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High Quality Math Instruction

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Components of a Balanced Mathematics Program

Conceptual UnderstandingProblem-SolvingComputation/Mental MathMath FactsExplicit Vocabulary InstructionCommon Formative Assessment

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Conceptual Understanding

Concepts are the entry points to understanding mathematics, and are often the most challenging component to teach.

Often students come with inaccurate understanding of concepts, which leads to struggles in other components.

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What would we observe in a quality conceptual lesson?Can use concrete or visual modelsCan use literatureCan see teachers modeling with concrete or

visual modelsCan see students manipulating concrete or

visual representationsCan hear students and teachers discussing

mathematical ideas with appropriate terminology

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Problem Solving

Problem solving involvesUnderstanding which pieces of information are

needed to answer questions about a given situation

translating a situation described in words into mathematical number sentences and/or representing the situation visually

analyzing if any calculations result in a reasonable solution to the given problem

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What would we observe in a quality problem-solving lesson?Students creating visual models to

represent the problemsStudents and teachers discussing

possible methods for solving the problems

Students and teachers analyzing results from calculations

Calculators or addition/subtraction tables and multiplication/division tables available as resources

Few questions, but much thought

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Computation & Mental MathComputational skills build upon conceptual

understanding.Computational skills also build upon

prerequisite computational skills.Students should be encouraged to do as much

computation mentally as possible. Backmapping recently learned skills to

connect them to prior knowledge helps students to gain deeper understanding.

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What would we observe in a quality computation lesson?

Fewer problems and more discussionLinking computation to other standards to

give a context, such as measurement, geometry or data analysis

The use of engaging tools, such as dice, cards and dominoes, that provide visual models

Student justification of thinking

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Math FactsFrom Elementary and Middle School Mathematics: Teaching Developmentally by John Van der Walle

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 ad 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.

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What would we observe in quality math facts instruction?

Preassessment to determine entry pointsInstruction with visual modelsEmphasize patternsEmphasize connections between

addition/subtraction & multiplication/division

Drill and practice through gamesPeriodic assessmentPartnering of students based upon

appropriate levels of development

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What does quality explicit Vocabulary Instruction look like?Using the word lists selected for academic

vocabulary at each grade level helps to focus instruction on key terms.

Introducing terms in practical context with visuals

Utilize the vocabulary notebooks to document student understanding with linguistic and non-linguistic representations

Utilize games for review of termsEmphasize student discussion and proper use

of terminology in context (both written and oral)

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Common Formative AssessmentFrequency of assessments should be high so

that adjustment of instruction is made when needed (minimum 2 week increments).

Assessments should focus on key concepts, skills and vocabulary terms.

Feedback on formative assessments should be timely and specific.

Only summative assessments should be graded.

Tiered MathSamples

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Tier 1 = Core InstructionTier 2 = Interventions Tier 3 = Specialized program

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Trophies

TIER 1

Small groups of 3-8 students ( K-5) 45-225 addi tional minutes weekl y Support Classes Coordinate d with Core Instruction (6-12)

Co-teaching with common plan periods Instruction supports core curriculum

Tutoring connected to core Targeted groups based o n 5 big areas of Math

K-12

Conceptua l Understanding

Manipulatives Visual Represent ations Demonstr ation Literat ure Technology (N LVM, etc.)

Problem Solving Bar Model Drawing Strategies Instruction Calculators, etc. when approp riate

Computation/ Mental Math

I-We-2-You Instruc tion Games

Math Facts Games Flash C ard Prac tice Instruction based on ILS or CRS

Mathematical Language

Explicit Vocabular y Instruction/notebook Small group/partn er discus sions Word Wall

Assessment Common Forma tive Assessment Pretest/Post Test Short Cycle Assessment

K-2 Developin g Number Concepts Camelot Learning (1-5) Do the Math (3-5) [Scholas tic] AMP (3-5) [Pearso n]

I Can Learn (6-8) AMP (6-8) [Pearso n] Camelot Learning (6-8) Correc tive Mat h [SRA]

Individua lized Instru ction Instruc tion may suppor t core curricul um or foundatio n skills (Supplements or supplant s)

Small groups up to 5 students 300-450 minutes per week

Assessment CBM meas ures Short Cycle Probes

TIER 2

TIER 3

K-12 Concret e/Represe ntational/ Abstract Instruc tion Developin g Number Concepts Techn ology

Assessment Assessing Math Concepts (K-5) mClass CBM Measures Short Cycle Probes

Tiered Math Instruction

Action Plan Math

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Roles -- Who is your team’sFacilitator and Recorder?Time keeper?

Let’s review the SAMPLE

Action Plan Math

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Use Your Computer & LCD to complete the reading action plan

Write Student, Professional Development, & Parent Strategies

Monitoring Review using SIP Monitoring Prompt