Overview

Session Summary

This session examines how a strength-based approach to formative assessment can be used to gather information about students' strengths and needs, and how this information can inform instructional decisions that engage all students in substantive and challenging mathematics work.


"All students come to the classroom knowing and understanding some aspects of mathematics. Work with students begins with what they know and understand, with what makes sense to them, with what they are able to do. Having someone recognize and appreciate one's knowledge and ability as a math thinker develops and builds one's mathematical identity."

A Framework for Reflecting about Equity in the Elementary Mathematics Classroom
- Russell et al, 2023​

What is a Strength-based Approach?

Formative Assessment in Action

Watch 8th grade math teacher, Leah Alcala, use formative assessment to inform her teaching during a daily warm-up routine in her classroom. Consider the following questions:

  • How does Ms. Alcala use a strength-based approach to formative assessment to adapt her teaching to meet students' learning needs?
  • How does Ms. Alcala support students in taking ownership of their learning and in serving as learning resources for one another?

Ms. Alcala uses the activity “My Favorite No” as a tool for formative assessment. What is one example of an activity you use for formative assessment with your students? Share your thinking on the Overview Forum.

Activity 1: Formative Assessment: Observing Students at Work


This activity focuses on using observation as a tool to assess student learning. In the previous session, you considered how thinking about the mathematics, anticipating student solutions, and observing students at work helps teachers plan and prepare for whole class discussions. In this activity, you will consider how these same steps can be used to assess student understanding.

Preparing to Observe: Doing the Mathematics and Anticipating Student Strategies

Thinking about the mathematics and solving the problems students will be working on ahead of time helps teachers anticipate possible problem-solving approaches students may use. This in turn prepares teachers for what they are likely to observe as students are working on an activity.

Doing the Mathematics and Anticipating Student Strategies: A Grade 4 Example

In the following Grade 4 activity, taken from the Investigations curriculum, students are interpreting and solving multi-step addition and subtraction problems.

Watch as the teacher discusses how she prepares for the activity and introduces the activity to students.

Review the four pages of problems introduced in the video above. Solve Problems 1-3 using at least two different strategies. After solving the problems, consider how students might approach these problems.

 

Conducting Student Observations

Observing students at work provides teachers with an opportunity to learn about students’ thinking. Teachers can gather powerful formative assessment data by asking questions that uncover thinking and actively listening to students as they voice their understandings and confusions.

Read the following blog post in which Mark Chubb shares how teachers can ask questions that encourage students to explain and reason, and the importance of carefully listening to students’ responses.

Watch 4th grade students at work on the problems you solved above. Pay particular attention to the questions the teacher poses to her students. Record these questions on a separate sheet of paper.

What information did the teacher gather about students’ understanding of the problems through her use of questioning? Does the teacher ask funneling or focusing questions?

Activity 2: Formative Assessment: Interviewing Students

This activity focuses on using interviews to assess student understanding. You will watch an interview with two 1st grade students and read about a math coach’s experience conducting a student interview in a 4th grade class. You will also consider how connecting to students’ current thinking and working to build on their strengths can help teachers both uncover and further students’ mathematical understandings during interviews.

In the following video, the teacher is interviewing two first grade students as they play a few rounds of the game "Race to the Top: How Many Tens?", which is a part of the Investigations curriculum. Read the game directions shown below (click on the image of the directions to enlarge them).

Race to the Top: How Many Tens Game Directions

This game focuses on using ten-frame cards to represent 2-digit numbers as a group of tens and a group of ones, determining the quantity represented, and then determining the number of tens. The students are quite familiar with the game having played this and other versions during math class.

Watch as the students in this video play 2 rounds of this game. After watching each round, pause and quickly jot down your responses to the questions:

  • What about these students' dispositions toward math stood out to you as you watched them play this round of the game?
  • What do these students appear to understand about the structure of 2-digit numbers?
  • What questions do you have about these students as learners?
  • What did the teacher learn about each student’s understanding of the structure of 2-digit numbers by asking students questions about adding/subtracting ten?

