predictors of achievement. A number of different factors such as SES, prior knowledge, concentrations of Asian students, percent special education and school district were significant predictors of between classroom variation. Students' performance on the Open Ended and Problem Solving subtests were above national means, despite the fact that many began below this level. Their progress on the Procedures subtest was less stellar with districts ending below national means. This is perhaps not surprising since these curricula do not focus on paper and pencil calculation to the same extent as more traditional curricula. Results suggest that Standards based students do learn traditional mathematics topics, at least those topics assessed by the two tests used. This study continues to raise the question "What mathematics is most valued and what type of a curriculum is most likely to provide it?
The Mathematics Enthusiast, 2014
As educational systems around the world attempt to reform their mathematics programs to increase ... more As educational systems around the world attempt to reform their mathematics programs to increase students' opportunities to engage in processes central to the practice of mathematics such as proof, it is important to understand how this mathematical act is portrayed in national curriculum documents that drive that change. This study examined the presence of reasoningand-proving (RP) in Ireland's national reform-oriented secondary syllabi for junior cycle (ages 12-15) and senior cycle (ages 15-18) students. The analyses reveal that there were no differences among direct and indirect RP learning outcomes within each syllabus, but statistically significant differences did exist across syllabi in these categories. Students were provided with statistically different opportunities to engage in pattern identification, conjecture formulation, and argument construction in both syllabi. There were significantly fewer opportunities to engage in conjecture formulation for junior cycle students and significantly more opportunities to construct arguments for senior cycle students. There were no instances of proof as falsification across both syllabi, but students were given similar opportunities to experience proof as explanation, verification, and generation of new knowledge. Across both syllabi there were statistically significantly more RP learning outcomes that were divorced from content than those that were connected to content. The results as well as the implications of these results for the design of national curriculum documents are discussed.
Irish Mathematical Society Bulletin, 2013
This study examined student tasks in the area of complex number operations in six Irish secondary... more This study examined student tasks in the area of complex number operations in six Irish secondary mathematics textbooks and a Project Maths teaching and learning plan for reasoningand-proving (RP) opportunities. At the ordinary level, 9.1% of 1274 student tasks were coded as RP. At the higher level, 13.3% of 1373 tasks were coded as RP. The majority of argument opportunities in ordinary level materials were the lowest form of argument-proofwriting exercises. At the higher level, the majority of argument opportunities were within argument-specific or argument-general categories. Less than 2% of the tasks at the ordinary or higher level involved pattern identification or conjecture development. Students were not asked to test conjectures, construct counterexamples, develop proof subcomponents, or formulate RP objects in any of the seven sets of materials. Only one RP task appearing across all seven sets of materials involved the use of technology. The implication of these results as well as how textbook materials could be redesigned using the RP framework are discussed. 2010 Mathematics Subject Classification. 97C99.
This study examined the college mathematics placement exam results of 1,277 students learning fro... more This study examined the college mathematics placement exam results of 1,277 students learning from nine secondary mathematics curricula and two Advanced Placement (AP) mathematics programs in 25 different high schools in the United States. The results suggest that students learning from several traditional mathematics programs and AP Calculus significantly outperformed students learning from the reform-oriented mathematics program, Core-Plus Mathematics Project, on algebra manipulation and calculus readiness questions. Prior mathematics achievement, course completion, and gender also significantly influenced mathematics placement scores. Students cross a number of divides as part of their schooling in different countries around the world. The divide between secondary and postsecondary education, which the majority of students in the United States encounter at some point on their educational journeys, is one of the most difficult for students to cross for several reasons. First, post...
R E Source, Nov 20, 2014
This study investigated how a group of 10 prospective secondary mathematics teachers (PST) read, ... more This study investigated how a group of 10 prospective secondary mathematics teachers (PST) read, evaluated, and adapted a textbook lesson involving the symbolic manipulation capabilities of computer algebra systems (CAS-S). PST read the entire lesson and tended to focus on the organizing question at the beginning of the student lesson and the CAS-S sections of the lesson. PST frequently evaluated the lesson with respect to the teacher and whether lesson elements would promote student understanding. Only one PST evaluated the lesson with respect to the student and how they student might interpret lesson elements. There were five categories of curricular adaptations exhibited by PST: following, additive, mix, reductive, and adaptive. In general, the adaptations made to the lesson by PST were positive. CAS-S based elements were occasionally removed by PST but typically due to non-technology based reasons such as problem redundancy. Several positive adaptations were made by PST to CAS-S based elements such as asking students to make predictions before using CAS-S and understanding the hidden procedures used by the technology.
