Number Sense

Learning Labs: Using Videos, Exemplary STEM Instruction and Online Teacher Collaboration to Enhance K-2 Mathematics and Science Practice and Classroom Discourse

This project will develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the CCSS and NGSS. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches.

Lead Organization(s): 
Award Number: 
1417757
Funding Period: 
Wed, 04/15/2015 to Sat, 03/31/2018
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. The investigators of this study propose to develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the Common Core State Standards in Mathematics (CCSS) and the Next Generation Science Standards (NGSS). They will develop two modules in each subject area and an introductory module that prefaces and integrates the science and mathematics materials. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches. New instructional materials aligned with the standards are needed to assist teachers in meeting the challenging instructional practices recommended. To date, scant few resources of this type exist and, given many school districts have limited resources, more cost-effective forms of development such as this must be found. A particular strength of this project is that teachers will be able to engage in the courses online, on an ongoing basis and integrate what they have learned into their daily teaching practice.

The investigators propose a program of design research to develop and improve the modules. The central hypothesis is a test of the Teaching Channel model--that the modules and professional learning communities result in significant changes in the quality of instructional practice. Text analytics will be performed on the online discussion to detect changes in group discourse over time. Changes in instructional quality and vision will be measured by observing the videos posted by teachers. Pre-post tests of student work will be performed. The findings of the research will be disseminated through conference presentations, publications, and the Teaching Channel website.

CAREER: Advancing Secondary Mathematics Teachers' Quantitative Reasoning

Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge.

Award Number: 
1350342
Funding Period: 
Tue, 07/15/2014 to Tue, 06/30/2020
Full Description: 

Science, Technology, Engineering and Mathematics [STEM] and STEM education researchers and policy documents have directed mathematics educators at all levels to increase emphasis on quantitative reasoning so that students are prepared for continued studies in mathematics and other STEM fields. Often, teachers are not sufficiently prepared to support their students' quantitative reasoning. The products generated by this project fill a need for concrete materials at the pre-service level that embody research-based knowledge in the area of quantitative reasoning. The accessible collection of research and educational products provides a model program for changing prospective mathematics teachers' quantitative reasoning that is adoptable at other institutions across the nation. Additionally, the support of early CAREER scholars in mathematics education will add to the capacity of the country to address issues in mathematics education in the future.

Advancing Reasoning addresses the lack of materials for teacher education by investigating pre-service secondary mathematics teachers' quantitative reasoning in the context of secondary mathematics concepts including function and algebra. The project extends prior research in quantitative reasoning to develop differentiated instructional experiences and curriculum that support prospective teachers' quantitative reasoning and produce shifts in their knowledge. Three interrelated research questions guide the project: (i) What aspects of quantitative reasoning provide support for prospective teachers' understanding of major secondary mathematics concepts such as function and algebra? (ii) How can instruction support prospective teachers' quantitative reasoning in the context of the teaching and learning of major secondary mathematics concepts such as function and algebra? (iii) How do the understandings prospective teachers hold upon entering a pre-service program support or inhibit their quantitative reasoning? Advancing Reasoning addresses these questions by enacting an iterative, multi-phase study with 200 prospective teachers enrolled in a secondary mathematics education content course over 5 years. The main phase of the study implements a series of classroom design experiments to produce knowledge on central aspects of prospective teachers' quantitative reasoning and the instructional experiences that support such reasoning. By drawing this knowledge from a classroom setting, Advancing Reasoning contributes research-based and practice-driven deliverables that improve the teaching and learning of mathematics.

CAREER: Leveraging Contrasting Cases to Investigate Integer Understanding

Most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers. 

Lead Organization(s): 
Award Number: 
1350281
Funding Period: 
Thu, 05/15/2014 to Sat, 04/30/2022
Full Description: 

Currently, most students learn about negative numbers long after they have learned about positive numbers, and they have little time or opportunity to build on their prior understanding by contrasting the two concepts. Therefore, they struggle to make sense of negative integer concepts, which appear to conflict with their current understanding. The purpose of this CAREER project is to identify language factors and instructional sequences that contribute to improving elementary students' understanding of addition and subtraction problems involving negative integers. A second objective is to identify how elementary teachers interpret their students' integer understanding and use research findings to support their teaching of these concepts. This project is expected to contribute to theories regarding the development of integer understanding as well as what makes a useful contrasting case when learning new, related concepts. Moreover, the results of this project can contribute to our understanding of how to build on students? prior number knowledge rather than contradict it.

