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Select a category then a presentation title for more information:
MOST Framework:
MOST Framework (Earlier Instantiation):
Nature of Student Thinking/Attributes of MOSTs:
Perceptions of Use of Student Thinking:
Perceptions of Use of Student Thinking/Goals, Orientations and Resources:
Building/Teacher Responses to Student Mathematical Thinking:
Barriers to Building on Student Mathematical Thinking   Abstract:
In our work with teachers, we have identified barriers that inhibit them from productively implementing the teaching practice of building on student thinking. We share examples of barriers and ways we have supported teachers to make progress toward overcoming them.
Citation:
Stockero, S. L., Van Zoest, L. R., Leatham, K. R., & Peterson, B. E. (2017, February). Barriers to building on student thinking. Presentation at the 21st Annual Meeting of the Association of Mathematics Teachers Educators, Orlando, FL.
Beyond the Move: A Coding Scheme for Teacher Responses to Instances of Student Mathematical Thinking Abstract:
In our work with teachers, we have identified barriers that inhibit them from productively implementing the teaching practice of building on student thinking. We share examples of barriers and ways we have supported teachers to make progress toward overcoming them.
Citation:
Rougée, A. O. T., Peterson, B. E., Van Zoest, L. R., Freeburn, B., Stockero, S. L., Leatham, K. R., & Gunn, R. M. (2017, February). Beyond the move: A coding scheme for teacher responses to instances of student mathematical thinking. Poster presented at the 21st Annual Meeting of the Association of Mathematics Teachers Educators, Orlando, FL.
Imprecision in Classroom Mathematics Discourse Abstract:
We theorize about ambiguity in mathematical communication and define a certain subset of ambiguous language usage as imprecise. For us, imprecision in classroom mathematics discourse hinders in-the-moment communication because the instance of imprecision is likely to create inconsistent interpretations of the same statement among individuals. We argue for the importance of attending to such imprecision as a critical aspect of attending to precision. We illustrate various types of imprecision that occur in mathematics classrooms and the ramifications of not addressing this imprecision. Based on our conceptualization of these types and ramifications, we discuss implications for research on classroom mathematics discourse.
Citation:
Leatham, K. R., Peterson, B. E., Merrill, L., Van Zoest, L. R., & Stockero, S. L. (2016, November). Imprecision in classroom mathematics discourse. Presentation at the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ.
Conceptualizing the Teaching Practice of Building on Student Mathematical Thinking Abstract:
An important aspect of effective teaching is taking advantage of in-the-moment expressions of student thinking that, by becoming the object of class discussion, can help students better understand important mathematical ideas. We call these high-potential instances of student thinking MOSTs and the productive use of them building. The purpose of this paper is to conceptualize the teaching practice of building on MOSTs as a first step toward developing a common language for and an understanding of productive use of high-potential instances of student thinking. We situate this work in the existing literature, introduce core principles that underlie our conception of building, and present a prototype of the teaching practice of building on MOSTs that includes four sub-practices.
We conclude by discussing the need for future research and our research agenda for studying the building prototype.
Citation:
Van Zoest, L. R., Peterson, B. E., Leatham, K. R., & Stockero, S. L. (2016, November). Conceptualizing the teaching practice of building on student mathematical thinking. Presentation at the 38th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ.
Abstract:
Despite the fact that the mathematics education field recognizes the critical role that student thinking plays in high quality instruction, little is known about productive use of the in-the-moment student thinking that emerges in the context of whole-class discussion. We draw on and extend the work of others to theorize the mathematical understanding an instance of such student thinking can be used to build towards—the mathematical point (MP). An MP is a mathematical statement of what could be gained from considering a particular instance of student thinking. Examples and non-examples are used to illustrate nuances in the MP construct. Articulating the MP for an instance of student thinking is requisite for determining whether there is instructional value in pursuing that thinking.
Citation:
Van Zoest, L. R., Stockero, S. L., Leatham, K. R., & Peterson, B. E. (2016, August). Theorizing the mathematical point of building on student mathematical thinking. Presentation at the 40th Conference of the International Group for the Psychology of Mathematics Education, Szeged, Hungary.