practice. Thirty percent of the teachers planned lessons from unit/chapter materials to become fa... more practice. Thirty percent of the teachers planned lessons from unit/chapter materials to become familiar with the mathematical content of the lesson, the presentation of the mathematics in the materials, and the context in which the lesson was couched. Thirty-two percent of the teachers went beyond becoming familiar with the content, presentation, and context to make decisions for student learning, for example, potential student questions, possible misunderstandings, anticipation of various solution strategies, accommodation of various ability levels, or conceptual development within a unit. One MiC teacher planned lessons that emphasized higher order thinking, depth of knowledge, and/or understanding. For example, the teacher planned questions that engaged students in interpreting a solution in terms of the problem context, exploring connections among equivalent representations of numbers, or summarizing the mathematics in a series of lessons. Planning forms of instruction that promote classroom discourse for the purpose of the lesson varied among all teachers in Districts 1-4. Forty-two percent of the teachers anticipated using whole-class discussion and small-group or pair work. Although these teachers planned for such lesson formats, the focus was primarily on completing tasks rather than on facilitating or encouraging substantive conversation of mathematics concepts. Twenty-eight percent planned for students' participation and collaboration for during instruction, but these still were not the primary focus of the lesson plan. Twenty-five percent of the teachers rarely planned students' discourse in the classroom as part of the lesson. Instead, instruction focused on factual information or presentation of algorithms and procedures. One MiC teacher planned forms of instruction that promoted substantive conversation. The teacher planned classroom activities that encouraged students to participate in discussion, evaluate other's ideas, interpret their own ideas in terms of comments from others, and build substantive conversation. Similarly, planned student activities that promoted discussion, problem solving, and reflection on the content of the lesson varied among the teachers. Forty-seven percent of the teachers included investigation of problems and discussion of answers and solution strategies (whether during small-group work or whole-class discussions) in lesson plans. Twenty-five percent of the teachers included investigation of problems and discussion of answers and solution strategies as important elements in lesson plans, although questions or activities that encouraged students to reflect on or summarize lessons were rarely included. Twenty-one percent of the teachers rarely planned investigation of problems and discussion of mathematical ideas for the lessons. Emphasis, instead, was placed on practicing routine calculations, and little discussion among students was anticipated. For two MiC teachers, investigation of problems and discussion of answers and solution strategies were dominant in lesson plans. Mathematical Interaction during Instruction Six subcategories characterized the mathematical interaction during instruction: lesson presentation and development; nature of mathematical inquiry during instruction; interactive decisions during instruction; nature of students' explanations; elicitation of multiple strategies; and lesson reflection, summary, or closure. With respect to lesson presentation and development, the results for the 35 teachers in Districts 1 and 2 revealed differences by grade level, type of curriculum taught, and by district. By grade level, more fifth-and seventh-grade teachers taught mathematics for conceptual understanding than sixth-grade teachers (7 of 13 fifth-grade teachers compared to 2 of 12 sixth-grade and 4 of 10 seventh-grade teachers). Only one teacher, a fifth-grade teacher, emphasized conceptual understanding with active participation by students with teacher support. Lesson presentations set the stage for students to explore the mathematical content of the lesson on their own. Student solutions and generalizations were later presented and compared during discussions orchestrated by the teacher. Nine teachers (one sixth grade) emphasized conceptual understanding with active participation by students and teacher. Lesson presentations featured a conceptual basis for the mathematical content, and the mathematical work was shared by students and teacher. The greatest number of teachers, however, demonstrated procedures and 11 strategies for students to use. Five of the 13 fifth-grade teachers, 7 of 12 sixth-grade teachers, and 4 of 10 seventh-grade teachers presented and emphasized particular procedures or strategies. An additional pattern of variation was found when the levels of lesson presentation were reviewed by curriculum taught. Twelve of the 24 teachers using MiC either attempted to teach for or clearly emphasized conceptual understanding in contrast to only 1 of the 11 teachers using conventional curricula. On the other hand, 8 of the 11 teachers using conventional curricula presented particular procedures or strategies in class in comparison to 8 of the 24 MiC teachers. When these results were reviewed by district, however, differences became apparent for teachers using MiC. In District 2, 7 of the 12 MiC teachers either attempted to teach for or clearly emphasized conceptual understanding in comparison to 5 of the 12 MiC teachers in District 1. Also, both teachers using MiC and teachers using conventional curricula were less likely to teach particular procedures in District 2 than in District 1. Teachers also varied in the nature of inquiry during instruction. Differences were noted by grade level and type of curriculum taught. Nine of 13 fifth-grade teachers, in comparison to 5 of 12 sixth-grade and 3 