NOTE: Jot down your responses. You will return to them later in this activity.

Pause, consider and write down your responses to the video questions.

Watch these students play a 2nd round of the game.

Pause, consider and respond to the video questions.

Look over your notes. How did your perception of these students' mathematical understandings change over the course of the interview?

Activity 3: Formative Assessment: Looking at Student Work

This activity focuses on the importance of using student work as another window into understanding what students know and understand. After reflecting on a student interview and the work produced, you will listen to how one teacher organizes and uses student work to inform her instruction.

Listening and Looking: Uncovering What Students Know

Read the blog post Presuming Competence: Using Clinical Interviews to Support Classroom Instruction by Jenna Laib, in which she discusses her experience interviewing Ali, a 4th grade student. Ms. Laib's reflections illustrate the importance of using a strengths-based lens when listening to students' thinking and examining the work they produce.

Share your thoughts on the Looking and Listening Forum.

  • Refer back to the definition of strength-based assessment from the Overview section of Session 3. Reflect on Ali's verbal responses and the work she produced. What did Ali appear to know and understand about multiplication and division? What seemed to make sense to her? What was she able to do?
  • What evidence did you see of Ms. Laib's understanding of the mathematics? How did this understanding help her assess Ali's responses and the work she produced?

Collecting and Reviewing Student Work Over Time

Portfolios are a powerful way to document and assess a student's mathematical learning over time. Student work samples, alongside anecdotal notes, and more formal assessments can offer a comprehensive view of how a student’s understanding is developing.

In order for portfolios to be effective, teachers have to find a system that works for their students. Some teachers use a non-digital management system. Others may use digital systems.

Look through the student portfolios as 2nd grade teacher, Kat Callard, discusses how she documents and assesses student work over time in her classroom. You may pause the video at any point to look more closely at the student work.

Read the following quotes from teachers about different digital tools they use to collect and look at student work, and what about these particular tools they find useful.


"Recently I began using the Book Creator app for Chromebooks with my students. One of their first projects was to take the class data they collected in Unit 6 and create a book with it. Students are exploring the digital tool while representing and summarizing their work. This is an opportunity for me to see how creative they can be with their math thinking about data. It also provides a way to share with each other and with families."

-First Grade Teacher


"I use Seesaw in my classroom. One reason I like this digital tool is that it allows me to view student work on my time. The student's work is saved and I am not having to take home math papers every night to see the different ways my students are thinking about the problem. Another reason I like the tool is that it allows the students to show their work in different ways.They can use the pen tool for writing or the drawing feature to make representations. It also allows them to record their voices to explain their thinking."

-Third Grade Teacher

What management system(s) and/or digital tools do you currently use to gather and assess student work over time? What about those systems and/or tools works well? What, if anything, might you like to change about the system(s)/tools you currently use? Share your thoughts on the Assessing Student Work forum.

Forums

  • Return to the Overview Forum and read others’ descriptions of how they currently use formative assessment in their work. Respond to at least one other post that is of interest to you. You may also wish to reread your response on this forum and reflect on any new thoughts or questions about formative assessment that have come up for you over the course of this session. Feel free to add these to the forum.
  • Return to the Assessing Student Work Forum and read about some of the management system(s) others are currently using to gather and assess student work over time. Respond to at least one post that is of interest to you.
  • Return to the Looking and Listening Forum to read and respond to other's posts about Ms. Laib and her student."

Readings

Videos

The Teaching Channel (2015). My Favorite No [Video file]. Retrieved from https://www.youtube.com/embed/srJWx7P6uLE

Key Takeaways

  • Observing students, conducting interviews, and looking closely at students’ work are 3 key ways that teachers can gather formative assessment data.
  • Using a strength-based approach to formative assessment helps teachers build on what students know in order to move their thinking forward.
  • Teachers develop a deeper understanding of what students understand and what they are working on by listening actively as students describe their mathematical thinking and by posing questions that encourage students to voice their mathematical understandings and confusions.