Mathematics Around Us

In this workshop, we will explore the ways we can use the world around us as inspiration for math class. From incorporating student data collection to using the school building as the basis for exploration, there are myriad ways to build lessons that will meet your standards while engaging your students.

Learner Outcomes:

• Create lessons that align to their classroom standards and capitalize on the world their students know
• Reinforce that mathematics is a tool for understanding our world through sensemaking and pattern finding.
• Engage students in mathematics that is meaningful to their lives

Playful Mathematics

This research-based workshop introduces the elements of a playful mathematics classroom. Using straightforward language and classroom-based examples, we will explore how to change any math opportunities into playful ones for your students.

Learner Outcomes:

• Name and apply the principles of playful mathematics classrooms
• Adapt any task to be more playful for students
• Foster lively discussion in their classroom

Patterns & Structures

Mathematics, at its core, is about making sense of the patterns and structures in our world. Yet, we tend to teach it in K-12 as a series of vaguely related concepts. In this professional learning, we will explore some core structures and patterns in mathematics that cut across a wide array of topics. The goal for this is to help teachers rethink how to make connections between and among ideas for their students.

Learner Outcomes:

• Identify key mathematical structures that cut across topics they teach
• Create opportunities for students to engage with pattern finding and sense making in mathematics
• Better understand the ways that mathematicians think about mathematics so they can create experiences that allow their students to engage with “real” mathematics

Fostering Mathematical Discussions

Orchestrating classroom discussions that support student learning takes more

than making good tasks. In this workshop, we will look at best practices for supporting mathematical discussions as well as some practical ways to have discussions in any math classroom.

Learner Outcomes:

• Discuss practices to foster and support a wide range of classroom discussions in their own classrooms
• Experience productive argumentation in ways that allow them to teach with it
• Identify tasks to support math discussions
• Orchestrate discussions so they value a wide range of student ideas while also fostering meaningful understanding

Discussion-Worthy Math Tasks

Building from research on playful mathematics classrooms, we unpack the elements of tasks that make them engaging for students to discuss. We will talk about the four critical aspects that have been uncovered in recent research and the ways those can be built into any math classroom.

Learner Outcomes:

• Name the four elements of discussion worthy tasks
• Alter any task to make it more discussion worthy
• Identify multiple ways playfulness can appear in discussion-worthy tasks

Problem Solving

Problem solving is at the heart of mathematics teaching and learning, but what counts as a problem? And what does problem solving mean if it’s more than just solving a page full of math problems? In this workshop, we will talk about how mathematics education research thinks about problem solving, how open-ended and open-middle problems promote conceptual understanding, and how problem solving can be used in the classroom.

Learner Outcomes:

• Discuss the importance of problem solving for developing conceptual understanding
• Identify tasks that promote problem solving
• Talk about elements of problem-solving heuristics and how they are useful (such as Polya and computational thinking)

Fraction Operations

Fractions are one of the most important ideas in number, yet students struggle to use them and reason about them. In this course, we will explore the root of some common student misunderstandings. We will also explore fractions and fraction operations using a variety of representations and software to support reasoning about them as quantities. Particular attention will be paid to referent units and to the invariant relationships within fractions. Our approach will be grounded in playful discussion and mathematical exploration.

Learner Outcomes:

• Solve fraction problems in a variety of ways ranging from standard algorithm to reasoning about relationships
• Use a variety of drawn and dynamic representations to explore fraction relationships.
• Describe common student misunderstandings about fractions and offer strategies to challenge those misunderstandings

Algebraic Thinking in Middle Grades

In the middle grades, algebraic thinking too often morphs into “algebra” without regard to the development of underlying understandings. In this course, we will explore the kinds of thinking students need to be able to do to succeed in algebra. We will look at moving between representations such as words, equations, graphs, and table. We will talk about patterns and how they support important reasoning, functions and how they are special, and we will look at relationships that are not lines and talk about how to support students in moving beyond linear thinking.

Learner Outcomes:

• Discuss algebraic topics from the perspective of patterns and structures
• Move fluidly between a variety of representations
• Engage with a variety of algebraic reasoning strategies
• Identify instructional approaches to support student learning
• Discuss common misunderstandings students have about algebra and ways to address those

Statistics and Probability in the Middle Grades

We will introduce the GAISE II framework created by the American Statistics Association and consider what it means for teachers and students in middle school as well as how it aligns to current tested standards. Because GAISE II has the goal of developing a statistically-literate public, some aspects of this workshop may exceed the expectations of your current standards. We will engage in following the framework to formulate a statistical question, collect data to answer that question, analyze the data, and create data displays aligned to those in the standards (e.g., dot plots and box-plots). We will also discuss using existing datasets, understanding sampling, and continuous and discrete data.

Learner Outcomes:

• Pose statistical investigative questions that align to a given research topic and that look at variables over time
• Collect and prepare data for statistical analysis using different kinds of data collection
• Use and explain measures of central tendency and key features of distributions (center, variability, and shape)
• Explore patterns of association between variables
• Generalize beyond a sample but also know the limitations of sample information as it relates to the population
• Compare and interpret statistical results

Euclidean Geometry is geometry on the plane. It is the focus of high school mathematics, yet many high school math teachers have not had a chance to take a course focused on this fascinating area of mathematics beyond their own high school experience. In this class, we will use explorations designed for teachers to engage with the ideas of geometry that are taught in the high school classroom. These will include topics of congruence, similarity, symmetry, coordinate geometry, transformations, and some of the basics of right triangle trigonometry. Special attention will be given to laws and postulates that form the basis for the work in the classroom. Work will be done with both paper and pencil and dynamic tools that teachers can use with their own students. While proof will not be the focus of this course, it will be a component of it given the role of proof in the high school geometry course.

Learner Outcomes:

• Engage in all aspects of high school geometry in a way that is grounded in meaningful understanding
• Talk about connections between and among geometry and other areas of mathematics (e.g., equations, right triangle trigonometry)
• Use dynamic tools and traditional tools to explore geometric relationships
• Formulate formal proofs

We will introduce the GAISE II framework created by the American Statistics Association and consider what it means for teachers and students in high school as well as how it aligns to current tested standards. Because GAISE II has the goal of developing a statistically-literate public, some aspects of this workshop may exceed the expectations of your current standards. We will engage in following the framework to formulate a statistical question, collect data to answer that question, analyze the data, and create data displays and numerical summary statistics aligned to those in the standards. We will also discuss randomness, standard deviation, data handling, and other related topics.

Learner Outcomes:

• Formulate questions that can be answered with multivariate statistics, that lead to comparisons and associations, and/or that relate to causality and prediction
• Know how to develop a good data collection plan and the variety of data types that may be used (e.g., survey, experiment, observation)
• Understand bias and confounding variables
• Know to how ethically and responsibly handle data, including issues of privacy and confidentiality
• Summarize and describe relationships among multiple variables
• Identify appropriate ways to analyze and present statistical data
• Describe associations between variables
• Conduct statistical simulations
• Understand and use confidence intervals, standard deviations, outliers, and other measures of variability in interpreting statistical data