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INFORMative Assessment: Formative Assessment to Improve Math Achievement, Grades K–6
INFORMative Assessment: Formative Assessment to Improve Math Achievement, Grades K–6
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What is formative assessment? Why do we do it and what do students gain? Formative assessment is not a one-time event. It is not the product or end result of a set of well-defined steps. Rather, formative assessment is a process identified in this resource as INFORMative assessment when it is a collection of strategies that engage teachers and students in becoming partners to support students' learning.

This resource uniquely presents a collaborative learning journey in which educators

  • understand the INFORMative perspective;
  • explore must-have practices; and
  • discuss how to implement them.

More than forty reflections support teachers in confidently

  • evaluating tasks;
  • making inferences about student understandings based on their written work;
  • creating plans to address student misconceptions;
  • developing probing questions;
  • giving actionable feedback; and more.

Each chapter includes a place for you to record notes about your use of INFORMative assessment—the changes in your thinking, your questions, your frustrations, and, most importantly, your successes!

Jeane M. Joyner and Mari Muri
336 pages


ISBN/Item Number: 9781935099192
  • Additional Information
  • Praise for...
  • Author Bio
  • Awards
  • Reviews

"INFORMing yourself about formative assessment is one of the most important journeys you can take as a teacher, and I can’t think of any better guides for your learning adventure than Jeane Joyner and Mari Muri. Their guidebook is easy to read, with the kind of practical guidance and common-sense advice that can only come from years of experience and study. Enjoy the trip!"

Cathy Seeley, Author of Faster Isn’t Smarter: Messages About Math, Teaching, and Learning in the 21st Century
Past President, National Council of Teachers of Mathematics
Senior Fellow, Charles A. Dana Center, The University of Texas at Austin


"Many talk about formative assessment and much research touts its importance, but few have been able to translate the tenets of meaningful formative assessment as effectively as Mari and Jeane do in this wonderfully written and most helpful book. Using a slew of practical examples, classroom vignettes, and student work, the authors bring the powerful ideas of continuously assessing student understanding to life in very accessible ways."

Steve Leinwand, Principal Research Analyst
American Institutes for Research


"Understanding the use and impact of assessments is challenging for many. INFORMative Assessmentcaptures the elusive nature and importance of varied assessments beautifully, including the link to curriculum and instruction and the critical role of formative assessment. As schools and school districts transition to the Common Core State Standards and their related assessments, this amazing resource will become an important “use every day” reference!"

Francis (Skip) Fennell
L. Stanley Bowlsbey, Professor of Education and Graduate and Professional Studies
McDaniel College, Westminster, Maryland
Project Director, Elementary Mathematics Specialists and Teacher Leaders Project
Past President, National Council of Teachers of Mathematics


"In clear, practical terms, the authors show what formative assessment really is and how to implement it in your classroom. The readable style, the examples of student work, and the opportunities for reflection make the use of formative assessment feel doable as well as essential for improving student understanding of mathematics."

Nancy Teague, Grades 4–6 Mathematics Specialist
Greensboro Day School, North Carolina


"Each chapter in INFORMative Assessmentis a professional development handbook packed with strategies to assist teachers with the tools needed to improve instruction; it’s an ideal resource for a district workshop or a college mathematics methods class."

Audrey Jackson
Board of Directors (2005–2008), National Council of Teachers of Mathematics
Director of Professional Development, St. Louis Public Schools, St. Louis, Missouri


"INFORMative Assessmentis a powerful resource for helping districts and teachers move from covering curriculum in their approach to teaching, learning, and assessment to clearly defining learning targets and assessments that inform instruction."

Sally Alubicki
Director of Teaching and Assessment, West Hartford Public Schools
West Hartford, Connecticut


"Getting directly to the heart of the matter, INFORMative Assessmentillustrates beautifully how to use assessment as a tool to impact instruction rather than as a tool to label and rank."

Catherine Twomey Fosnot
Founding Director, Mathematics in the City
Coauthor, Young Mathematicians at Work
Author, Contexts for Learning Mathematics


"This resource helps teachers use formative assessment to better understand student thinking and plan appropriate instruction; it’s an ideal match for today’s emphasis on assessment."