Conceptualizing Teacher Discourse Moves Using Different Focal Lengths Abstract:
Using the metaphor of camera focal length, three research groups will share their conceptualizations of teacher moves to facilitate meaningful mathematical discourse. The approaches will be analyzed in relationship to each other to better understand teacher actions in response to student contributions during instruction.
Citation:
Van Zoest, L. R., Stockero, S. L., Leatham, K. R., Peterson, B. E., Conner, A., Singletary, L. M., … O'Connor, C. (2016, April). Conceptualizing teacher discourse moves using different focal lengths. Presentation at the 2016 National Council of Teachers of Mathematics Research Conference, San Francisco, CA.
How We Can "Attend to Precision" in Classroom Mathematics Discussions Abstract:
Explore examples of teacher and student imprecision in classroom mathematics discourse. Discuss types of imprecision that occur in classrooms, the ramifications of this imprecision, and strategies for addressing that imprecision. Learn how to minimize your own imprecision and to view student imprecision as an opportunity to learn mathematics.
Citation:
Leatham, K. R., Peterson, B. E., & Merrill, L. (2016, April). How we can "attend to precision" in classroom mathematics discussions. Presentation at the 2016 National Council of Teachers of Mathematics Annual Conference, San Francisco, CA.
I've got my Students Sharing Their Mathematical Thinking—Now What? Abstract:
Once students share their ideas, creating meaningful mathematics discourse requires that teachers decide which ideas are worth pursuing and how to capitalize on those ideas. We will share a framework for determining which student ideas have significant potential to support mathematics learning, and we will discuss how teachers might productively use those ideas.
Citation:
Stockero, S. L., Van Zoest, L. R., & Leatham, K. R. (2016, April). I've got my students sharing their mathematical thinking—Now what? Presentation at the 2016 National Council of Teachers of Mathematics Annual Conference, San Francisco, CA.
Engaging Teachers in Identifying the Point of Student Mathematical Thinking Abstract:
Explore productive use of student thinking through activities related to identifying the mathematical point an instance of student thinking can be used to build toward. Discuss the potential of such activities for supporting teachers to productively use student mathematical thinking.
Citation:
Van Zoest, L. R., Fraser, E. H., & Ochieng, M. A. (2016, January). Engaging teachers in identifying the point of student mathematical thinking. Presentation at the 20th Annual Meeting of the Association of Mathematics Teachers Educators, Irvine, CA.
Productive Use of Student Mathematical Thinking is More than a Single Move Abstract:
We will introduce the teaching practice of building and its constituent components as the most productive use of worthwhile student mathematical thinking, analyze teaching examples for evidence of building, and consider how to support teachers' development of this practice.
Citation:
Peterson, B. E., Van Zoest, L. R., Stockero, S. L., & Leatham, K. R. (2016, January). Productive use of student mathematical thinking is more than a single move. Presentation at the 20th Annual Meeting of the Association of Mathematics Teachers Educators, Irvine, CA.
Attributes of Student Mathematical Thinking That is Worth Building on in Whole Class Discussion Abstract:
This study investigated the attributes of 297 instances of student mathematical thinking during whole-class interactions that were identified as having the potential to foster learners' understanding of important mathematical ideas (MOSTs). Attributes included the form of the thinking (e.g., question vs. declarative statement), whether the thinking was based on earlier work or generated in-the-moment, the accuracy of the thinking, and the type of the thinking (e.g., sense making). Findings both illuminate the complexity of identifying student thinking worth building on during whole-class discussion and provide insight into important attributes of MOSTs that teachers can use to better recognize them. For example, 96% of MOSTs were of three types, making these three particularly salient types of student mathematical thinking for teachers to develop skills in recognizing.
Citation:
Van Zoest, L. R., Stockero, S. L., Atanga, N. A., Leatham, K. R., Peterson, B. E., & Ochieng, M. A. (2015, November). Attributes of student mathematical thinking that is worth building on in whole class discussion. Presentation at the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI.