The principal investigator will conduct a series of four experimental studies involving a preparation for learning component with students randomly assigned to treatment or control groups. Study 1 will involve second and fourth graders and will test the language factors that support students' understanding of integers. Studies 2-4 will involve second and fifth graders and will test the optimal order in which integer addition and subtraction problems are presented in contrast with each other versus sequentially without contrasts. Using items that measure students? understanding of integers and integer operations, the PI will compare students' gains from pre-tests to post-tests between groups. Further, the investigator will qualitatively code students? solution strategies based on follow-up interviews and written work for additional information on the differences between groups. Following the experimental studies, the PI will work with elementary teachers over three lesson study cycles, during which teachers will implement instruction based on the prior studies? results. The PI will compare the performance of students who participate in the lesson study unit versus control classrooms to measure impact of the unit.

Videos of the lesson study unit, as well as the negative integer lesson plans will be made available for other teachers and teacher educators to use. Further, the investigator will incorporate the research results into an undergraduate mathematics methods course. To ensure that the results of this research reach a wider audience, the investigator will create an integer game and storybook, illustrating key concepts identified through the research, that parents can explore together with their children during family math nights and at home. On a broader scale, this project has the potential to illuminate ways to develop more coherence in the sequencing of mathematics topics to more effectively build on students? current understanding.

Supports for Science and Mathematics Learning in Pre-Kindergarten Dual Language Learners: Designing and Expanding a Professional Development System

SciMath-DLL is an innovative preschool professional development (PD) model that integrates supports for dual language learners (DLLs) with high quality science and mathematics instructional offerings. It engages teachers with workshops, classroom-based coaching, and professional learning communities. Based on initial evidence of promise, the SciMath-DLL project will expand PD offerings to include web-based materials.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1417040
Funding Period: 
Tue, 07/01/2014 to Sat, 06/30/2018
Full Description: 

The 4-year project, Supports for Science and Mathematics Learning in Pre-Kindergarten Dual Language Learners: Designing and Expanding a Professional Development System (SciMath-DLL), will address a number of educational challenges. Global society requires citizens and a workforce that are literate in science, technology, engineering, and mathematics (STEM), but many U.S. students remain ill prepared in these areas. At the same time, the children who fill U.S. classrooms increasingly speak a non-English home language, with the highest concentration in the early grades. Many young children are also at risk for lack of school readiness in language, literacy, mathematics, and science due to family background factors. Educational efforts to offset early risk factors can be successful, with clear links between high quality early learning experiences and later academic outcomes. SciMath-DLL will help teachers provide effective mathematics and science learning experiences for their students. Early educational support is critical to assure that all students, regardless of socioeconomic or linguistic background, learn the STEM content required to become science and mathematics literate. Converging lines of research suggest that participation in sustained mathematics and science learning activities could enhance the school readiness of preschool dual language learners. Positive effects of combining science inquiry with supports for English-language learning have been identified for older students. For preschoolers, sustained science and math learning opportunities enhance language and pre-literacy skills for children learning one language. Mathematics skills and science knowledge also predict later mathematics, science, and reading achievement. What has not been studied is the extent to which rich science and mathematics experiences in preschool lead to better mathematics and science readiness and improved language skills for preschool DLLs. Because the preschool teaching force is not prepared to support STEM learning or to provide effective supports for DLLs, professional development to improve knowledge and practice in these areas is required before children's learning outcomes can be improved.

SciMath-DLL is an innovative preschool professional development (PD) model that integrates supports for DLLs with high quality science and mathematics instructional offerings. It engages teachers with workshops, classroom-based coaching, and professional learning communities. Development and research activities incorporate cycles of design-expert review-enactment- analysis-redesign; collaboration between researcher-educator teams at all project stages; use of multiple kinds of data and data sources to establish claims; and more traditional, experimental methodologies. Based on initial evidence of promise, the SciMath-DLL project will expand PD offerings to include web-based materials, making the PD more flexible for use in a range of educational settings and training circumstances. An efficacy study will be completed to examine the potential of the SciMath-DLL resources, model, and tools to generate positive effects on teacher attitudes, knowledge, and practice for early mathematics and science and on children's readiness in these domains in settings that serve children learning two languages. By creating a suite of tools that can be used under differing educational circumstances to improve professional knowledge, skill, and practice around STEM, the project increases the number of teachers who are prepared to support children as STEM learners and, thus, the number of children who can be supported as STEM learners.

Re-Imagining Video-based Online Learning

Despite the tremendous growth in the availability of mathematics videos online, little research has investigated student learning from them. The goal of this exploratory project is to create, investigate, and provide evidence of promise for a model of online videos that embodies a more expansive vision of both the nature of the content and the pedagogical approach than is currently represented in YouTube-style lessons.

