Foundational Math Skills and Behavioral Insights: KATE Lab Professional Development Notes

Introduction and Presentation Background

• Host & Presenters:
  • Kim Volzendalczak: CEO of KATE Lab. She has over two decades of experience in the education space and has served on a school board in Minnesota for nearly $23\,\text{years}$. She leads growth strategy and innovation at KATE Lab.
  • Dr. Joe Davis: Originally from Wilson, North Carolina. He spent $20\,\text{years}$ in public school districts as a math teacher in middle and high schools, and as a principal across all levels (elementary, middle, and high). He served as a superintendent for $13\,\text{years}$ ($3\,\text{years}$ in North Carolina and $10\,\text{years}$ in Ferguson, Missouri) and a deputy in Chicago Public Schools. His area of expertise is math anxiety.
  • Beau Scott: An Indiana native and Purdue University alumnus. He taught in London, UK, for $4\,\text{years}$ and earned a master’s degree from Purdue in $2016$. He worked as a math and science specialist for the Indiana Department of Education, developing the statewide math framework. He is currently pursuing a doctorate at IU in learning design and adult education, focusing on AI in instructional practices.
• KATE Lab Mission: To support every learner to excel in mathematics through innovation and technology that captures behavioral data.
• Context of the Math Crisis: Math scores have been declining since $2013$. While COVID-19 acted as a catalyst, the decline was a pre-existing trend. The goal is to address the roots of this crisis through foundational practices.

The Core of Mathematics: Number Sense in K-2

• Foundational Importance: Number sense is the bedrock of math. Dr. Joe Davis argues that grades K-2 are the "make or break" years for mathematical development.
• Key Components of Number Sense:
  • Counting: Understanding the order of numbers (first, next, etc.).
  • Cardinality: Understanding the amount or "how much" a number represents. This is often taught using tools like dot cards and $10\,\text{frames}$.
  • Comparing: Evaluating the relative magnitude of different numbers.
  • Composing and Decomposing: Learning how to put numbers together and break them apart.
• The Writing Connection: KATE Lab emphasizes the importance of handwriting in math over clicking buttons on a screen. Research indicates that writing numbers engages the brain, assists in processing, and helps move information into long-term memory, rather than just simple rote memorization.
• Progression to Operations: Proficiency in the "Cs" (Counting, Cardinality, Comparing, Composing/Decomposing) identifies how well a student will transition into basic operations ($\text{addition}$, $\text{subtraction}$, $\text{multiplication}$, and $\text{division}$). Without these, deeper manipulation of numbers is impossible.

Learning Gaps and the "Ruthlessly Cumulative" Nature of Math

• Cumulative Progression: Math is described as "ruthlessly cumulative." A student who lacks a foundation in K-2 will face widening gaps as they enter grades 3-5 and 6-8.
• The Reading-Math Analogy: In literacy, students "learn to read" in K-2 and "read to learn" thereafter. Dr. Davis proposes a parallel: students should "learn to compute" in K-2 so they can "compute to learn" in later grades.
• Critical Transition Points:
  • State testing in the USA typically begins in third grade ($\text{Grade } 3$).
  • Many students enter third grade ill-prepared, leading to "drill and kill" test preparation that ignores conceptual roots.
  • Multiplication is conceptually "repeated addition." If a student does not understand addition, they will struggle with multiplication.
  • Algebra success depends on foundational skills. For example, understanding the quadratic formula in high school requires fluency with fractions and middle-school level logic.

Math Anxiety and the Language of Success

• Language Impact: Phrases like "I'm not a math person" or "I wasn't good at math" create a cycle of math anxiety. This language often transfers from parents and teachers to students, particularly impacting young girls.
• Teacher Preparation: Elementary teachers often have generalist licenses and may not have taken rigorous pure mathematics courses. This can lead to an anxiety towards teaching math, which manifests as a focus on procedures rather than conceptual understanding.
• The History of Math Anxiety: Research into this field began in the $1970\text{s}$ with the Math Anxiety Rating Scale (MARS) by Richardson and Suinn, which identified that feelings toward math directly correlate with performance.
• Addressing Anxiety: Confidence breeds success. Solutions include supporting teacher content knowledge, using high-quality materials, and encouraging a classroom culture where mistakes are welcome as part of the learning process.

Instructional Methodologies

• The CRA Model:
  • Concrete: Using physical manipulatives (e.g., popsicle sticks, pretzel sticks, or counting blocks) to build physical models of math problems.
  • Representational: Transitioning to drawings, graphs, tables, and charts to visualize the math.
  • Abstract: Moving to purely numerical expressions and traditional algorithmic solving.
• Seeing Math in the Real World: Beau Scott advocates for "IC Math" (I See Math) activities, where students and teachers take photos of math in everyday life (e.g., rows of bricks, sets of silverware, clipper lengths in a barbershop which are fractions).
• Automaticity and Mastery: Mastery is generally defined as reaching approximately $80\%$ proficiency. Automaticity involves the quick recall of facts (math muscles), allowing the brain to focus on complex problem-solving rather than basic calculations.

KATE Lab Solution and Behavioral Data

• Behavioral Data Tracking: Unlike traditional software that only marks answers right or wrong, KATE Lab uses a smart pen to capture how a student solves a problem. It tracks where students pause, how long they take (to measure automaticity), and what strategies they use.
• The "Understanding Index": This metric evaluates the student's reasoning and logic beyond the final answer.
• Adaptive Training: The system aligns training with a student's Zone of Proximal Development (ZPD). Training is designed to be in the "sweet spot"—not too easy, but not so hard it causes frustration.
• Digital-Physical Hybrid: Students work with a smart pen on paper (offline) to minimize screen time distractions, then Bluetooth-enable the pen to sync work and receive hints and feedback.
• Case Study Results: In a study from September to January, one class used KATE Lab for $15\,\text{minutes}$ twice a week. Compared to three control classes using traditional iReady training, the KATE Lab class showed significantly higher annual typical growth within just five months.

Questions & Discussion

• Q: Are there tips for bringing physical math learning to a virtual setting?
  • A (Beau Scott): Use low-cost, high-impact household items like paper clips for counting/grouping. Use thumbtacks and yarn to create "hallway math" at home to explore perimeters of complex shapes. Open compound shapes to show how the perimeter remains the same when made concave.
• Q: How should we think about AI tools in math?
  • A (Kim Volzendalczak): Not all AI is created equal. Distinguish between generative AI and toolsets that provide live feedback or track automaticity via time-stamped behavioral data. Behavioral AI can show if a student's understanding is becoming clearer even if they always get the right answer.
• Q: When will I ever use algebra in real life?
  • A (Dr. Joe Davis): Algebra is essentially finding the missing number. Conceptually, it is all around us, specifically in functions. Your pay is a function of hours worked and rate; comparing unit prices (price per sheet of paper towel) is a functional calculation.
• Q: What is the best amount of training time?
  • A: Minimum usage recommended is $15\,\text{minutes}$, twice a week, though it can be integrated into traditional $50\,\text{to } 60\,\text{minute}$ math blocks.