Barbara J. Reys
President, Association of Mathematics Teacher Educators
Distinguished Professor, University of Missouri-Columbia


"INFORMative Assessmentmakes the process of assessment, and the reasons it is critical to student achievement, very clear. It is a wonderful resource for the classroom teacher, as well as teacher leaders looking to build capacity."

Gail Englert
Mathematics Department Chair, W. H. Ruffner Academy
Norfolk Public Schools, Norfolk, Virginia


"Teachers need the support and information that INFORMative Assessmentso carefully and thoroughly presents, and they need it right now."

Miriam A. Leiva
Founding President, TODOS: Mathematics for ALL
Distinguished Professor of Mathematics Emerita, University of NC Charlotte


"Good teaching is not following a script; INFORMative Assessmenttakes teachers on a thoughtful, reflective journey to making instruction decisions based on what their students know and still need to learn."

Kathy Richardson
Program Director, Math Perspectives
Developer, Assessing Math Concepts/AMC Anywhere Formative Assessments

Jeane M. Joyner is a research associate in the Department of Mathematics and Computer Science at Meredith College. A former elementary mathematics consultant and a classroom assessment consultant with the North Carolina Department of Public Instruction, Joyner has taught preschool through college courses. She is the coauthor of Dynamic Classroom Assessment.
Mari Muri consults with schools in Connecticut through PIMMS at Wesleyan University. She was a math specialist with the Connecticut Department of Education and currently serves on several math-related boards of directors.

2012 Finalist Distinguished Achievement Award: Professional Development: Methodology

The Association of Educational Publishers (AEP) Awards seal is recognized by teachers and parents as a mark of excellence in education. Finalist or winner status in the awards tells readers that the product has met rigorous standards for quality, professional content for education.

A review by Professor Bernie Krawczyk at Quinnipiac University in North Haven, CT
icon pdf Download PDF of Review

With my course, Teaching Mathematics in the Primary Grades, the first of two math methods courses, the Teacher Candidates have completed their second semester in a two year program. The mathematics methods classes taught at Quinnipiac University require Teacher Candidates to look at how children learn the mathematics and deepen the Teacher Candidate's understanding of the content through a hands-on and minds-on process. As part of the course, the Teacher Candidates refine lesson planning in order to promote students’ learning of mathematics. As they develop their ability to write lesson plans, the Teacher Candidates take a comprehensive look at assessment. They learn to align their objectives with the CCSS, and show how they can best assess students based on this alignment. For this purpose, the best resource for the learning process of assessment has been the book Informative Assessment: Formative Assessment to Improve Math Achievement, Grades K–6. Jeane Joyner & Mary Muri (2011). We have used the Muri and Joyner book in several ways:  1) For on-going weekly discussions and reflections regarding assessment as it informs instruction; 2) As a resource to develop a variety of ways to informally assess students; 3) To understand how to maximize student learning of mathematics. In one final reflection, a Teacher Candidate wrote:

"In reading Chapter 10 in INFORMative Assessment, I realized just how much we have learned about formative assessment and its impact on teaching and learning in the classroom. I appreciate the importance that is placed on this type of assessment, as I believe it is much more effective than most other types of assessment such as paper-and-pencil tests. I believe that putting in the time to set up an environment that utilizes these strategies will yield much better teaching and increased learning in the classroom. Though I understand that it takes a lot of time and energy, it shows that a teacher really cares about his/her students. I have learned a lot from this book and know that I will take many of the suggestions and strategies with me as I continue my education and as I enter my future career as an educator."

The outcomes of using this book have resulted in an overwhelming advanced understanding by our Teacher Candidates of how informal assessment will and can work in the elementary classroom. The following are some of the wonderful excerpts from the assessment section of some of the Final lesson plans written for this course. These attest to the success in learning about assessment:

  • As the students complete this part of the assignment, I will walk around the room to fill out the assessment checklist. I will also be posing interview questions as an assessment. Since this lesson is a partner activity, I decided to do a checklist and interview questions due to the quick and efficient manner these assessments can be completed. Interview questions will allow me to fix any misunderstandings and it will inform my lesson for tomorrow.
  • Though I will be conducting informal observation and note taking throughout the lesson, and no work will be handed in, I am confident that through the interview process I will be able to tell which students have gained an accurate understanding of grouping materials based on multiple attributes.
  • Based on detailed observations and questions, the teacher will have a comprehensive view of each student's understanding. If a student shows weaknesses or lack of understanding, the teacher is able to assist the student right away—as soon at the problem arises. This allows for faster, more targeted instruction for those who need it. The students who are struggling will be identified in today's lesson, and can be given a review and extra support in tomorrow’s lesson.The students who excel in today's lesson can be challenged in tomorrow's lesson. This form of assessment is very effective, especially in an introductory lesson.
  • Performance Assessment Checklist forms will be filled out with reference to student work on the collected materials, as well as to observations of and communications with students throughout the lesson. Thus, some sections can be filled out (such as writing comments in the comments section) during the lesson as the teacher makes informal observations of students. The forms will be completed afterwards while evaluating the collected student work. These assessments will be formative in nature, used to maintain anecdotal and analytic records as informal evidence of student progress toward mastery of intended content and concepts, which will inform instructional decisions. The forms can also be shown to students to provide actionable feedback and promote mindfulness of their own learning progress. In addition, regular questioning and answering will take place throughout the lesson, in both directions between the teacher and the students, as well as other informal observations of student work, progress, dispositions, etc.; this will both aid in filling out the assessment form and will serve as ongoing formative assessment so the teacher can decide how to adjust and proceed with the lesson during this very period, as well as during the following period. This is an appropriate assessment for this lesson because it evaluates a product that was completed through the natural course of the lesson. The students were asked to measure and label the rectangles so that they could achieve the learning objectives, but the product can be collected as a useful basis for assessment; the form also takes into account performance observable during the actual learning process, including the student’s degree of success or difficulty with the task, quality of participation in discussions, nature of questions asked, success in sorting themselves with other rectangles of equivalent area and/or perimeter, etc. This assessment form is fairly straightforward but provides the option of adding comments so the teacher can include as much detail as appropriate to substantiate ratings.
  • I will use my observation checklist and performance checklist to assess learner's ability to correctly count the amount of whole and half squares within each area of the dinosaur picture. Learners will be given a journal at the end of the lesson. The second observational checklist will be used to determine learner’s ability to use square units when explaining the area of each dinosaur. The observational checklist and journals are forms of assessment to evaluate learner’s knowledge that they have gained. The performance checklist will provide me with an idea if learner’s are "not there yet", "on target", or went "above and beyond" their understanding of area and square units. Based on the observational checklist and journals, 85% of learners have reached the objectives of the day. The objective was to correctly count the amount of squares and half squares within each dinosaur, and then write the answer in terms of square units. Learners will be expected to write down the number of half square units and whole square units on their individual dinosaur sheets. These assessments are appropriate for this lesson because I can determine which learners are approaching the target, on target, or above and beyond. Using journals is beneficial as a source of assessment because it provides a summary of what learners are able to do as they progress in the lesson. As students are measuring their dinosaurs, I will go around the room and observe students in how they determine the total area of the dinosaurs using my observational checklist and interview students individually. Again, roughly 85% of learners should be on target, 10% of learners should be on their way to reach their target, and 5% should have gone above and beyond what I expected of them. Based on these percentages, I know that I will have to work in small groups for the next day with those among the 10%. For the next day’s lesson, I will take a few minutes to review the dinosaur lesson and provide extra guidance for the 10% by going of the activity in a smaller setting and model more examples of how to determine the number of half square units and whole square units. I will also have students teach me as though they were the teacher to get a better understanding of what they may find difficult. I am assured that learners have met, are close to meeting or have not met the performance expected through student engagement, the type of questions asked by students, how many questions are asked, and through these assessments during and after the activity.
  • Assessment: Classroom observation: Listening to student conversations and watching them at work helps me gain insight on student thought processes. It provides another opportunity for understanding/misunderstanding to be revealed. Outcomes: I expect all students to be engaged in thoughtful conversation about their tile arrangements. I want to hear them talking about grouping strategies for quickly counting, and strategies they’ve developed for identifying groupings. I will redirect conversations that seem to be off task or guided by misunderstanding and will lead students toward appropriate conversation through prompts, suggestions, and inquiry into their work.

 

 

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