Award Number: 
1416789
Funding Period: 
Mon, 09/01/2014 to Fri, 08/31/2018
Full Description: 

The goal of this exploratory project is to create, investigate, and provide evidence of promise for a model of online videos that embodies a more expansive vision of both the nature of the content and the pedagogical approach than is currently represented in YouTube-style lessons. This goal is pursued through the development and research of videos for two mathematics units--one focused on proportional reasoning at the middle grades level and the other focused on quadratic functions at the high school level, using an approach that could be applied to any STEM content area. The media attention on the Khan Academy and the wide array of massive open online courses has highlighted the internet phenomenon of widespread accessibility to mathematics lessons, which offer many benefits, such as student control of the pace of learning and earlier access to advanced topics than is often possible in public schools. Yet, despite the huge range of topics presented in online videos, there is surprising uniformity in the procedural emphasis of the content and in the expository mode of presentation. Moving beyond the types of videos now used, primarily recorded lectures that replicate traditional classroom experience, this project advances our understanding about how students learn from video and from watching others learn - vicarious learning - as opposed to watching an expert. This project addresses the need for an alternative approach. Rather than relying on an expository style, the videos produced for this project focus on pairs of students, highlighting their dialogue, explanations and alternative conceptions. This alternative has the potential to contribute to learning sciences and to develop a usable tool.

Despite the tremendous growth in the availability of mathematics videos online, little research has investigated student learning from them. This project develops dialogue-intensive videos in which children justify and explain their reasoning, elucidate their own comprehension of mathematical situations, and argue for and against various ideas and strategies. According to Wegerif (2007), such vicarious participation in a dialogic community may help learners take the perspective of another in a discussion, thus "expanding the spaces of learning" through digital technology. Consequently, a major contribution of this proposed work will be a set of four vicarious learning studies. Two qualitative studies investigate the particular meanings and ways of reasoning that learners appropriate from observing the dialogue of the students in the videos, as well as the learning trajectories of vicarious learners for each unit. Two quantitative studies isolate and test the effectiveness of the dialogic and the conceptual components of the model by comparing learning outcome gains for (a) conceptual dialogic versus conceptual expository conditions, and (b) dialogic conceptual versus dialogic procedural conditions. Another mark of the originality of the proposed work is the set of vicarious learning studies that contributes to the emerging literature across several dimensions, by (a) using secondary students rather than undergraduates; (b) exploring longer periods of learning, which is more conducive to deeper understanding; and (c) examining the nature of reasoning that is possible, not just the effectiveness of the approach.

Teaching STEM with Robotics: Design, Development, and Testing of a Research-based Professional Development Program for Teachers

Using design-based research, with teachers as design partners, the project will create and refine project-based, hands-on robotics curricula such that science and math content inherent in robotics and related engineering design practices are learned. To provide teachers with effective models to capitalize on robotics for elucidating science and math concepts, a design-based Professional Development program will be built using principles of technological, pedagogical, and content knowledge (TPACK).

Lead Organization(s): 
Award Number: 
1417769
Funding Period: 
Mon, 09/01/2014 to Fri, 08/31/2018
Full Description: 

Offering meaningful and motivating engineering contexts, such as robotics, within science and math courses constitutes a compelling strategy to address the Next Generation Science Standards and the Common Core State Standards for Math while enhancing science and math learning for all students. Using design-based research, with teachers as design partners, the project will create and refine project-based, hands-on curricula such that science and math content inherent in robotics and related engineering design practices are learned. To provide teachers with effective models to capitalize on robotics for elucidating science and math concepts, a design-based Professional Development program will be built using principles of technological, pedagogical, and content knowledge (TPACK). To ensure that teachers are well prepared, research-based practices and features of effective Professional Development will be adopted. Experts in robotics, engineering, education, curriculum design, and assessment--with experience in K-12 education, training, and outreach--have formed an interdisciplinary team to make robotics central to and sustainable in middle school science and math classrooms.

The research questions addressed in this project are qualitative in nature as appropriate for design research questions. The methodologies include teacher needs assessment, teachers' perceptions of robotics, pre and post testing, classroom observations, and surveys. Examples of the research questions are:

What characteristics of robotics promote effective learning of middle school science and math?

What elements of Professional Development engender teachers' TPACK of robotics and link it with classroom science and math?

What are student prerequisites to effectively use robotics in science and math learning?

What are the gains in students' STEM engagement, interest, persistence, and career awareness?

