Research-Based Practice to Improve Student Math Outcomes Lynn - - PowerPoint PPT Presentation

Research-Based Practice to Improve Student Math Outcomes

Sourcewell Technology & Spring Math

Lynn Lamers

Who Am I?

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• Classroom teacher for 20 years
• District Math Coordinator for 6 years
• Consultant for national assessment

company for 5 years

• Currently: Implementation Specialist at

Sourcewell Technology

Spring Math

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A comprehensive math MTSS solution for the whole school that aims to improve achievement for all

• Screeners determine classwide or individual need
• Classwide intervention protocols
• Individual Intervention protocols
• Weekly progress monitoring
• Built by Dr. Amanda VanDerHeyden

www.springmath.com

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Proficiency in mathematics is “a socially meaningful action that, in effect, can be an economic gateway to their future lives.”

• Belief-Based Versus Evidence-Based Math

Assessment and Instruction: Amanda VanDerHedyen & Robin Codding

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Greater success in math is related to entering and completing college, earning more in adulthood, and making optimal decisions concerning health.

• Developing Mathematics Knowledge: Rittle-

Johnson, 2017

2017 NAEP Data

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• Only 41% of fourth-graders performed at/above proficiency
• Only 34% of eight-graders performed at/above proficiency
• Rates even lower for students of color or from low-income

homes It is critical to understand how children learn math and how teachers can support the process

Reading Wars

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Reading Comprehension = Language x Decoding

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Myth #1: Timed Assessments are Bad

Timed Oral Reading Fluency

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• We want to check to see if decoding is automatic
• Allows for cognitive capacity to be allocated to

comprehension

• Why is timing acceptable in reading?
• It’s not about speed; it’s about good decision-making
• Indicator of overall reading health
• Consistent way to monitor progress
• We know it’s not the whole of our reading program

Timed Math Assessments

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• Check for automaticity in foundational skills
• Relieves the cognitive load, freeing up resources required

when for complex problems

• Timing gives us superior information about mastery
• Why don’t we accept timing in math?
• Causes anxiety
• Emphasizes speed over thinking
• Communicates that math is all about memorization

The Need for Timed Assessment

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0% 20% 40% 60% 80% 100% 50 100 150

Percent Correct Digits Correct Per Two Minutes

Fluency by Accuracy

(VanDerHeyden, McLaughlin Algina & Snyder, 2012) Mastery Range Instructional Range Frustration Range

Highly unlikely to retain Highly likely to make errors

Evidence about Math Anxiety

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• Positive correlation between math test anxiety and test anxiety
• Negative correlation between math anxiety and math fluency &

performance

• Weak math skills predicted anxiety

Hart & Ganley, 2019; Gunderson et. al., 2018; Namkung, Peng, & Lin, 2019

Evidence about Math Anxiety

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• Teacher mindset: Mastery vs. Performance Orientation
• Student mindset: Incremental vs Entity Framework
• Limitations in working memory hinder math performance
• Offset this by building automaticity
• Less information to keep in mind, more capacity to process new or

complex material

Beilock, 2011 & 2016; Ramirez, 2013; Riccomini, 2016

Teacher Mindset: Hard Work or Innate Ability?

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• Teachers of 5-10 year-olds: Hard Work
• Teachers of 11-14 year-olds: Innate Ability
• Special Ed Teachers: Innate Ability
• More experienced teachers: Innate Ability
• Those who believe math requires brilliance tended to believe

girls lacked the ability

K-8 Teachers’ Overall and Gender-Specific Beliefs About Mathematical Aptitude, Yasemin Copur- Gencturk (2020).

What Can You Do?

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1.

Don’t avoid timed assessments, but don’t overemphasize them either

2.

Target skill deficits

3.

Set goals and focus on growth

4.

Frame it for students to take away the anxiety

• Gamification: “Can you beat your previous score?”
• This is not graded; it’s to help me know what I need to teach you
• Timing is a way to help us see your growth, like a yardstick
• Feedback/practice loop to remedy anxiety

Myth #2: Conceptual Understanding Must Precede Procedural Instruction

How Did We Get Here?

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• State a rule
• Provide

Example

• Students

practice

1700s

• “New Math”
• Teaching for

understanding

• Manipulatives
• “Noisy”

1950s- 1960s

• “Back to

Basics”

• Memorization
• “Tricks”
• Bad language

1970s- 1980s

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Hiebert (1986) described the knowledge types as Procedural Conceptual

• Superficial
• Sequential
• Symbols & syntax
• Rules & procedures
• “Prescriptions for manipulating

symbols”

• Rich in relationships
• Connected web of knowledge

Bi-Directional Relationship

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• Procedural knowledge predicts

and supports conceptual knowledge and vice versa

• Effective instruction includes both
• Both promote procedural

flexibility

Conceptual Understanding Procedural Fluency

Rittle-Johnson, 2017

National Research Council: Adding It Up

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Procedural fluency and conceptual understanding are often seen as competing for attention in school mathematics. But pitting skill against understanding creates a false dichotomy … Understanding makes learning skills easier, less susceptible to common errors, and less prone to forgetting. By the same token, a certain level of skill is required to learn many mathematical concepts with understanding, and using procedures can help strengthen and develop that understanding. (p. 122).

What Can You Do?

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Most math curricula do not contain enough of both procedure and concept-building You will likely need to supplement

What Can You Do?

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Comparing/Contrasting

• Compare incorrect

procedures to correct ones

• Compare examples and non-

examples of key ideas

• Rittle-Johnson, 2017

What Can You Do?

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Self-Explaining

• Links new information to prior knowledge
• Promotes transfer
• Supports retention of correct procedures
• Prompts can help
• Justification prompts (Why is this correct?)
• Meta-cognitive prompts (How does it relate to something else we’ve learned?)
• Step-focused prompts (Can you tell me about the steps you took?)

Rittle-Johnson, 2017

Myth #3: Explicit Instruction is only for Struggling Learners

What is “Explicit Instruction”?

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• Clearly identified goals and success criteria
• Clear & concise modeling by the teacher with input from

students

• Sufficient time for students to practice
• Timely feedback from the teacher
• Main points reinforced at the end of the lesson

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Explicit Instruction is the most effective mathematics instructional practice

 Marzano, 2018  Hattie, 2009  Swanson, 2009, 2011  Gersten, Chard, et al., 2009  National Mathematics Advisory Panel, 2008  Institute for Education Services, 2009

Effect Size of Explicit Instruction: 0.59 Inquiry-based Teaching: 0.31

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• Explicit Instruction is especially effective for students with

math difficulties and other types of disabilities – much more so than “discovery-oriented” approaches

• Also important for typically performing students
• NMAP recommended inclusion of explicit instruction along

with student-centered approaches to core instruction

Elements of Explicit Instruction

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Doabler and Fien (2013)

• Clear & consistent

wording

• Unambiguous

language

• Think-alouds
• Involve students

Teacher Modeling

• Sequence

problem difficulty

• Verbal prompts

(“assessing” & “advancing” questions)

Guided Practice

• Use positive

language specific to the error

• Provide another
• pportunity to

practice

Academic Feedback

Spring Math

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Frustrational Range Instructional Range Mastery Range Restrict task Explicit Instruction Immediate Feedback Task variation Opps to respond Delayed feedback Goals More task variation Feedback may increase briefly Performance Errors

Haring, et al., 1978

Effective Practices

 Timed Assessments to check for mastery  Procedural and Conceptual every day  Explicit Instruction

Thank you!

Lynn Lamers

Lynn.Lamers@sourcewelltech.org