Elementary Mathematics Pedagogy and Fact Fluency

Vocabulary flashcards covering problem structures, basic fact fluency, assessment alternatives, and operational algorithms for addition, subtraction, multiplication, and division.

Additive Situation Problem Structures

Problem structures involving joining, separating, part-part-whole, and comparison where the unknown can be in any position.

Multiplicative Situation Problem Structures

Problem structures involving equal groups, comparison, area, and arrays where the unknown can be in any position.

Word Problem Solving Methods

Effective approaches that include analyzing the problem, thinking about the answer before solving, working on a simpler problem, and avoiding looking for key-words.

Kindergarten to 2nd Grade Fact Fluency Foundation

Early fact fluency development focused on decomposing numbers and understanding one more and one less.

2nd Grade Fact Fluency Milestones

The expectation for students to have automaticity or mastery of addition facts, while being introduced to multiplication and division fact fluency through exploring doubles.

Addition Strategies

Specific strategies used to help students develop addition fact fluency, including Make 10, Near-Doubles, and Pretend-A-Ten.

Subtraction Strategies

Specific strategies used to help students develop subtraction fact fluency, including Think-Addition, Down under 10, and Take from 10.

Multiplication and Division Fact Strategies

Strategies used to build multiplication and division fact fluency, including Doubling, Add A Group, Subtract a Group, Near Squares, and Break Apart.

Limitations of Timed Tests

Drawbacks of timed assessments: they do not measure fluency or time spent per question, fail to provide needed data on fact knowledge, cause anxiety, and negatively impact number sense and fact recall.

Assessment Alternatives to Timed Tests

Effective alternative evaluation methods including observations, interviews, student self-assessments, and journal writing.

Basic Fact Interventions

Methods for ongoing practice and intervention that involve observing known and unknown facts and reasoning strategies, providing explicit strategy instruction, building in success opportunities, and discussing strengths to provide hope.

Multiplication Algorithm Models

Recording approaches and visual representations used to develop the multiplication algorithm, including area models, open arrays, standard algorithms, and direct modeling.

Division Reasoning Strategies

Strategies grounded in place value and properties of operations, including decomposing, applying standard algorithms, using think-multiplication, repeated subtraction, and fair share.

Division Algorithm Timeline

The developmental timeline for the standard division algorithm, which students are typically introduced to in 4th grade and expected to master by 6th grade.

Computational Estimation Strategies

Strategies used for multi-digit multiplication and division to foster student flexibility and help them identify reasonable answers, including front end, rounding, and compatible numbers.