Uncovering Teachers' Goals, Orientations, and Resources Related to the Practice of Using Student Thinking Abstract:
Improving teachers' practice of using student mathematical thinking requires an understanding of why teachers respond to student thinking as they do; that is, an understanding of the goals, orientations and resources (Schoenfeld, 2011) that underlie their enactment of this practice. We describe a scenario-based interview tool developed to prompt teachers to discuss their decisions and rationales related to using student thinking. We examine cases of two individual teachers to illustrate how the tool contributes to (1) inferring individual teachers' goals, orientations and resources and (2) differentiating among teachers' uses of student thinking.
Citation:
Stockero, S. L., Van Zoest, L. R., Rougee, A., Fraser, E. H., Leatham, K. R., & Peterson, B. E. (2015, November). Uncovering teachers' goals, orientations, and resources related to the practice of using student thinking. Presentation at the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, East Lansing, MI.
Toward a Theory of Productive Use of Student Mathematical Thinking Abstract:
This research symposium consists of three presentations that consider: (1) the nature of student mathematical thinking (SMT) available to teachers during instruction, (2) teachers' perceptions of productive use of SMT, and (3) teachers' abilities to recognize and productively respond to SMT. The work will be discussed in the broader context of developing a theory of productive use of SMT.
Citation:
Van Zoest, L. R., Stockero, S. L., Peterson, B. E., Leatham, K. R., Atanga, N., Merrill, L., & Ochieng M. (2015, April). Toward a theory of productive use of student mathematical thinking. Presentation at the 2015 National Council of Teachers of Mathematics Research Conference, Boston, MA.
Defining and Developing Teaching Practices Related to Responding to Students' Mathematical Thinking Abstract:
This session builds on research on professional noticing of students' mathematical thinking by unpacking different ways of
conceptualizing the teaching practice of responding to student thinking. Four projects focused on defining and developing this practice will be presented and discussed. The MOST project presented on Discerning Student Mathematical Thinking in Whole Class Discussion.
Citation:
Webel, C., DeLeeuw, W., Empson, S., Jacobs, V., Land, T., Leatham, K., … Conner, K. (2015, February). Defining and developing teaching practices related to responding to students' mathematical thinking. Presentation at the 19th Annual Meeting of the Association of Mathematics Teachers Educators, Orlando, FL.
Teachers' Perceptions of "Use" of Student Mathematical Thinking in Whole Class Discussion Abstract:
What does it mean to productively "use" student mathematical
thinking in whole-class discussion? The MOST project interviewed
mathematics teachers about their perceptions of such use. We
discuss our framework for categorizing teachers' perceptions of use
and implications for professional development.
Citation:
Ochieng, M. A., Leatham, K., Stockero, S. L., & Van Zoest, L. R. (2015, February). Teachers' perceptions of "use" of student mathematical thinking in whole class discussion. Presentation at the 19th Annual Meeting of the Association of Mathematics Teachers Educators, Orlando, FL.
What's the Point? Identifying Important Mathematics Underlying Student Thinking Abstract:
This session focuses on understanding the instructional practice of building on student thinking and supporting teachers to enact this practice through activities related to identifying the mathematical point of an instance—that is, what the instance of student thinking can be used to build towards. In the MOST project (see LeveragingMOSTs.org), we define building as the teaching practice of making student thinking the object of consideration by the class in order to engage the class in making sense of that thinking to better understand an important mathematical idea. ...MORE...A critical aspect of building is recognizing what important mathematical idea the student thinking can be used to better understand; we call these important mathematical ideas mathematical points. As a result of our own learning through the process of identifying mathematical points, we hypothesized that teachers would also benefit from engaging with and developing skill in identifying mathematical points. To facilitate teacher learning, we defined mathematical point as a concise statement of a specific mathematical idea that students could learn and constructed activities that would develop teachers' knowledge of and skill with mathematical points. Session attendees will engage in these mathematical point activities and discuss the potential of identifying and conceptualizing mathematical points for an instance of student mathematical thinking as a "learning to teach" activity for preservice teachers and an "improving teaching" activity for practicing teachers. Research data from using the activities with preservice teachers will be used to inform the discussion. Focusing on the mathematical point of an instance of student thinking supports teachers in focusing on the mathematics in the student thinking and to recognize which student thinking can be pursued to meet CCSSM. This focus is seen as an antidote both for the temptation to see transmitting content to students as the only way to meet the CCSSM and for the idea that having students share their thinking is sufficient to meet the CCSSM. The research and examples are from work with secondary preservice teachers, but the session will be relevant to anyone involved in supporting teacher learning.
