# Teacher’s Guide to Formative Assessment in Math

## Accelerate algebraic thinking!

Formative assessment is one of the most important ways to guide your students in their mathematics learning and success. Formative assessment can be the pathway to breaking through what is one of the most difficult areas for math learners: algebra.

The shift from the concrete world of computation to the abstract world of algebra can be daunting for many learners—and their teachers. Algebra’s importance as a gatekeeper course and high school graduation requirement has made it an important aspect of access and equity, the earlier learners start the better.

**one grade leap**in achievement when it’s used in the classroom.

## What Math Formative Assessment is All About

In this guide, you’ll find formative assessment strategies for primary, secondary and middle school. When teachers evaluate, question, and reflect upon real-time student learning, they can quickly and efficiently adjust their instruction based on student understanding. The ongoing assessment techniques allow a teacher to activate student learning and use performance data to consistently differentiate.

It’s also beneficial in structuring a more regular cycle of student feedback. This informs targeted instruction, create appropriate strategy groups, and communicate more effectively with students, parents, and guardians.

## A Formative Math Assessment Technique for Primary Guides

Here’s an example from the Guide that includes the formative assessment and data collection technique to use:

By second grade, most learners can work beyond the simple computational fluency of 2 + 3 =5 and consider new relationships among numbers and unknown quantities. Asking students to compute quantities that relate to a defined sum, instead of simply counting up to find the sum, helps them think more conceptually about mathematical generalizations using algebraic notation.

**Shift from 2 + 3 = N to 2 + N = 5**

Formative assessment: Early on, students learn the concepts of numbers, counting, addition, subtraction, and cardinality to understand basic mathematical relationships, sums, and differences. These first algebraic reasoning experiences (2+__=5) may cause confusion because students may have only developed one view in their minds as to how to solve an equation (2 + 3 = __). Formative assessment techniques can lead a teacher to analyze a student’s progress in both the basic computation of numbers and in the new concepts of algebraic reasoning. A teacher may choose to formatively assess quickly with the entire class by asking a computation based question and having the entire class hold up how many fingers represent the answer.

In each question posed to the students, the placement of the missing quantity, either as a sum ( 2 + 3 = __) or as an addend (2 + __ = 5) in the equation, differentiates whether a student struggles with the basic computation involved in addition (unknown sum) or the algebraic thinking involved in adding to an unknown quantity (unknown addend). Immediately responding to incorrect patterns of thinking observed when students hold up their fingers to answer allows for a swift intervention and a new teaching opportunity.

Data Collection: Using these observations, teachers can choose to group students based on common mistakes, mutual understanding of concepts, and/or mastery. Whether the next steps are remedial, practice, or extension, the teacher has real-time data to support student learning.

## Formative Assessment Resources You Can Use Right Now

You can never have enough resources to help you and your students communicate better and learn more. These online math toolboxes provide thousands of formative assessments, tasks and rubrics and lesson study resource kits for algebra and geometry:

Mathematics Formative Assessment System (MFAS)

The system includes tasks or problems that teachers can implement with their students, and rubrics that help the teacher interpret students’ responses. Teachers using MFAS ask students to perform mathematical tasks, explain their reasoning, and justify their solutions.

Mathematics Assessment Project

The Mathematics Assessment Project is part of the Math Design Collaborative initiated by the Bill & Melinda Gates Foundation. The project set out to design and develop well-engineered tools for formative and summative assessment that expose students’ mathematical knowledge and reasoning, helping teachers guide them towards improvement and monitor progress.

Inside Mathematics Performance Assessment Tasks

Provides grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics.

### Teacher Formative Assessment Resources

**Video:** Seamless Formative Assessment for Personalized Learning

**White Paper:** From Formative Assessment to Informative Assessing in the Math Classroom

**Blog: Formative Assessments:** Help Me Help You

### About the Author: Stefani Kauppila

Stefani Kauppila is an experienced classroom educator who worked in elementary and middle school settings in Sammamish, Washington, for six years before joining the DreamBox Learning Curriculum Design team in 2014. She earned a Masters degree in Teaching with endorsements in Reading and Language Development and currently holds a Washington State teaching certificate. She works passionately to create innovative math curriculum designed to adapt and individualize learning for all students.