# MSP:MiddleSchoolPortal/Math Assessment

### From Middle School Portal

## Introduction

Assessment has become the “big stick” in the school world. What should be a gathering of information to help teachers make instructional decisions or to help students and parents gauge progress in learning math has often turned into a refocusing of classroom instruction on a standardized test. Avoiding the politics of this situation, this publication offers insights into assessment—its purpose, its possibilities for enhancing instruction, the many ways teachers can gather evidence of student progress.

The **Background Information for Teachers** section features a rich set of provocative material for teacher-to-teacher discussion. Further thoughts for discussion are found in **NCTM Assessment Standards** section.

Resources to help you prepare your students make up the section titled **Preparing for Assessment**. Here are instructional modules, including a set of problem-solving lessons. The **Classroom Assessment** section includes selected articles and a book with stimulating ideas on ways to assess your middle school students. The more students become familiar with different types of assessment, the more comfortable and capable they will be on a real performance; therefore, problems of all types are presented in **Problems for Practice**. Together these three sections aim to help your students “get ready, get set, and go!” We believe you will find here material that will support your efforts and enrich your approaches to assessment.

## Contents

## Background Information for Teachers

Here you will find provocative material on assessment from a professional angle. These online reports and articles could launch interesting discussions among middle school teachers.

If you are looking for additional in-depth professional development resources, *Learning from NAEP: Professional Development Materials for Teachers of Mathematics*, a manual plus CD (not available online - more information can be found at http://www.nctm.org/news/content.aspx?id=12714&LangType=1033), offers activities and tools necessary to facilitate high-quality workshops.

**Finding Balance: Assessment in the Middle School Classroom**
This article from the National Middle School Association's *Middle Ground* journal contends that in a balanced classroom assessment system, neither formative or summative assessment is over- or under-used; they work together to generate the combined effects that are greater than the sum of the individual parts. When summative and formative classroom assessments are high quality and purposefully planned, they are synergistic parts of the same system and can help form a more complete and accurate picture of student learning.

**Measuring What Counts: A Conceptual Guide for Mathematics Assessment**
To achieve national goals for education, we must measure the things that really count. This online book, developed by the Mathematical Sciences Education Board, establishes crucial research-based connections between standards and assessment. Arguing for a better balance between educational and measurement concerns in mathematics assessment, the board sets out three principles related to content, learning, and equity, which can form the basis for new assessments that support the national standards.

**Students Take Center Stage in Classroom Assessment**
If you are considering performance assessment, this article offers insights from real classrooms that have put it into practice. Here a Vermont middle school shares its experiences as it redesigned its assessment process to include student portfolios.

**Framework for Classroom Assessment in Mathematics**
This proposed framework, based on some 20 years of developmental research, discusses the value of classroom assessment as well as its aims, principles, and methods. An insightful report!

**Will This Be on the Test?**
Authors Nicole F. Ice and Wendy B. Sanchez contend that “In a very real sense, what teachers choose to put on tests helps students determine what mathematics is important, and in fact, helps shape their view of the nature of mathematics.” Teachers are encouraged to examine their own tests to see if the tests reflect their beliefs about mathematics.

**Some Common Errors in Interpreting Test Scores**
This article lays out a few common misconceptions among the public related to test scores and educational research, such as thinking that all students can be at or above "grade level." A good article for professional discussion!

**The Nation’s Report Card: Mathematics 2005**
This report presents the national and state results of the National Assessment of Educational Progress (NAEP) in mathematics. A nationally representative sample of about 162,000 eighth-grade students nationwide participated in this 2005 assessment. The 52-page report looks at the data from several angles; for example, it shows that average scores for white, black, and Hispanic students were higher in 2005 than in any previous assessment year. The **2007 Report** is also available.

## Preparing for Assessment

These resources may add to your ideas for helping your students prepare for the many forms and levels of assessment they will face. The first sites use assessment as an essential part of the instructional process itself. The two collections of test items can be used to familiarize middle school students with the standardized testing format if used as warm-up activities, review, or challenge questions on classroom quizzes and tests.

**Test Prep Magic**
Ten-year teaching veteran Heather Wolpert-Gawron is no great fan of standardized testing, but the middle grades ELA teacher figures: if you gotta do it, don't be a bubblehead -- do the prep! In this article at the Teacher Magazine website, the former California regional teacher of the year shares several ways in which teachers can help students develop self-defense skills that will protect them (and you) in the testing wars.

**Math Partners: Mathematics Mentoring for America’s Youth**
The materials here were designed for use by mentors for students in kindergarten through grade 9 in afterschool programs, but are useful in any teaching situation. In each grade band (K-2, 3-5, 6-8, and 8-9 algebra), you will find four units focused on number and operation, geometry and measurement, statistics and probability, and patterns and functions. Each unit has separate pre-assessment activities to help determine individual prior knowledge as well as student needs.

**NAEP Questions**
Over 2,000 questions are archived. Online tools allow you to search the collection by content area, grade level, and difficulty. The site also shows what students at each achievement level are likely to know and how NAEP questions are scored.

**New York State Regents Exams**
You can use these released test items for warm-ups, quizzes, review, and class discussion. It doesn’t matter that your school isn’t in New York! It’s the practice that matters.

## Classroom Assessment

Although today’s middle school teachers are required to focus on district and national testing, you know that valuable —perhaps the most valuable - assessment takes place in your classroom. These online articles and books offer exemplary, classroom-oriented techniques for assessing what your students know.

**Classroom Assessment Techniques**
This is a short but easy-to-read matrix of classroom assessment techniques, outlining descriptions, what to do with the data, and the time required for each type of assessment. The techniques included are the minute paper, chain notes, memory matrix, directed paraphrasing, one-sentence summary, exam evaluations, application cards, and student-generated test questions.