Citation:
Van Zoest, L. R. (2015, March). What's the point? Identifying important mathematics underlying student thinking. Presentations at the Teachers Development Group 2015 Leadership Seminar, Portland, OR.
Teachers' Perceptions of Productive Use of Student
Mathematical Thinking Abstract:
We argue that the teaching practice of productively using student
mathematical thinking [PUMT] needs to be better conceptualized
for the construct to gain greater traction in the classroom and
in research. We report the results of a study wherein we explored
teachers' perceptions of PUMT. We interviewed mathematics teachers
and analyzed these interviews using and refining initial conjectures
about the process teachers might go through in learning PUMT.
We found that teachers' perceptions of PUMT ranged from valuing
student participation, to valuing student mathematical thinking,
to using that thinking in a variety of ways related to eliciting,
interpreting and building on that thinking.
Citation:
Leatham, K. R., Van Zoest, L. R., Stockero, S. L., & Peterson, B. E. (2014, July). Teachers' perceptions of productive use of student
mathematical thinking. Presentation at the Joint Meeting of PME 38 and PME-NA
36, Vancouver, Canada.
Abstract:
Participants will be introduced to and use a framework that considers
the significance of student mathematical thinking and the pedagogical
opportunities that thinking might create. The affordances and
complexities of using the framework to analyze classroom discourse
and to support teachers in productively using student thinking
will be discussed.
Citation:
Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest,
L. R. (2014, April). Recognizing opportunities for productive
use of student thinking. Presentation at the 2014 National
Council of Teachers of Mathematics Research Conference, New Orleans,
LA.
Making the MOST of Student Mathematical Thinking Abstract:
This session draws on research about which student thinking during
mathematics lessons is most productive to pursue in the moment
to consider how to support teachers in productively using student
thinking to meet the CCSS for Mathematical Practice and Content.
The Mathematical Opportunities in Student Thinking (MOST) framework
will be considered as a way to identify student thinking that
has considerable potential to engage students in developing their
understanding of significant mathematics. One of the strengths
of the framework is the way in which it focuses teachers on mathematics.
This session will be relevant to anyone interested in thinking
about how to support teachers in productively using student thinking.
Citation:
Van Zoest, L. R. (2014, February). Making the MOST of student
mathematical thinking. Presentation at the Teachers Development
Group 2014 Leadership Seminar, Portland, Oregon.
What Does it Mean to Build on Student Mathematical
Thinking? Abstract:
"Attend to," "respond to," "pursue," and "use" are terms often
used synonymously with "build on" student mathematical thinking.
This imprecision contributes to teachers' difficulty in implementing
the practice. Our discussion will work toward developing common
definitions among mathematics teacher educators.
Citation:
Peterson, B. E., Leatham, K. R., & Van Zoest, L. R. (2014, February). What
does it mean to build on student mathematical thinking? Presentation
at the 18th Annual Meeting of the Association of Mathematics Teacher
Educators, Irvine, CA.
Classroom Mathematics Discourse: Broadening Perspectives
by Integrating Tools for Analysis Abstract:
This working group explores tools for analyzing mathematics classroom
discourse across two projects with different, but complementary
perspectives. The goals of the working group include generating
interaction about the theoretical lenses that we use to analyze
and discuss classroom mathematics discourse and the relationships
between these different theoretical frameworks. Participants
will engage with the individual frameworks in the first two sessions
and discuss interactions of the two frameworks in the third session. The attached presentation is from the MOST group on "Mathematically Significant Pedagogical Opportunities to Build on Student Thinking."
