# Math Chat Mondays #5: Encouraging Progress with Formative Assessment

## A Math Moment with Cheryl Rose Tobey, K-5 Reveal Math Author

Welcome to Math Chat Mondays, a series where we highlight many of the expert authors, advisors, and thought leaders behind our new *Reveal Math* K-5 core mathematics program. Each Monday we will introduce a *Reveal Math* contributor, asking them questions about their mathematical research and expertise, their contributions to the *Reveal Math *curriculum, and above all, why they are passionate about all things math. Read on to meet our fifth guest, Cheryl Rose Tobey!

## Meet Cheryl Rose Tobey

Cheryl is currently a mathematics specialist at Maine Mathematics and Science Alliance (MMSA) who provides supports and developed materials for mathematics educators across the country. Throughout her 20 years of providing mathematics professional learning support at Education Development Center (EDC) and MMSA, she has led multiple National Science Foundation (NSF) and state-funded grants focused on increasing student achievement for struggling learners. Along with 10 years as a classroom educator, Cheryl has extensive experience coaching teachers and using math probes and other formative assessment techniques to better understand student learning.

# 1. Why have you chosen a career supporting math classrooms?

Students and educators deserve to view mathematics as an engaging, useful subject. This happens when the learning environment supports students to be flexible, resourceful, and reflective problem solvers as they learn and apply mathematical concepts and procedures with deep understanding.

Educators are eager to create such an environment and look for support along the way, especially given their own experiences as a math learner often looked very different. **I thrive on this excitement from educators and am continually re-energized to co-develop tools and processes that support educators progress towards making mathematics meaningful and joyful for all students.**

# 2. How do you encourage students to enjoy math?

Students enjoy math when they are engaged in meaningful activities leading to purposeful learning. Throughout these activities they must be given time to express their thinking, compare and contrast with others’ ideas and to engage in iterative revision as their understanding progresses.

## Learn more about how to engage students in math:

# 3. Describe the importance of formative assessments and how students benefit.

Classrooms in which teachers and students engage in the process of formative assessment are ones in which teachers are explicit about expectations for learning, and both teachers and students monitor students’ work in terms of progress toward those expectations.

The shared element of reflecting on students’ understanding in the context of clearly identified goals helps students learn to monitor their progress, receive feedback intended to promote further learning, and incorporate the feedback into subsequent work.

# 4. How might educators utilize formative assessments effectively in classrooms and learning environments today?

Introducing students to the learning targets at a key point during a lesson and revisiting these throughout a core set of learning activities is foundational to the formative assessment process. **Students who have a clear sense of what they’re supposed to be learning are often more willing to engage in the lesson. **Revisiting the target provides a much-needed opportunity for students to summarize their learning to that point (“What do we know so far in relation to our learning target?”), to refocus learning (“How does the activity we just did relate to our learning target?”), or to further clarify the learning target (“Remember, the learning target is about *comparing* fractions. How are these two strategies …”).

Misunderstandings are likely to develop as a normal part of learning mathematics. These misunderstandings are often considered overgeneralizations — that is, information extended or applied to another context in an inappropriate way.

A teacher’s role is to minimize the chances of students harboring misconceptions by knowing the potential difficulties students are likely to encounter, using formative assessments to elicit misconceptions, and implementing instruction to help students build conceptual understanding of the mathematics.

Formative assessment probes are a tool to support teachers in uncovering student thinking. A formative assessment probe is a short, highly focused, quick-to-administer diagnostic assessment designed to pinpoint specific misconceptions students may have regarding a particular mathematics concept.

**While a probe may look like a familiar assessment, it has a distinguishing design feature.** Each probe typically includes three to six items and each item requires a two-part response from the student: a selected response and a written or verbal/oral explanation using words and/or pictures.** Together, this combination helps to reveal underlying patterns in incorrect answers and shows whether correct selected responses are supported by strong or by faulty reasoning. **Probes are considered diagnostic until a teacher acts on the data to move student learning forward. Learning about common student difficulties and misconceptions and their root causes helps teachers to chunk the learning into systematic and manageable pieces**. **Probe evidence won’t tell a teacher everything about a student’s understanding of a concept like fractions. Rather, a particular probe can yield a just-right amount of information about a small slice of conceptual understanding upon which a teacher can act strategically to move learning forward.

## Hear more from Cheryl about using formative assessment math probes:

# 5. How did you get involved with Reveal Math and what are you most excited about?

Page Keeley, who designed the process for developing science diagnostic assessment probes and who tirelessly promotes the use of these assessments for formative assessment purposes, worked with MHE to develop probes for the *Inspire Science** *program. Page and I have worked together for many years, starting when we were both at MMSA. Through this collaboration, I was introduced to the *Reveal Math *MHE team.

I often receive requests from schools and districts to support a process for aligning existing formative assessment probes with various programs. Having a probe purposefully embedded within each Reveal unit will enable educators to use these formative assessment tools efficiently and effectively.

*K-5 Reveal* integrates many critical components including routines, inquiry, using and connecting representations, fluency development, and formative assessment.

# 6. What is the most important aspect of elementary mathematics today and how do you see it evolving?

There has been a focus for some time on the need to create learning environments that support students as flexible, resourceful, and reflective problem solvers as they learn and apply mathematical concepts and procedures with deep understanding. In the last few years, there has been a shift from this as a lofty goal to becoming a reality.

# 7. What is your fondest math memory?

As a student, I always felt I was good at mathematics. It wasn’t until I became a teacher that I realized what I was good at was memorizing and following a set of rules and procedures that had been shown to me in a step by step format. My teacher education program taught me important ideas around student engagement but I didn’t truly understand the difference between student engagement versus student ownership and involvement in their learning.

My fondest memory was when a student asked me, “But why do we flip and multiply?” and I realized I didn’t know and also didn’t know that students would care why and that not understanding the why would hinder the learning process.

It is my fondest memory because I remember the moment like it was yesterday and from that day forward I began my quest to support student understanding through inquiry and discussion.