Chapter 8

Mathematics Assessment

Introduction Math is a cumulative process. Follow continuum of concrete

to abstract. Foundation skills are taught first and new skills build upon

them. Math scope and sequence is essential-teachers use this to

identify skills need to be taught and then direct instruction. New evaluations: criterion-referenced, providing feedback to

students about strengths and weaknesses, formative evaluations rather summative,

Continuous monitoring of student progress How do students represent math ideas by writing,

verbalizing, and through visual representations such as graphs, charts and illustrations?

Students must be directly involved in the learning process: cooperative learning, self-evaluation, using math in real-life situations.

Basic Components Content: understanding mathematical processes

Operations: written or oral calculation skills from counting to solving multi-digit equations using estimation and reasoning

Application: knowledge and ability to use practical math skills (time, money, measurement, graphing, etc.)

Problem Solving: reading, comprehending and solving the computation of word problems

Consumer Skills: real life vocational, survival skills (managing money, banking, purchasing skills)

Section 1

• Mathematical Procedures• Interviews: Teachers, parents and students

• Analysis of math work samples• Observation during math activities

• Student self-assessment• Peer assessment

Interviews Teachers and parents have information about

conceptual and strategic knowledge; a unique perspective.

We can gain insight into students’ dispositions about math, feelings of competency, likes and dislikes, how do they approach math problems?

How do we format an interview? Ask student how he/she would perform a task. Ask student to solve problems non-verbally. Ask students to solve problems verbally.

Math Work Samples Analysis

Look at products: class assignments, board work, worksheets, pages in work book, performance activities

process rather than product Homework Teacher’s observations during work

Self-Assessment Students describe their own competency levels

and confidence Students communicate how they solve problems

and how they identify relevant and irrelevant information

Students let us know what they know and what they need help with

Students take more responsibility for their learning

Students use established criteria to evaluate their own work (and the work of others with peer assessment)

Section 2

• Assessment of Common Mathematical Problem Areas

• Mathematical language assessment• Cultural and language differences• Cognitive factors• Attitudes toward math and emotional factors• Ineffective instruction• Poor abstract or symbolic thinking• Poor reading skills• Failure to use common sense in mathematics• Information processing problems

Types Math Language

Assessment: Students with disabilities have difficulty with math comprehension, organizing, using math language

Cultural Differences: semantics, linguistics, symbols

Attitudes toward Math: positive or negative impact students’ performance

Processing Problems: Unable to process information

Ineffective Instruction: Student may lack good examples, opportunities to apply math

Poor Abstract or Symbolic Thinking: Students need manipulatives, concrete examples, and have difficulties with abstract concepts

Poor Reading Skills or Using Common Sense: Unable to read problems and use logic or reasoning skills

Mathematics Language Assessment Questions to ask: Does the student….

Comprehend the meaning of commonly used math terms (equivalent, place value, minus)?

Recognize the multiple meanings of math terms, such as the same word used as a noun and a verb (circle)?

Grasp the meaning of synonyms that describe the same operation (subtract, minus, take away)?

Understand and distinguish between operational signs and symbols?

Have the ability to use math language appropriately to ask clear questions and, if needed, to say he/she is confused while solving math tasks?

Implementation Have students demonstrate their understanding of

and ability to use math terms correctly. Relationship words: before, after, top, bottom, greater than, less

than, shorter, longer, long, narrow, near, far, in front of, next, between, after, behind.

Have students demonstrate their ability to communicate using math terms, explaining how they solved problems, what difficulties they encountered and what they learned from the process.

Using a math journal, students should select a math problem and explain how they solved it, what was easy, what they learned. Then, students select a math problem that was difficult and explain why. Lastly, students write about how they learn best.

Section 3• Mathematical Assessment Measures

• Mathematics curriculum-based measurement• Curriculum based math probes• Graphing math probe results• Mathematical error analysis• Oral math interview• Task analysis• Checklists• Mathematical inventory• Mathematical journal writing• Performance based assessment• Math Portfolio• Life consumer skills

Types CBM: effective and efficient,

uses math probes; quick and helpful in monitoring progress

CBM Math Probes: times samples that assess skills accuracy and fluency –When graphing results, if scores are below the aimline, teacher should develop interventions to address deficits.