of 10 seventh-grade teachers, emphasized conceptual understanding, relationships among mathematical ideas, or linking procedural and conceptual knowledge. Also, more sixth-grade teachers (3 of 12 in comparison to 2 of 13 fifth-grade and 2 of 10 seventh-grade teachers) provided limited attention to conceptual understanding. The nature of inquiry for 4 of 12 sixthgrade and 5 of 10 seventh-grade teachers, in comparison to 2 of 13 fifth-grade teachers, was limited to lower order thinking. Lessons did not promote conceptual understanding, connections among mathematical ideas, and connections between mathematics and students' lives. Teachers' interactive decisions also varied among the 35 teachers in Districts 1 and 2. Differences were revealed by grade level, by curriculum taught, and by district. By grade level, more fifth-grade teachers made interactive decisions that were aligned with teaching mathematics for understanding than did sixth-and seventh-grade teachers (5 of 13 compared to no sixth-grade teachers and 2 of 10 seventh-grade teachers). In contrast, more sixth-grade teachers made interactive decisions that were least aligned with teaching for understanding (7 of 12 compared to 3 of 13 fifth-grade teachers and 4 of 10 seventh-grade teachers). An additional pattern of variation was found when reviewed by curriculum taught. Fourteen of the 24 MiC teachers made interactive decisions that supported teaching mathematics for understanding in contrast to one of the teachers using conventional curricula. On the other hand, 8 of the 11 teachers using conventional curricula made interactive decisions least aligned with teaching for understanding compared to 6 of the 24 MiC teachers. Differences by district were also apparent for teachers using MiC. In District 2, 8 of the 12 MiC teachers made interactive decisions that were aligned with teaching mathematics for understanding in comparison to 5 of the 12 MiC teachers in District 1. Students' explanations in most classes were focused on procedures or students' responses were limited to answers only. By curriculum, significant differences in students' explanations were evident among ratings in each district in favor of teachers using MiC. Nonetheless, the results suggest that encouragement of students' explanations in classes in which MiC and conventional curricula are used needs further attention. Multiple strategies were generally not elicited from students during instruction. By curriculum, multiple strategies were elicited more frequently during MiC lessons than in lessons using conventional curricula. Few opportunities, if any, were provided for reflection on or summary of lesson content. Nine teachers provided some opportunities each week for students to reflect on the mathematics or summarize what they had learned in a lesson or in a series of lessons. Only three teachers frequently provided such opportunities for students. 12 Classroom Assessment Practice Three subcategories of Instruction characterized classroom assessment practice: evidence sought during classroom assessment; purpose and coherence of feedback given in response to classroom assessment; and content of feedback provided in response to classroom assessment. In Districts 1 and 2, 57% of the 35 study teachers (11 of the 24 MiC teachers and 9 of the 11 teachers using conventional curricula) sought evidence of procedural competence based on student homework and classwork during their assessment practice. Five teachers (all MiC) sought student explanations in addition to procedural competence and answers. However, these explanations were often void of mathematical substance and were used to generate some form of communication rather than assess student understanding. Three teachers (2 MiC) were somewhat effective at eliciting student responses and orchestrating substantive whole-class discussions. However, the overriding focus of their classroom practice was to use correct answers and procedures as evidence of student learning. Six teachers (5 MiC) viewed student explanations as evidence of student learning. The teachers sought both process...
Digital Experiences in Mathematics Education
Research suggests that tasks that use technology as a reorganizer (technology is used to produce ... more Research suggests that tasks that use technology as a reorganizer (technology is used to produce dynamic representations) are linked with the development of students' conceptual knowledge, yet many secondary mathematics textbooks in the USA predominantly include tasks that use technology as an amplifier (technology is used to produce static images). Thus, if teachers wish to incorporate tasks that use technology as a reorganizer, they must locate these resources elsewhere or construct them themselves. This study took place in a technology, pedagogy, content course where each prospective teacher (PT) engaged in at least one component of an ideation, rehearsal/ refinement, enactment, and reflection intervention, where they were asked to adapt traditional textbook lessons to promote students' rich conceptual understandings of function transformations via technology as reorganizer tasks. A total of 15 PTs agreed to participate, 8 seeking a grade K-8 certification and 7 seeking a grade 6-12 certification. On the initial lesson plan involving linear function transformations, the majority of PTs (13 out of 15) used technology as an amplifier, but on the final lesson plan involving absolute value function transformations, 13 PTs used technology as a reorganizer. There were also increases in the incidence of lesson elements that promoted moderate or rich forms of conceptual knowledge between the initial and final lesson plans. We discuss the implications of these results and introduce readers to dynamic conceptual components as manipulable bridges between different mathematical representations that hold the potential to develop students' richer forms of conceptual knowledge.
