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

Research-Based Practice to Improve Student Math Outcomes Lynn Lamers Sourcewell Technology & Spring Math

Who Am I?  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 2

Spring Math 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 3

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 4

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 5

2017 NAEP Data  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 6

Reading Wars Reading Comprehension = Language x Decoding 7

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Myth #1: Timed Assessments are Bad

Timed Oral Reading Fluency  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  10

Timed Math Assessments  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 11

The Need for Timed Assessment Fluency by Accuracy Highly 100% unlikely to 80% Percent Correct retain 60% 40% Highly likely Frustration Instructional Mastery 20% to make Range Range Range 0% errors 0 50 100 150 (VanDerHeyden, McLaughlin Digits Correct Per Two Minutes Algina & Snyder, 2012) 12

Evidence about Math Anxiety  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 13

Evidence about Math Anxiety  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 14

Teacher Mindset: Hard Work or Innate Ability?  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). 15

What Can You Do? Don’t avoid timed assessments, but don’t overemphasize 1. them either Target skill deficits 2. Set goals and focus on growth 3. Frame it for students to take away the anxiety 4. • 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 16

Myth #2: Conceptual Understanding Must Precede Procedural Instruction

How Did We Get Here? • “New Math” • “Back to • State a rule • Teaching for Basics” 1950s- 1970s- • Provide understanding 1700s • Memorization Example • Manipulatives 1960s 1980s • “Tricks” • Students • “Noisy” practice • Bad language 18

Hiebert (1986) described the knowledge types as Procedural Conceptual • • Superficial Rich in relationships • • Sequential Connected web of knowledge • Symbols & syntax • Rules & procedures • “Prescriptions for manipulating symbols” 19

Bi-Directional Relationship  Procedural knowledge predicts and supports conceptual Conceptual Procedural Understanding Fluency knowledge and vice versa  Effective instruction includes both  Both promote procedural flexibility Rittle-Johnson, 2017 20

National Research Council: Adding It Up 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). 21

What Can You Do? Most math curricula do not contain enough of both procedure and concept-building You will likely need to supplement 22

What Can You Do? Comparing/Contrasting  Compare incorrect procedures to correct ones  Compare examples and non- examples of key ideas -Rittle-Johnson, 2017 23

What Can You Do? 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 24

Myth #3: Explicit Instruction is only for Struggling Learners

What is “Explicit Instruction”?  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 26

Explicit Instruction is the most effective mathematics instructional practice Effect Size of  Marzano, 2018 Explicit  Hattie, 2009  Swanson, 2009, 2011 Instruction: 0.59  Gersten, Chard, et al., 2009  National Mathematics Advisory Panel, 2008 Inquiry-based  Institute for Education Services, 2009 Teaching: 0.31 27

 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 28

Elements of Explicit Instruction Guided Practice Academic Feedback Teacher Modeling • Sequence • Use positive • Clear & consistent problem difficulty language specific wording • Verbal prompts to the error • Unambiguous • Provide another (“assessing” & language opportunity to “advancing” • Think-alouds practice questions) • Involve students Doabler and Fien (2013) 29

Spring Math Instructional Mastery Frustrational Range Range Range Task variation Restrict More task task variation Opps to respond Explicit Feedback Instruction may Delayed increase feedback Immediate briefly Feedback Goals Performance Haring, et al., 1978 30 Errors

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

Thank you! Lynn Lamers Lynn.Lamers@sourcewelltech.org