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Math PK-2

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Math PK-2>Factors>Linearity

Linearity

Factor Connections

Hover to see how factors connect to Linearity. Then click connected factors to explore strategies related to multiple factors.

Created with Highcharts 6.0.4HearingHearingHome Learning EnvironmentHome Learning EnvironmentSpatial SkillsSpatial SkillsWorking MemoryWorking MemoryEstimationEstimationLinearityLinearityOperationsOperationsPlace ValuePlace Value
Linearity is knowing that the distance between each consecutive number is the same. Children begin considering numbers on a logarithmic scale (e.g., believing the difference between 0 and 1 is much larger than from 10 to 11) and develop a linear understanding over time.
A linear understanding of number is fundamental for the development of Estimation skills, magnitude understanding, and arithmetic performance. Typically, most children develop Linearity; however, the rate at which they do may impact their math performance.

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Research-Based Strategies For This Factor

Cumulative Review

Continual use of foundational skills with different problems reinforces a conceptual understanding of math skills.

Adverse ExperiencesPhysical FitnessSafetySleepSocioeconomic StatusAttentionInhibitionSpatial SkillsSpeed of ProcessingArithmetic Fact RetrievalCardinalityCountingEstimationLinearityMathematical FlexibilityOperationsPlace ValueSymbolic Number
Daily Review

Daily review strengthens previous learning and can lead to fluent recall.

Adverse ExperiencesPhysical FitnessSafetySleepSocioeconomic StatusEmotionAttentionInhibitionSpatial SkillsSpeed of ProcessingArithmetic Fact RetrievalCardinalityCountingEstimationLinearityOperationsPlace Value
Direct Instruction: Patterning

Thinking of and about patterns encourages learners to look for and understand the rules and relationships that are critical components of mathematical reasoning.

Adverse ExperiencesHome Learning EnvironmentPhysical FitnessSafetySleepSocioeconomic StatusMotivationAttentionInhibitionSpatial SkillsSpeed of ProcessingWorking MemoryCardinalityCountingLinearityMathematical FlexibilityOperations
Guided Inquiry

In guided inquiry, teachers help students use their own language for constructing knowledge by active listening and questioning.

Adverse ExperiencesHome Learning EnvironmentPhysical FitnessSafetySleepSocial SupportsSocioeconomic StatusEmotionAttentionCognitive FlexibilityInhibitionSpatial SkillsSpeed of ProcessingWorking MemoryArithmetic Fact RetrievalCardinalityCountingEstimationLanguage SkillsLinearityMathematical FlexibilityOperationsPlace ValueSymbolic Number
Guided Practice

Spending time with new content helps move concepts and ideas into Long-term Memory.

Adverse ExperiencesPhysical FitnessSafetySleepSocioeconomic StatusEmotionAttentionCognitive FlexibilityInhibitionSpatial SkillsSpeed of ProcessingArithmetic Fact RetrievalCardinalityCountingEstimationLinearityMathematical FlexibilityOperationsPlace Value
Individual Deliberate Practice

Practicing until achieving several error-free attempts is critical for retention.

Adverse ExperiencesPhysical FitnessSafetySleepSocioeconomic StatusEmotionInhibitionSpatial SkillsSpeed of ProcessingArithmetic Fact RetrievalCardinalityCountingEstimationLinearityOperationsPlace Value
Math Centers

Math centers with math games, manipulatives, and activities support learner interests and promote the development of more complex math skills and social interactions.

Adverse ExperiencesHome Learning EnvironmentPhysical FitnessSafetySleepSocial SupportsSocioeconomic StatusEmotionMotivationSense of BelongingSocial Awareness & Relationship SkillsAttentionCognitive FlexibilityInhibitionSensory IntegrationSpatial SkillsSpeed of ProcessingWorking MemoryArithmetic Fact RetrievalCardinalityCountingEstimationLanguage SkillsLinearityNon-symbolic NumberOperationsPlace ValueSymbolic Number
Math Games: Numerical & Spatial

Math games use numbers and Spatial Skills, allowing students to practice many math skills in a fun, applied context.

Adverse ExperiencesHome Learning EnvironmentPhysical FitnessSafetySleepSocioeconomic StatusEmotionMotivationAttentionInhibitionSpatial SkillsSpeed of ProcessingArithmetic Fact RetrievalCardinalityCountingEstimationLinearityMathematical FlexibilityNon-symbolic NumberOperationsSymbolic Number
Model Assignment or Skill

By talking through their thinking at each step of a process, teachers can model what learning looks like.

Adverse ExperiencesHome Learning EnvironmentPhysical FitnessSafetySleepSocioeconomic StatusEmotionAttentionInhibitionWorking MemoryArithmetic Fact RetrievalCardinalityCountingEstimationLanguage SkillsLinearityOperationsPlace ValueSymbolic Number
Multiple Representations: Number Line

Easy access to seeing the relationships between numbers promotes number sense as students see these connections repeatedly.

Adverse ExperiencesHome Learning EnvironmentPhysical FitnessSafetySleepSocioeconomic StatusWorking MemoryArithmetic Fact RetrievalCardinalityCountingEstimationLinearityMathematical FlexibilityOperationsSymbolic Number
Real-world Math

When teachers connect math to the students' world, students see how math is relevant and applicable to their daily lives.

Adverse ExperiencesHome Learning EnvironmentSafetySocial SupportsSocioeconomic StatusEmotionMotivationSense of BelongingSocial Awareness & Relationship SkillsStereotype ThreatAttentionInhibitionSpatial SkillsArithmetic Fact RetrievalCardinalityCountingEstimationLanguage SkillsLinearityOperationsPlace Value