Citation:
Johnson, K. R., Steele, Michael D., Herbel-Eisenmann, B. A., Leatham,
K. R., & Peterson, B. E., Stockero, S. L., … Merrill, L. (2013, November). Classroom mathematics
discourse: Broadening perspectives by integrating tools for analysis. Presentation at the 35th Annual Meeting of the North American Chapter of the
International Group for the Psychology of Mathematics Education, Chicago, IL.
Conceptualizing Mathematically Significant Pedagogical
Opportunities to Build on Student Thinking Abstract:
The mathematics education community values using student thinking
to develop mathematical concepts, but the nuances of this practice
are not clearly understood. We conceptualize an important group
of instances in classroom lessons that occur at the intersection
of student thinking, significant mathematics, and pedagogical
openings—what we call Mathematically Significant
Pedagogical Openings to Build on Student Thinking
(MOSTs)—and introduce a framework for determining when
they occur. We discuss how the MOST construct contributes to
facilitating and researching teachers' mathematically-productive
use of student thinking through providing a lens and generating
a common language for recognizing and agreeing upon high-leverage
student mathematical thinking.
Citation:
Van Zoest, L. R., Leatham, K. R., Peterson, B. E., & Stockero,
S. L. (2013, July). Conceptualizing mathematically significant pedagogical
openings to build on student thinking. Presentation at the 37th Conference of the International
Group for the Psychology of Mathematics Education, Kiel, Germany.
A Framework for Recognizing Teachable Moments in
Mathematics Classrooms Abstract:
We describe a tool for identifying when student thinking provides
a pedagogical opening for working towards a mathematical goal.
Attendees will discuss ideas for using the tool to analyze and
discuss instances of student mathematics thinking with teachers.
Citation:
Leatham, K. R., Stockero, S. L., Peterson, B. E., & Van Zoest,
L. R. (2013, January). A framework for recognizing teachable
moments in mathematics classrooms. Presentation at the 17th
Annual Meeting of the Association of Mathematics Teacher Educators,
Orlando, FL.
Mathematically Important Pedagogical Opportunities
(MIPO) Abstract:
The mathematics education community values using student thinking
to develop mathematical concepts, but the nuances of this practice
are not clearly understood. For example, not all student thinking
provides the basis of productive discussions. In this paper we
describe a conceptualization of instances in a classroom lesson
that provide the teacher with opportunities to extend or change
the nature of students' mathematical understanding—what
we refer to as Mathematically Important Pedagogical Opportunities
(MIPOs). We analyze classroom dialogue to illustrate how this
lens can be used to make more tangible the often abstract but
fundamental goal of pursuing students’ mathematical thinking.
Citation:
Leatham, K. R., Peterson, B. E., Stockero, S. L., & Van Zoest,
L. R. (2011, October). Mathematically important pedagogical opportunities. Presentation at the 33rd
Annual Meeting of the North American Chapter of the International
Group for the Psychology of Mathematics Education,
Reno, NV.
Investigating Mathematically Important Pedagogical
Opportunities Abstract:
Mathematically Important Pedagogical Opportunities (MIPOs) are
instances in a classroom lesson in which the teacher has an opportunity
to move the class forward in their development of significant
mathematics. Although this construct is widely recognized in
the literature as important to mathematics teaching and learning,
it is neither well defined nor clearly identified as a construct
that can be studied. This working group will build on the efforts
of two research groups, represented by the organizers, to define,
identify, and characterize MIPOs. Specifically, Session 1 will
focus on identifying MIPOs, including questioning and critiquing
working definitions and preliminary dimensions of MIPOs. Session
2 will explore sub-constructs of MIPOs and the potential of sub-constructs
to provide leverage in studying the broader construct. The first
two sessions will include examining instances of classroom practice
(written/video) that have been identified as containing MIPOs.
Session 3 will focus on issues around developing a research agenda
for investigating MIPOs and generating plans for continuing work
on MIPOs.
Citation:
Leatham, K. R., Stockero, S. L., Van Zoest, L. R., & Peterson,
B. E. (2010, October). Investigating mathematically important pedagogical
opportunities. Presentation at the 32nd Annual Meeting of the North
American Chapter of the International Group for the Psychology
of Mathematics Education,
Columbus, OH.
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