Making Mathematical Connections
Note: This page describes the Making Mathematical Connections programs that ran from 2009-2012 and from 2015-2017. If your district is interested in collaborating with us to design a professional development program in mathematics for your teachers, please contact Eric Kuennen at firstname.lastname@example.org.
Every year of the program, each participant will attend two weeks of full-day intensive summer workshops on mathematics content. The workshops sessions will be taught using a student-centered collaborative learning model with participants working in small groups, and collaborating vertically between grade levels in order to develop a continuum of knowledge and skills that build from one grade level to the next. Teachers will be supported by five mathematics faculty members in order to maximize participant/ faculty interaction. Following small group work, the faculty will lead larger group discussions of the key content and math practice ideas generated by the problem-solving activities. Each day of the summer workshop will focus on a specific mathematics topic within the Common Core, via three types of sessions:
Problem-Based Inquiry (PBI)
Participants will deepen their understanding of a specific content topic through problem solving in small groups on rich problems designed to spark and sustain conversation about, and exploration of, a specific piece of the Common Core. These sessions will engage the teachers in analyzing solutions and methods, exploring representations, communicating, and making mathematical arguments. These sessions will represent about half of each day’s workshop.
Focus on Children’s Thinking
In the afternoons, we will study children’s thinking and misconceptions about the specific content topic that was the focus of the morning’s problem solving. Participants will appraise children’s methods and discuss whether they are correct and generalizable. We will view video clips of children thinking aloud as they solve problems in order to better understand the ways children reason mathematically. We will also discuss how to respond to common student questions (as established in the research literature) related to the content, and address how to assess student written work (constructed response) in mathematics.
Connections to the Common Core
Finally, each day participants will study how the specific content topic is treated in the Common Core and in classroom lessons. We will analyze lessons and activities, such as from the NCTM Navigations Series and Common-core aligned textbooks and discuss the underlying concepts and the purpose and motivation for their approach. Participants will collaborate in grade bands in vertical teams and present their ideas for how they teach the content in the classroom.
A key component of all workshop sessions will be the focus on making connections in mathematics, not only the connections among the mathematics content studied in the PBI sessions and the curriculum, but also connections among mathematical concepts. Each day, we will visit the Common Core Practice Standards and identify and discuss when the teachers were themselves engaged in each practice during the PBI sessions.
While making connections to children’s thinking, mathematics practices and to teaching strategies, the professional development workshops will be driven by mathematics content in the Common Core. Each year of the program there will be a different content theme. In year one (1) the theme will be “Numbers and Algebraic Thinking”, with a focus on the Common Core content strands of Operations and Algebraic Thinking, Number and Operations in Base Ten, Number and Operations – Fractions, Number Systems, and Expressions and Equations. In year two (2), the theme will be “Geometry and Measurement” with a focus on the Common Core strands of Geometry, Measurement and Data, and Ratios and Proportional Relationships. In year three (3) the theme will be Probability and Statistics, with a focus the content strands of Probability and Statistics, Measurement and Data, and Ratios and Proportional Relationships. While each year will have an identified content theme, the Common Core mathematical practice standards will be specifically addressed and identified in the workshop activities throughout the three-year program. Furthermore, key concepts involving number and algebraic thinking from year one will reinforced throughout the program.
At the end of each workshop day, teachers will be given time to write and submit online a reflection on what they learned that day. Questions to guide their reflections will include “What is the most important or useful thing you learned today?” and “What questions or confusions are you left with today?” These reflections will not only be a learning tool for the teachers, but also formative evaluation tool for the mathematics faculty, as the faculty will read and respond to these reflections by email nightly.
Academic Year Follow Up
During the academic year, teachers will be expected to collaborate in vertical teams to discuss mathematics lessons share data collected on their students. Specific objectives for this collaboration will be provided by the mathematics faculty in the form of “Classroom Projects”. In one classroom project, teachers will be asked to select an upcoming unit from their curriculum and identify the key content and practice standards underlying the unit, and develop strategies and lessons to implement in the classroom that will have a high level of cognitive demand for student understanding. The participants will be charged with implementing these lessons in their classrooms and reflecting on the results. In another classroom project, teachers will be asked to pay particular attention to students reasoning and misconceptions and to collect and analyze examples of student misconceptions and common errors. Teachers will be expected to make use of an online learning community through UWO to facilitate this collaboration and to interact with mathematics faculty during the academic year. These collaborative classroom projects will take place primarily in the Fall in years 2 and 3, and represent 8 contact hours each of those years. In-service time will be provided by the teacher’s district for these activities.
In June of Year 1, there will be one four-hour Opening Workshop that will be focused on the nature of mathematics and mathematical problem-solving, and starting the discussion between teachers and mathematics faculty on interpreting and implementing the Common Core content and practice standards. In January of years 2 and 3, there will be one four-hour workshop during in-service time, focused on classroom implementation of the skills and knowledge that they gained in the summer. This workshop will begin with sessions where participants reflect and discuss the mathematical issues arising their “Classroom Projects” and Content-focused Coaching.