**Measuring Up: Prototypes for Mathematics Assessment**
This book features 13 classroom exercises that demonstrate inquiry, performance, communication, and problem solving as standards for mathematics education. Although created for fourth grade students, the exercises are easily adapted for fifth and sixth graders. The entire book is available to read online (for free!) or to buy as a print copy.

**Portfolio Assessment**
A portfolio is a collection of student work that exhibits the student’s efforts, progress, and achievements in one or more areas of the curriculum. This resource discusses the characteristics of an effective portfolio, types of portfolios, and the phases of portfolio assessment. It offers guidelines on how to get started using portfolios and how to evaluate them, plus additional resources on portfolio assessment.

## Problems for Practice

These problems offer a wide range of mathematical content and assessment approaches. They aim to familiarize students with the usual type of test items as well as challenge them with more open-ended, compelling questions. Besides these online resources, an exceptional book deserves mention here: *Mathematics Assessment Sampler* offers a representative sample of assessment items that support the NCTM Standards and focus on classroom assessment in grades 6–8. Because most formal testing includes multiple-choice items, these are included here as well, but with an added “explain your thinking,” “justify your thinking,” or “how do you know?” component. For information on ordering: http://www.nctm.org/catalog/product.aspx?ID=12940.

**Balanced Assessment**
A set of more than 300 assessment tasks actually designed to inform teaching practice! Most tasks, indexed for grades K-12, incorporate a story problem format and include hands-on activities. Some intriguing titles include Confetti Crush, Walkway, and Hockey Pucks. Rubrics for each task are provided.

**Figure This! Math Challenges for Families**
Created for students in grades 6 to 8, the site offers math challenges that focus on everyday life, such as how fast your heart beats, what shape container holds the most popcorn, and how much of you shows in a small wall mirror.

**Word Problems for Kids**
A wide range of carefully selected problems organized by grade level from 5 through 12. Each problem links to a helpful hint and to the answer; the more difficult problems offer complete solutions.

**Problems with a Point**
Here you can search for word problems by topic, lesson time, required mathematical background, and problem-solving strategy. Take the time to do the short, guided tours of the site, and then look at favorite problems selected by teachers — a great set of problems at the middle school level.

**NAEP Questions**
Over 2,000 questions are archived. Online tools allow you to search the collection by content area, grade level, and difficulty. The site also shows what students at each achievement level are likely to know and how NAEP questions are scored.

**NAEP Assessment Items: Proportionality**
Prepared by the Ohio Resource Center, this collection of problems includes not only test items on proportion but also access to performance data by subgroups of students, a scoring key, and discussion of the tested content.

**Fermi Questions**
Fermi questions emphasize estimation, numerical reasoning, communicating in mathematics, and questioning skills. Students often believe that word problems have one exact answer and that the answer is derived in a unique manner. Fermi questions encourage multiple approaches, emphasize process rather than the answer, and promote nontraditional problem-solving strategies. The Questions Library features classic Fermi questions with annotated solutions, a list of questions for use with students, questions with a Louisiana twist, and activities for the K-12 classroom.

**Open-ended Assessment in Math**
This resource, available online for a small fee, provides more than 450 open-ended questions. All involve significant mathematics, are solvable in a variety of ways, elicit a range of responses, and enable students to reveal their reasoning processes. The site also offers samples of student answers, a scoring rubric, and additional narrative material that addresses the nature, construction, and reasons for using open-ended items.

## SMARTR: Virtual Learning Experiences for Students

Visit our student site **SMARTR** to find related math-focused virtual learning experiences for your students! The **SMARTR** learning experiences were designed both for and by middle school aged students. Students from around the country participated in every stage of SMARTR’s development and each of the learning experiences includes multimedia content including videos, simulations, games and virtual activities.

## Careers

**The FunWorks**
Visit the FunWorks STEM career website to learn more about a variety of math-related careers (click on the Math link at the bottom of the home page).

## NCTM Assessment Standards

In its Assessment Principle, the National Council of Teachers of Mathematics (NCTM) supports assessment as “an integral part of mathematics instruction,” stating that

*Assessment should be more than merely a test at the end of instruction to see how students perform under special conditions; rather, it should be an integral part of instruction that informs and guides teachers as they make instructional decisions. Assessment should not merely be done to students; rather, it should also be done for students, to guide and enhance their learning (NCTM 2000, 22).*

Assessment, then, is an ongoing process of gathering information from a variety of equitable sources, such as interviews, observations, open-ended problem solving, and portfolios, as well as the usual multiple-choice and short-response tests. Also, appropriate assessment enhances learning as it guides the teacher in making informed decisions.

NCTM states that much of the actual information gathering occurs during the process of teaching, which leads to the conclusion that a standardized test is not best calculated to determine students’ progress. In fact, “teachers are the persons who are in the best position to judge the development of students’ progress and, hence, must be considered the primary assessors of students” (NCTM 1995, 1).

We hope the resources in this unit will offer you a greater variety of ways to gather evidence of student achievement and insights into connecting assessment to instruction.

**References**

NCTM. 1995. *Assessment standards for school mathematics*. Reston, VA: NCTM

NCTM. 2000. *Principles and standards for school mathematics*. Reston, VA: NCTM

## Author and Copyright

Terese Herrera taught math several years at middle and high school levels, then earned a Ph.D. in mathematics education. She is a resource specialist for the Middle School Portal 2: Math & Science Pathways project. This page was last updated on February 21, 2011. Please email any comments to msp@msteacher.org or join the discussion at our social network for middle school math and science teachers at http://msteacher2.org.

Copyright March 2009 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0840824. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.