The robotics curriculum will include physical science used in robot performance expectations and motion stability. Additionally the curriculum will include the engineering design process consisting of problem definition, solution development, and design improvement. Robotics provides opportunities to support science and engineering practices of the Next Generation Science Standards such as developing and using models, planning and conducting investigations, designing solutions, and analyzing and interpreting data. The project will be aimed at middle school students and will provide substantial teacher professional development to implement the new curriculum modules. The partner schools have student bodies drawn from a diverse student population in New York City.

Developing Rich Media-Based Materials for Practice-Based Teacher Education

This research and development project is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom.

Award Number: 
1316241
Funding Period: 
Thu, 08/15/2013 to Tue, 07/31/2018
Full Description: 

The 4-year research and development project, Developing Rich Media-based Materials for Practice-based Teacher Education, is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom. Furthermore, teacher educators and teachers can react to such animations or image sequences by making their own depictions of alternative moves by students or teachers in classroom interaction. And all of that can take place in an on-line, cloud-based environment that also supports discussion fora, questionnaires, and the kinds of capabilities associated with learning management systems. Such technologies offer important affordances to teacher educators seeking to provide candidates with course-based experiences that emphasize the development of practice-based skills. The focus of the project is on mathematics teacher education. This joint project of the University of Maryland Center for Mathematics Education and the University of Michigan will produce 6 to 8 field-tested modules for use in different courses that are a part of mathematics teacher preparation programs. The following two-pronged research question will be resolved: What are the affordances and constraints of the modules and the environment as supports for: (1) practice based teacher education and (2) a shift toward blended teacher education?

The project involves the following activities: (1) a teacher education materials development component; (2) a related evaluation component; and (3) two research components. The development phase seeks to develop both the LessonSketch.org platform and six to eight mathematics teacher education modules for use in preservice teacher education programs from around the country. The modules will be written with practice-based teacher education goals in mind and will use the capacities of the LessonSketch.org platform as a vehicle for using rich-media artifacts of teaching with preservice teacher candidates. LessonSketch Teacher Education Research and Development Fellows will be chosen through a competitive application process. They will develop their respective modules along with teams of colleagues that will be recruited to form their inquiry group and pilot the module activities. The evaluation activity will focus on the materials development aspect of the project. Data will be collected by the LessonSketch platform, which includes interviews with Fellows and their teams, perspectives of module writers, descriptive statistics of module use, and feedback from both teacher educator and preservice teacher end-users about the quality of their experiences. The first research activity of the project is design research on the kinds of technological infrastructure that are useful for practice-based teacher education. The PIs will identify tools that teacher educators need and want beyond the current capabilities for web-based support for use of rich media and will produce prototype tools inside the LessonSketch environment to meet these needs. The second research activity of the project will supplement the evaluation activity by examining the implementation of two of the modules in detail. This aspect of the research will examine the goals of the intended curriculum, the proposed modes of media use, the fidelity of the implemented curriculum, and learnings produced by preservice teachers. This research activity will help the field understand the degree to which practice-based teacher education that is mediated by an online access to rich media would be a kind of practice that could be easily incorporated into existing teacher education structures.

The project will produce 6 to 8 LessonSketch modules for use in teacher education classes. Each module will be implemented in at least eight teacher education classes across the country, which means that between 720 and 960 preservice teacher candidates will study the materials. The project aims to shift the field toward practice-based teacher education by supporting university programs to implement classroom-driven activities that will produce mathematics teachers with strong capabilities to teach mathematics effectively and meaningfully.

CAREER: Reciprocal Noticing: Latino/a Students and Teachers Constructing Common Resources in Mathematics

The goal of this project is to extend the theoretical and methodological construct of noticing to develop the concept of reciprocal noticing, a process by which teacher and student noticing are shared. The researcher argues that through reciprocal noticing the classroom can become the space for more equitable mathematics learning, particularly for language learners.

Lead Organization(s): 
Award Number: 
1253822
Funding Period: 
Wed, 05/15/2013 to Mon, 04/30/2018
Full Description: 

The goal of this project is to extend the theoretical and methodological construct of noticing to develop the concept of reciprocal noticing, a process by which teacher and student noticing are shared. The researcher argues that through reciprocal noticing the classroom can become the space for more equitable mathematics learning, particularly for language learners. Thus, the focus of the project is on developing the concept of reciprocal noticing as a way to support better interactions between teachers and Latino/a students in elementary mathematics classrooms.

