Gathering Intelligence in the Search for Students’ Zones of Proximal Development

December 2023

Teacher helping three students at desk

Teachers are spies. Wouldn’t you agree?

Teachers constantly gather intelligence to determine where students are in their learning process. They are searching for each student’s zone of proximal development (ZPD). The zone of proximal development is a concept in educational psychology that represents the space between what a learner is capable of doing unsupported and what the learner cannot do even with support. With any intelligence gathering, there are key opportunities to observe, assess, and then take action. In the classroom, these opportunities are known as “discretionary spaces.” Within a discretionary space, teachers can make choices to assess a student’s zone of proximal development and decide what actions they can take.

In a CPM classroom, a teacher typically takes action not only by posing purposeful questions, but also by implementing a Study Team and Teaching Strategy or transitioning to a different mode of instruction. However, when the intelligence that a teacher gathers is artificial (that is, the teacher assumes something will happen but it really has not), a teacher is at risk of incorrectly assessing a student’s ZPD. Teachers can gather “artificial” intelligence by only noticing the thinking of a single student in a team. An example of this would be to pose a question to a team, hear the response of one student in that team, and then make assumptions about each students’ ZPD based on that single response.

There is a difference between the team’s ZPD and each individual student’s ZPD—this is the fundamental rationale for implementing teams in the first place. A team is the support system that raises the ZPD of the individuals within the team. A well-functioning team should be able to reach a much higher level of thinking unsupported by a teacher than each individual within the team could reach alone. When a teacher pre-judges a team’s ability to think through a problem based on the past performance of individual students, they are using assumed, or “artificial,” intelligence of that team’s capabilities. Making statements such as, “This team has my low-kids, so they need more support,” is not only inequitable, but it is also limiting. When this happens, the teacher might incorrectly assume that the team needs the teacher to scaffold the problems.

A strategy that closes the gap between an individual student’s ZPD and the team ZPD is to exercise patience. When students have time to think about the problem before the teacher intervenes, they become a part of the problem-solving process with their team. Teachers who allow students this time or use strategies that include thinking time, such as Think-Ink-Share or Teammates Consult, seem to have more students involved in the problem-solving process. Both of these strategies benefit a teacher’s intelligence gathering. Patience and thinking before taking action help teachers craft better questions and make appropriate strategy decisions. Students may just surprise you with how little support they need.

Picture of John Hayes, Victoria Holt

John Hayes, Victoria Holt

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Algebra Tiles Blue Icon

Algebra Tiles Session

  • Used throughout CPM middle and high school courses
  • Concrete, geometric representation of algebraic concepts.
  • Two-hour virtual session,
  •  Learn how students build their conceptual understanding of simplifying algebraic expressions
  • Solving equations using these tools.  
  • Determining perimeter,
  • Combining like terms,
  • Comparing expressions,
  • Solving equations
  • Use an area model to multiply polynomials,
  • Factor quadratics and other polynomials, and
  • Complete the square.
  • Support the transition from a concrete (manipulative) representation to an abstract model of mathematics..

Foundations for Implementation

This professional learning is designed for teachers as they begin their implementation of CPM. This series contains multiple components and is grounded in multiple active experiences delivered over the first year. This learning experience will encourage teachers to adjust their instructional practices, expand their content knowledge, and challenge their beliefs about teaching and learning. Teachers and leaders will gain first-hand experience with CPM with emphasis on what they will be teaching. Throughout this series educators will experience the mathematics, consider instructional practices, and learn about the classroom environment necessary for a successful implementation of CPM curriculum resources.

Page 2 of the Professional Learning Progression (PDF) describes all of the components of this learning event and the additional support available. Teachers new to a course, but have previously attended Foundations for Implementation, can choose to engage in the course Content Modules in the Professional Learning Portal rather than attending the entire series of learning events again.

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Building on Instructional Practice Series

The Building on Instructional Practice Series consists of three different events – Building on Discourse, Building on Assessment, Building on Equity – that are designed for teachers with a minimum of one year of experience teaching with CPM instructional materials and who have completed the Foundations for Implementation Series.

Building on Equity

In Building on Equity, participants will learn how to include equitable practices in their classroom and support traditionally underserved students in becoming leaders of their own learning. Essential questions include: How do I shift dependent learners into independent learners? How does my own math identity and cultural background impact my classroom? The focus of day one is equitable classroom culture. Participants will reflect on how their math identity and mindsets impact student learning. They will begin working on a plan for Chapter 1 that creates an equitable classroom culture. The focus of day two and three is implementing equitable tasks. Participants will develop their use of the 5 Practices for Orchestrating Meaningful Mathematical Discussions and curate strategies for supporting all students in becoming leaders of their own learning. Participants will use an equity lens to reflect on and revise their Chapter 1 lesson plans.

Building on Assessment

In Building on Assessment, participants will apply assessment research and develop methods to provide feedback to students and inform equitable assessment decisions. On day one, participants will align assessment practices with learning progressions and the principle of mastery over time as well as write assessment items. During day two, participants will develop rubrics, explore alternate types of assessment, and plan for implementation that supports student ownership. On the third day, participants will develop strategies to monitor progress and provide evidence of proficiency with identified mathematics content and practices. Participants will develop assessment action plans that will encourage continued collaboration within their learning community.

Building on Discourse

In Building on Discourse, participants will improve their ability to facilitate meaningful mathematical discourse. This learning experience will encourage participants to adjust their instructional practices in the areas of sharing math authority, developing independent learners, and the creation of equitable classroom environments. Participants will plan for student learning by using teaching practices such as posing purposeful questioning, supporting productive struggle, and facilitating meaningful mathematical discourse. In doing so, participants learn to support students collaboratively engaged with rich tasks with all elements of the Effective Mathematics Teaching Practices incorporated through intentional and reflective planning.