Mathematical+Calculation

Definition and Implications (CDE)
Mathematical calculation includes the knowledge and retrieval of facts and the application of procedural knowledge in calculation. Typically, students with a mathematical calculation disability struggle in the area number and operations.

There is some evidence suggesting two subtypes of students who have disabilities in mathematics. One is a subset of children with a math only disability, the other has both math and reading disabilities. It is known that when reading and math deficits co-exist, both areas tend to be more severely impaired than when occurring in isolation.

PSD Benchmarks

 * Students will know addition and subtraction facts through nines at the rate of 3 seconds per problem by the end of second grade.
 * Students will know multiplication and division facts through nines at the rate of 3 seconds per problem by the end of third grade.

PSD Benchmarks - DRAFT (K. Canine)
**References Used** **Key** + Benchmark is above reference - Benchmark is below reference (PSD K.1.3a, CO K.1a, FC K, EDM K1-) || (PSD K.1.3b+, FC K) || (PSD K.1.2a, FC K) || (PSD K.1.2b, CO K.1a, FC K) || (CO K.2b || (PSD 1.1.3a, CO 1.1a, EDM 1.1f+) || (PSD 1..1.3b, EDM 1.1a,b-) || (PSD 1.1.2b, CO 1.1a) || (PSD 1.1.2b, CO 1.1a, EDM 1.1c+) || (PSD 1.6.1a, FC 1) || (CO 1.2d) || (PSD 1.6.1a, FC 1) || (CO 1.2d) || (PSD 2.1.3a, FC 2, EDM 2.1g) || (PSD 2.1.2b, CO 2.1a, FC 2) || (CO 2.2a, PSD 2.6.3a, FC, EDM 2.1b+, EDM 2.3g) || (PSD 2.6.1a, FC 2, EDM 2.4e+) || (CO 2.2a, PSD 2.6.3a, FC, EDM 2.3h+) || (PSD 2.6.1b, FC 2) || (PSD 3.1.2a, CO 3.2.a, FC 3) || (PSD 3.6.3a, CO 3.4a, FC 3, EDM 3.4d+) || (PSD 3.6.3c, CO 3.4a, FC 3) || (CO 4.2c, PSD 4.6.3a, FC 4, EDM 4.3f) || (CO 4.2a, PSD4.6.4b+, FC) || (CO 4.2c, PSD 4.6.3a, FC) || (CO 4.2a, PSD4.6.4b+, FC) || (CO 5.2a, PSD 5.1.1b, FC, EDM 5.6g) || (PSD 5.6.2.d, FC) || (PSD 5.6.2e, FC) ||
 * Examined grade level expectations for benchmarks that were**
 * Clear – understandable to vast populations
 * Measurable – easy to assess, quick, sensitive to growth
 * Concrete in demonstration – obvious can or cannot meet objective
 * High leverage
 * PSD Standards (PSD Grade.Standard.Benchmark, Indicator)
 * 2009 DRAFT Colorado State Number Sense Standards (CO Grade.Concept and Skill.Evidence Outcome)
 * NCTM Focal Points (FC Grade)
 * Everyday Mathematics Secure Learning Goals (EDM Grade.Unit, Goal)
 * ** Code ** || ** Topic ** || ** Grade ** || ** Sets # ** || ** Description ** ||
 * MC C1.1 || Counting || 1 || 1 || Count by ones to 50.
 * MC C1.2 || Counting || 1 || 2 || Count backwards from 50 to 0.
 * MC N1.1 || Numerals || 1 || 1 || Read numerals from 1 to 20.
 * MC N1.2 || Numerals || 1 || 2 || Write numerals from 1 to 10.
 * MC N1.3 || Numerals || 1 || 3 || Identify numbers one more or one less than a given number up to 10.
 * MC C2.1 || Counting || 2 || 1 || Count by ones to 100.
 * MC C2.1 || Counting || 2 || 1 || Count by ones to 100.
 * MC C2.2 || Counting || 2 || 2 || Count by 5’s and 10’s to 100.
 * MC N2.1 || Numerals || 2 || 1 || Read numerals from 1 to 100.
 * MC N2.2 || Numerals || 2 || 2 || Write numerals from 1 to 100.
 * MC A2.1 || Addition || 2 || 1 || Add whole numbers.
 * MC A2.2 || Addition || 2 || 2 || Demonstrate fluency with basic addition facts through sums to 10.
 * MC S2.1 || Subtraction || 2 || 1 || Subtract whole numbers.
 * MC S2.2 || Subtraction || 2 || 2 || Demonstrate fluency with basic subtraction facts through differences 10 to 0.
 * MC C3.1 || Counting || 3 || 1 || Count by 2’s, 5’s, 10’s and 100’s to 1000.
 * MC C3.1 || Counting || 3 || 1 || Count by 2’s, 5’s, 10’s and 100’s to 1000.
 * MC N3.1 || Numerals || 3 || 1 || Read and write numerals to 1000.
 * MC A3.1 || Addition || 3 || 1 || Demonstrate fluency with basic addition facts to sums to 20.
 * MC A3.2 || Addition || 3 || 2 || Add two-digit whole numbers.
 * MC S3.1 || Subtraction || 3 || 1 || Demonstrate fluency with basic subtraction facts through differences 20 to 0.
 * MC S3.2 || Subtraction || 3 || 2 || Subtract two-digit whole numbers.
 * MC N4.1 || Numerals || 4 || 1 || Read and write numerals to 10,000.
 * MC N4.1 || Numerals || 4 || 1 || Read and write numerals to 10,000.
 * MC M4.1 || Multiplication || 4 || 1 || Demonstrate fluency with multiplication facts with single digit factors of 0, 1, 2, 3, 5, and 10.
 * MC D4.1 || Division || 4 || 1 || Demonstrate fluency with division facts with single digit factors of 0, 1, 2, 3, 5, and 10.
 * MC M5.1 || Multiplication || 5 || 1 || Demonstrate fluency with multiplication facts 0 to 12.
 * MC M5.1 || Multiplication || 5 || 1 || Demonstrate fluency with multiplication facts 0 to 12.
 * MC M5.2 || Multiplication || 5 || 2 || Fluent use of efficient procedures to solve multi-digit whole number multiplication.
 * MC D5.1 || Division || 5 || 1 || Demonstrate fluency with division facts 0 to 12.
 * MC D5.2 || Division || 5 || 2 || Fluent use of efficient procedures to solve multi-digit whole number division.
 * MC R6.1 || Rational Numbers || 6 || 1 || Find equivalent forms of fractions, decimals, and percents.
 * MC R6.1 || Rational Numbers || 6 || 1 || Find equivalent forms of fractions, decimals, and percents.
 * MC R6.2 || Rational Numbers || 6 || 2 || Add and subtract commonly used fractions with like denominators.
 * MC R6.3 || Rational Numbers || 6 || 3 || Add and subtract commonly used decimals.

Probes
[|Numberfly Math Computation Probes]: Early Math Fluency - creates Missing Number, Quantity Discrimination, and Number Identification probes.
 * [|Missing Number Directions]
 * [|Quantity Discrimination Directions]
 * [|Number Identification Directions]


 * **Intervention Central Probe Generators**
 * [|Create Addition Probes]
 * [|Create Subtraction Probes]
 * [|Create Multiplication Probes]
 * [|Create Division Probes]
 * [|Create Mixed Calculation Probes]


 * **SuperKids.com Advanced Operations**
 * [|Create Fraction Probes]
 * [|Create Percentages Probes]
 * [|Create Rounding Probes]
 * [|Create Averages Probes]
 * [|Create Exponents Probes]
 * [|Create Factorials Probes]

Links
[|IES Practice Guide Recommendations] Screen all students to identify those at risk for potential mathematics difficulties and provide interventions to students identified as at risk.
 * Recommendation 1**

Instructional materials for students receiving interventions should focus intensely on in-depth treatment of whole numbers in kindergarten through grade 5 and on rational numbers in grades 4 through 8. These materials should be selected by committee.
 * Recommendation 2**

Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
 * Recommendation 3**

Interventions should include instruction on solving word problems that is based on common underlying structures.
 * Recommendation 4**

Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.
 * Recommendation 5**

Interventions at all grade levels should devote about 10 minutes in each session to building fluent retrieval of basic arithmetic facts.
 * Recommendation 6**

Monitor the progress of students receiving supplemental instruction and other students who are at risk.
 * Recommendation 7**

Include motivational strategies in tier 2 and tier 3 interventions.
 * Recommendation 8**