FLEXIBLE LEARNING-FOCUSED CONTENT KNOWLEDGE
Most teachers begin their careers drawing on their own experiences as mathematics learners. When those experiences were successful, and they naturally become a touchstone for how teachers understand what learning looks like and how mathematics should be taught. Challenges arise when students’ dispositions, strengths, experiences, and backgrounds differ from those of their teachers. Even when teachers have deep knowledge of mathematics, they need flexible learning-focused content knowledge to recognize where students are mathematically, anticipate how students might make sense of an idea, and adapt instruction to support growth.
Our workshops engage teachers grades 4 – 20 as learners of mathematics and deepen their content knowledge for teaching.
Teachers experience mathematics as learners in an environment that supports deep understanding and positive dispositions toward math.
On the fifth day, teachers reflect on their experience as learners and plan how to take that experience into their own classrooms.
Topics include:
Ratio & Proportional Reasoning
- rates, ratios and unit rates,
- scale and scale factor,
- what it means to reason proportionally,
- connections between proportional relationships, lines and linear relationships,
- the role and importance of clear communication using proper mathematical language and notation.
Functions
- coordinate graphing,
- transformations and their relationship to root functions,
- linear and quadratic relationships,
- rates of change and their connection to algebraic representations,
- geometric representations of linear and quadratic relationships.
Rational Numbers
- number theory including order of operations, and properties of number,
- equivalency with fractions, decimals and percent,
- computation with fractions and decimals,
- representing computation with rational numbers geometrically,
- Apply understanding of operations of whole numbers to operations with fractions and decimals,
- the nature of learning and characteristics of an optimal learning environment, and
- ways of assessing mathematical understandings.
Expressions & Equations
- Apply and extend previous understandings of arithmetic to algebraic expressions,
- Reason about and solve one-variable equations and inequalities,
- Represent and analyze quantitative relationships between dependent and independent variables,
- Use properties of operations to generate equivalent expressions,
- Solve real-life and mathematical problems using numerical and algebraic expressions and equations,
- Work with radicals and integer exponents,
- Understand the connections between proportional relationships, lines, and linear equations.
Probability
- theoretical and experimental probability
- diverse models for determining probability (for example: area models, tree diagrams, organized lists, matrices)
- events, possible outcomes, defining and constructing sample space
- Law of Large Numbers
- computation and interpretation of expected value in simple cases
- inductive and deductive reasoning
- mathematically convincing arguments
Data Science
- analyzing data and statistical arguments
- collecting and organizing data as a means of answering questions
- identifying trends in data
- tools to organize, interpret and represent data (for example: box and whisker, stem and leaf, circle graphs, line plots, histograms, scatter plots)
- measures of center, spread and shape
- normal distribution and standard deviation
Teacher growth takes time, community, and reflection. Effective teachers know mathematics, know their students, and have multiple ways to help students make sense of important ideas. Decades of mathematics reform have had limited impact, in part because we have not sufficiently invested in sustained, supported teacher learning.
Partner with us to bring learning focused content knowledge to your teaching team.
“As teachers, we sometimes forget how hard learning something new can be. Through these workshops, we were able to experience working hard to solve a problem, feeling frustrated at not reaching understanding yet, having our “aha” moments. Learning math differently and more deeply than I did when I went through school has been extremely valuable for me both as a student and as a teacher of mathematics.”
Middle School Teacher, WA