Math Error Analysis: Teacher can identify types of errors-content, operations, applications, problem solving and consumer math

Types of Math Errors: facts, regrouping, incorrect operation, directional, omissions, placement, attention to sign, random errors, calculation errors

Oral Math Review: How students approach a task, solve problems, use information, analyze problems,

Teachers can determine the student’s social-emotional response to math.

Task Analysis: each operation or process is broken down into discrete components

Continued Checklists: way to

monitor progress on IEP goals and objectives and helps with analyzing work samples, interviewing students or observing them.

Math Journal Writing: reflection of own work, self-evaluation, recording own progress

Math Inventory: provides an assessment where skills and concepts are listed, some were mastered, those emerging and those that need to be developed.

Performance Based Assessment: Used to evaluate students’ abilities in developing a product or demonstrate a skill indicating proficiency. The results are used for instructional development.

Math Portfolio: collection of samples over time-teachers can assess competence in problem solving, application, communication, disposition and work habits.

Life Consumer Skills: Daily living skills, application

Samples Math Task Analysis

Prerequisite skills Follows written and oral

directions Matches numerals Visually discriminates numbers Identifies numeral Identifies addition sign States the concept of adding

numbers States the concept of place

value Demonstrates the ability to

regroup numbers. Problem: 571

+ 299

Math Task Analysis Computation skills

Identifies the equation as addition

Adds in right to left direction Recognizes the starting point Adds 1 and 9 Writes a 0 under the 9, in the

ones Writes the 1 above the tens Moves to the tens place Adds 7 under the 9 in the tens Writes 7 under the 9 in the tens Moves to the hundreds Adds the 5 and 2 and carried 1 Writes the 8 under the 2 in the

hundreds

Math Portfolio Scoring

3-consistently demonstrates

2-usually demonstrates

1-inconsistently demonstrates

0-not demonstrated

Evidence that the student:

Selects portfolio artifacts with a clear rationale

Chooses artifacts that are relevant and appropriate

Keeps materials organized Includes artifacts demonstrating

a variety of concepts and skills Articulates why artifacts were

selected States learning goals Notes areas of strength and

weakness Works cooperatively on portfolio Summarizes progress Demonstrates pride in work

Life and Consumer Skills Does the student have mathematical knowledge

and skills needed to deal successfully with basic money, job and daily life experiences?

What we should do….. Provide students with real-life consumer tasks requiring

mathematical problem solving. Identify students’ ability to determine the information

needed, necessary components required and the mathematical processes to be used.

Observe the efficiency and accuracy of the skills they use to resolve the problem.

Section 4• Mathematical Scoring-Rating Procedures

• Mathematical holistic and analytic scoring: Holistic: points awarded for the whole product, Analytic: separate scores for different dimensions of the work.

• Mathematical rubrics: established guidelines or set of criteria

• Mathematical rating scales: Used to evaluate abilities; dimensions to be evaluated, may wish to use a Likert Scale (never, sometimes, always)

Group Activities• Groups 1 & 2• A student in your class is having difficulty with

mathematics. • What pre-referral strategies would you

attempt?• Describe the steps you would follow for the

pre-referral process.• Should a multi-disciplinary evaluation be

conducted?• What assessments would you recommend?

Group Activity• Groups 3 & 4• Design three informal assessment testing

procedures or strategies that can be used with a student having difficulty solving math word problems.

• What factors may complicate this skill acquisition for the student?

Group Activity• Groups 5 & 6• Choose a transition life skill and design three

mathematical performance assessment tasks that could be used to demonstrate the students’ ability to generalize the specific skill selected.

• Share with the class.

Websites Balanced Assessment in Math

http://balancedassessment.gse.harvard.edu ASPECT:

http://www.bgsu.edu/colleges/edhd/programs/ASPECT

2000-2001 Taskbank: http://rda.aps.edu/pdf/donna/website/dirlist.asp