Chapter+11-+Assessing+Math

Weekly Questions







= Six Principles of Math Instruction =

6 Technology- essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances student ’ s learning
= Readiness for Number Instruction =


 * == Several concepts are basic to understanding numbers: ==


 * === Classification- the study of relationships such as likenesses and differences ===


 * === ordering and seriation- ordering items on the basis of change in a property, such as length, size, or color ===


 * === one-to-one correspondence- basis for counting to determine how many, and is essential for mastering computation skills ===


 * === conservation- a fundamental to later numerical reasoning. The quantity of an object or number of objects in a set remains constant regardless of spatial arrangement. ===


 * == Mastering these concepts is necessary for learning higher-order math skills. ==

= Readiness for More Advanced Mathematics = Axiom: proposal that’s assumed without proof for the sake of studying consequences that follow from it.
 * == Once formal math instruction begins, students must master operations and basic axioms to acquire skills in computation and problem solving. ==
 * == Operations: ==
 * === addition ===
 * === subtraction ===
 * === multiplication ===
 * === division ===
 * == Some axioms that are especially important for teaching math skills to students with learning problems are: (def and example) ==
 * === commutative property of addition- no matter what order the numbers are combined in the sum remains constant (a+b=b+a) ===
 * === commutative property of multiplication- regardless of the order of numbers eing multiplied the product remains constant (a x b=b x a) ===
 * === associative property of addition and multiplication- regardless the grouping arrangements the sum of the product is unchanged ((a+b)c=a+(b=c)) ===
 * === distributive property of multiplication over addition- this rule relates the two operations (a(b+c)=(a x b)+ (a x c)) ===
 * === inverse operations for addition and multiplication- axioms relate operations that are opposite in their effects (a+b=c, c-a=b, c-b=a and a x b+c, c/a=b, c/b=a) ===

= Assessment Considerations = >> == == >> >> == == >> >> == == >> >> == == >> >> == == >> >> == == >> == Many students with learning problems produce accurate answers at a slow rate and use tedious procedures (such as counting on fingers and drawing tallies for large numbers) to compute answers without understanding the math concept or operation. Slow rates of computation are a primary problem of many students with math disabilities. ==
 * == Examining Math Errors: ==
 * === Computation- errors in computation can be classified into foru categories: random responses, basic fact error, wrong operation, and defective algorithm ===
 * === Problem Solving- primarily are assessed by means of word problems. ===
 * == Determining Level of Understanding: ==
 * === Concrete- involves manipulation of objects ===
 * === Semiconcrete- involves working with illustrations of items in performing math tasks ===
 * === Abstract- involves the use of numerals ===
 * === Algorithm- set of rules for solving a problem in an infinite number of steps ===
 * == Many students with learning problems produce accurate answers at a slow rate and use tedious procedures (such as counting on fingers and drawing tallies for large numbers) to compute answers without understanding the math concept or operation. Slow rates of computation are a primary problem of many students with math disabilities. ==
 * == Determining Level of Understanding: ==
 * === Concrete- involves manipulation of objects ===
 * === Semiconcrete- involves working with illustrations of items in performing math tasks ===
 * === Abstract- involves the use of numerals ===
 * === Algorithm- set of rules for solving a problem in an infinite number of steps ===

= Formal Math Assessment - Diagnostic Tests =
 * == In contrast to achievement tests, diagnostic tests usually cover a narrower range of content and are designed to assess the student ’ s performance in math skill areas. Diagnostic tests aim to determine the student ’ s strengths and weaknesses. No one diagnostic test assesses all mathematical difficulties. The examiner must decide on the purpose of the assessment and select the test that is most suited to the task. ==
 * === Comprehensive Mathematical Abilities Test- includes 6 core subtests that focus on addition, subtraction, multiplication, division, problem solving, and charts, tables and graphs. ===
 * === KeyMath — 3: Diagnostic Assessment- comprehensive norm-referenced measure of essential mathematical concepts and skills. ===
 * === Test of Early Mathematics Ability — 3- test of early math functioning takes aout 40 minutes to administer and measures informal as well as formal concepts and skills. ===
 * === Test of Mathematical Abilities — 2- in addition to information about a student ’ s skills in two major areas, story problems and computation, test provides relevant related information regarding expressed attitudes toward mathematics, understanding of mathematical vocabulary used in a mathematical sense ===

= Informal Math Assessment =
 * == Informal assessment involves examining the student ’ s daily work samples or administering teacher-constructed tests. Informal assessment is essential for the frequent monitoring of student progress and for making relevant teaching decisions regarding individual students. ==
 * == Curriculum-Based Measurement- offers teacher a standardized set of informal assessment procedures for conducting a reliable and valid assessment of a students achievement within the math curriculum ==
 * Identify a sequence of successive skills included in the school curriculum
 * Select a span of math skills to be assessed
 * Construct or select items for each skill within the ranged selection
 * Administer and score the survey test
 * Display the results in a box plot, interpret the results, and plan instruction
 * == Teacher Constructed Tests- essential for individualizing math instruction ==
 * Select a hierarchy that includes the content area to be assessed
 * Decide on the span of skills that needs to be evaluated
 * Construct items for each sill within the range selected
 * Score the test and interpret the student’s performance
 * == Assessment at the Concrete, Semiconcrete, and Abstract Levels – learning math facts and concepts progress through three levels of understanding, concrete, semiconcrete, and abstract. ==
 * == Diagnostic Math Interviews – as curriculum area math is different from other subjects ==

Teaching Students with Learning Problems, 8th Edition, Cecil D. Mercer; Ann R. Mercer; Paige C. Pullen (2011)