The project uses a transformative teaching experiment methodology and is guided by the initial conjectures that to make mathematics classrooms intellectually attractive places, Latino/a students and teachers need to learn to develop common resources for teaching and learning mathematics, and that reciprocal noticing as a process supports teachers and students in developing these common resources for teaching and learning mathematics. The project design centers around two research questions:How do teachers and Latino/a students tune to each other's mathematical ideas and explicitly indicate to one another how their ideas are important for discourse that promotes mathematical reasoning in classrooms characterized by reciprocal noticing? What patterns emerge across four classrooms when teachers and Latino/a students engage in reciprocal noticing?

The concept of reciprocal noticing can significantly enhance emerging research in mathematics education about the importance of teacher noticing. Further, this revised concept of noticing can transform mathematics classroom to better support English Language Learners.

The PI will incorporate project findings and videos into methods courses for preservice elementary teachers.

CAREER: Fraction Activities and Assessments for Conceptual Teaching (FAACT) for Students with Learning Disabilities

This project is documenting how students with learning disabilities (LD) access and advance their conceptual understanding of fractions.  Rather than focusing on the knowledge students do not have, this work is focused on uncovering students' informal knowledge that can bridge to fractions and how instruction can be used to promote conceptual change. 

 

Award Number: 
1708327
Funding Period: 
Tue, 07/01/2014 to Fri, 12/31/2021
Project Evaluator: 
Dr. Mary Little
Full Description: 

Dr. Hunt, a former middle school and elementary school mathematics in inclusive settings in a state-demonstration STEM school, works with students deemed to be at risk for mathematics difficulties or labeled as having disabilities. Hunt contends that research and pedagogical practice for children with disabilities should begin from a respect for children's ways of knowing and learning. Rather than focusing on whether students can or cannot develop conceptual understanding, research should attempt to uncover the complex understanding students DO have. She argues that teaching based in learning theory that positions children's learning as adaptation advances reasoning, sense-making, and co-construction of meaning.

The overall goal of this CAREER award project is to re-direct and re-conceptualized research and practice across mathematics education and special education to support students to build rich concepts in mathematics through student-based instructional interventions. FAACT accomplishes this goal by - toward (a) uncovering the understandings students with LD do have of fraction concepts, (b) documenting how cognitive and/or early mathematics skills might affect the processes and products of learning, and (c) understanding how growth of conceptual knowledge occurs in these students and how to nurture this growth through the learning process.

Through this award, Dr. Hunt is re-conceptualizing intensive intervention as children's knowing and learning in "Small Environments". This approach suggests a redirect of research and instructional practice in mathematics for an underserved population of students. The project has the potential to offer a transformative approach to mathematics instruction for students with LD, bringing together expertise on learning disabilities and mathematics education to address an area in which there is very little research. 

The main outcomes of the project include (1) a theory of knowing, learning, and teaching connected to students with LDs in the small environment of supplemental and intensive intervention, (2) a six stage research-based trajectory specific to the conceptual understandings of fractions evidenced by students with LD, and (3) an adaptive intervention program consisting of (a) a clinical interview educators can use to understand students’ initial fraction thinking, (b) an instructional trajectory [lesson planning framework, four task sets, and corresponding teacher moves to support student learning], and (c) an instructional decision making guide based on the instructional trajectory to aid teachers in designing student-centered instruction both in small groups and individualized formats.

This project was previously funded under award #1253254 and 1446250.

 


Project Videos

2019 STEM for All Video Showcase

Title: Fractional Reasoning: Students with Learning Disabilities

Presenter(s): Jessica Hunt, Andy Khounmeuang, Kristi Martin, Blain Patterson, & Juanita Silva


Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Stevens)

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

Partner Organization(s): 
Award Number: 
1222496
Funding Period: 
Wed, 08/15/2012 to Sun, 07/31/2016
Full Description: 

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:

1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?

2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?

To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.

The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.

This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.


Project Videos

2019 STEM for All Video Showcase

Title: Studying Teachers' Mathematical Habits of Mind

Presenter(s): Sarah Sword, Eden Badertscher, Al Cuoco, Miriam Gates, Ryota Matsuura, & Glenn Stevens

2017 STEM for All Video Showcase
Title: Assessing Secondary Teachers' Algebraic Habits of Mind

Presenter(s): Sarah Sword, Courtney Arthur, Al Cuoco, Miriam Gates, Ryota Matsuura, & Glenn Stevens

2016 STEM for All Video Showcase

Title: Assessing Secondary Teachers' Algebraic Habits of Mind

Presenter(s): Ryota Matsuura, Al Cuoco, Glenn Stevens, & Sarah Sword


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