We describe two metaphors that we hope can be used to better understand the contemporary mathemat... more We describe two metaphors that we hope can be used to better understand the contemporary mathematics curriculum context in U.S. middle schools, to see how this new context is both similar to and different from prior curriculum contexts. We explain the role and positioning of middle school mathematics curriculum materials over the last century or more and build from learning theory to develop the metaphors. The first metaphor, curriculum as delivery mechanism, builds from technical rational or scientific discourses and encompasses perspectives that are so pervasive they are often unstated and unquestioned. The second metaphor, curriculum as epistemic device, posits that role of curriculum is to provoke interactions that generate understanding. In this metaphor, the role of tasks in curriculum materials is to provoke and progressively refine student thinking, individually and collectively.
International Journal of Educational Research, 2018
We conceptualize curriculum ergonomics as a field that studies the interactions between users and... more We conceptualize curriculum ergonomics as a field that studies the interactions between users and curriculum materials. We identify five themes that a curriculum ergonomics lens brings into sharper focus: (1) teachers' relationships with and capacity to use curriculum resources; (2) alignment between design intentions and patterns of curriculum use; (3) ways in which curriculum resources influence instruction; (4) ways in which curriculum features are purposefully designed to achieve an educative purpose; and (5) the dissolution of boundaries between design and use. We first summarize the literature in curriculum ergonomics and then show how key themes from that literature inform the discussion of curriculum ergonomics.
We analyzed 52 middle school mathematics lessons from multiple states and curriculum contexts to ... more We analyzed 52 middle school mathematics lessons from multiple states and curriculum contexts to understand how teachers were enacting the CCSSM. The teachers stated that all of the lessons were CCSSM-aligned. We categorized curriculum materials according to two approaches, with one approach associated with curriculum programs funded by NSF and the other representing curriculum programs commercially produced, typically from a large publisher. We analyzed the nature of mathematical activity and level of interactions in the lessons. We found significant differences across curriculum approaches in the mathematical activity categories related to cognitive demand and in the level of interaction. The implications are that curriculum programs strongly mediated the enactment of the CCSSM.
ZDM – Mathematics Education, 2021
Background: The rates of overweight and obese adults in the United Arab Emirates (UAE) have incre... more Background: The rates of overweight and obese adults in the United Arab Emirates (UAE) have increased dramatically in recent decades. Several anthropometric measurements are used to assess body weight status. Some anthropometric measurements might not be convenient to use in certain communities and settings. The objective of this study was to assess the agreement of four anthropometric measurements and indices of weight status and to investigate their associations with cardiometabolic risks. Methods: The study design was a cross-section population-based study. Adults living in the Northern Emirates were surveyed. Fasting blood samples, blood pressure readings and anthropometric measurements were also collected. Results: A total of 3531 subjects were included in this study. The prevalence of obesity/overweight was 66.4% based on body mass index (BMI), 61.7% based on waist circumference (WC), 64.6% based on waist-hip ratio (WHR) and 71% based on neck circumference (NC). There were moderate agreements between BMI and WC and between WC and WHR, with kappa (k) ranging from 0.41 to 0.60. NC showed poor agreement with BMI, WC and WHR, with k ranging from 0 to 0.2. Overweight and obesity based on BMI, WC and WHR were significantly associated with cardiometabolic risks. Conclusion: Overall, there was a moderate to a poor agreement between BMI, WC, WHR and NC. Particularly, NC showed poor agreement with BMI, WC and WHR. BMI and WC showed better performance for identifying cardiometabolic risks than WHR and NC.
Mathematical Thinking and Learning, 2020
This study investigates the effects of a technology methods course containing a unique collaborat... more This study investigates the effects of a technology methods course containing a unique collaborative design experience on prospective elementary and secondary mathematics teachers’ technological beliefs, computer algebra system (CAS) beliefs, and technological pedagogical content knowledge (TPACK). Overall gain scores on all three instruments were statistically significant. Moreover, gender and level (elementary vs. secondary) were statistically significant predictors of TPACK gain scores. However, the influence of level on TPACK gain score was different for female prospective teachers (PTs) than male PTs. Even in the case of low gain scores PTs displayed beliefs that were aligned with productive uses of technology in the classroom. PTs showed greater gains on knowledge subdomains associated with technological knowledge than on technology free subdomains (e.g., pedagogical content knowledge).
International Journal of Research in Education and Science
This article may be used for research, teaching, and private study purposes. Any substantial or s... more This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden.