Critical Components of a Math Class

By Brandi Crouch

5 Steps to a Balanced Math Programby Larry Ainsworth and Jan Christinson

1. Computational Skills – Math Review and Mental Math

2. Problem Solving

3. Conceptual Understanding

4. Mastery of Math Facts

5. Common Formative Assessments

Step 1: Computational Skills

Math Review Mental Math “Number sense encompasses a wide range of

abilities, including being able to make reasonable estimates, think and reason flexibly, make sound numerical judgments, and see numbers and useful. Students with number sense have good numerical intuition,” Marilyn Burns, 1999.

Math Review

3-5 problems, teacher selected Math Review Quiz on Fridays

Math Review

3-5 problems, teacher selected Math Review Quiz on Fridays

Mental Math

3 problem computational workout for the brain 5 minutes of class immediately after math review Bar diagrams; part-part-whole relationships Mental Math in the Primary Grades Mini-lesson then reinforce in centers Most commonly skipped to “fit more in”, but

grave consequences

Mental Math themes (K-2)

One more/one less Counting by 2s, 5s, and 10s Anchors of 5 and 10 (five frames and ten

frames) Doubles Part-part-whole relationships (fact family groups) Number facts (addition and subtraction) Math vocabulary Measurement concepts

Mental Math Themes (3-5) Number facts (+, -, x, ÷) Combining operations Multiplying/dividing by 10, 100, 1000 Number properties Math vocabulary Fractional parts Skip-counting (3s, 5s, 9s, and so on…) Part-Part-Whole relationships Fraction-decimal equivalency Measurement concepts

Step 2: Problem Solving Focus on process and on communication “Writing in math class supports learning because

it requires students to organize, clarify, and reflect on their ideas – all useful processes for making sense of mathematics. In addition, when students write, their papers provide a window into their understandings, their misconceptions, and their feelings about the content they’re learning,” - Marilyn Burns, 2004.

Problem Solving

Gradual release of responsibility Model, model, model Cooperative groups Pairs Individual

Choose problems that allow them to apply the math they are currently learning

Problem Solving The end goal in grades 3-5 is: “for them

to be able – before the end of the school year – to solve independently a multistep problem and to communicate verbally and in writing the process they used.” p. 33 of Upper Elementary Grades.

The end goal in the primary grades is: “to solve independently a two-step or a multistep problem and to communicate verbally (kindergarten) and in writing (grade 1 and grade 2) the process they used, p. 35 of Primary Grades.

Step 3: Conceptual Understanding

Concept vs. procedure Big Ideas: diving deep rather than

skimming the surface Investigations Introduce, explore, explain, explore,

evaluate

Step 4: Mastery of Math Facts

“Memorization plays an important role in computation. Calculating mentally or with paper and pencil requires having basic number facts committed to memory. However, memorization should follow, not lead, instruction that builds children’s understanding. The emphasis of learning in mathematics must always be on thinking, reasoning, and making sense,” - Marilyn Burns, 1999.

Math Facts

“Fortunately we know quite a bit about helping children develop fact mastery, and it has little to do with quantity of drill or drill techniques. Three components or steps to this end can be identified:

1. Help children develop a strong understanding of the operations and of number relationships.

2. Develop efficient strategies for fact retrieval through practice.

3. Then provide drill in the use and selection of those strategies once they have been developed.”- Van De Walle, 2004.

Math Facts

Pre-assess Teach patterns Provide daily practice Assess Mrs. Hutcheson’s boot camp

About Timed Tests

“Teachers who use timed tests believe that the tests help children learn basic facts. This perspective makes no instructional sense. Children who perform well under time pressure display their skills. Children who have difficulty with skills, or who work more slowly, run the risk of reinforcing wrong practices under pressure. Also, they can become fearful about, and negative toward, their mathematics learning,”- Burns, 1999.

Step 5: Common Formative Assessment

Collaborative Frequent DCAs too short, consider adding 5 more

questions that your grade level develops together

Sample Schedule

Week Mon Tue Wed Thur Fri

1Math Review – 20Prob. solving – 30Concept – 15Math Facts* – 5

Math Review – 20Mental Math – 5Prob. solving – 20Concept – 20Assign h.w. – 5

Math Review – 20Mental Math – 5Prob. solving – 15Concept – 25Assign h.w. – 5

Math Review – 20Mental Math – 5Prob. solving – 15Concept – 25Assign h.w. – 5

Math Review Quiz – 30Concept assess – 20Centers – 20

2Math Review – 20Prob. solving – 30Concept – 15Math Facts* – 5

Math Review – 20Mental Math – 5Prob. solving – 20Concept – 20Assign h.w. – 5

Math Review – 20Mental Math – 5Prob. solving – 15Concept – 25Assign h.w. – 5

Math Review – 20Mental Math – 5Prob. solving – 15Concept – 25Assign h.w. – 5

Math Review Quiz – 30Concept assess – 20Centers – 20

3Math Review – 20Prob. solving – 30Concept – 15Math Facts* – 5

Math Review – 20Mental Math – 5Prob. solving – 20Concept – 20Assign h.w. – 5

Math Review – 20Prob. solving – 15Concept – 30Assign h.w. – 5

DCA/BA Review test results