Reflecting on Practice: Making Connections that Support Learning Unit 1, Session 4 2016 Reflecting on Practice Park City Mathematics Institute

Responding to questions Presentations Number Systems bit.ly/pcmi16number Expressions & Equations bit.ly/pcmi16express Ratios & Proportional Reasoning bit.ly/pcmi16ratios Functions bit.ly/pcmi16functions Geometry bit.ly/pcmi16geometry Statistics & Probability bit.ly/pcmi16stats Presentations here: tinyurl.com/pcmi16prezs Great questions from yesterday Respond to your questions on Padlet  Reflecting on Practice Park City Mathematics Institute

There are 3 key findings that come out of How People Learn Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute How People Learn 1.Teachers must draw out and work with the pre-existing understandings that their students bring with them. Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they may fail to grasp the new concepts and information that are taught, or they may learn them for purposes of a test but revert to their preconceptions outside the classroom. Reflecting on Practice Park City Mathematics Institute NRC, 2001

Park City Mathematics Institute How People Learn 2.Teachers must teach some subject matter in depth, providing many examples in which the same concept is at work and providing a firm foundation of factual knowledge. To develop competence in an area of inquiry, students must: (a) have a deep foundation of factual knowledge, (b) understand facts and ideas in the context of a conceptual framework, and (c) organize knowledge in ways that facilitate retrieval and application. Reflecting on Practice Park City Mathematics Institute NRC, 2001

Park City Mathematics Institute How People Learn 3.The teaching of metacognitive skills should be integrated into the curriculum in a variety of subject areas. A "metacognitive" approach to instruction can help students learn to take control of their own learning by defining learning goals and monitoring their progress in achieving them. Reflecting on Practice Park City Mathematics Institute NRC, 2001

Learning progressions These documents indicate what students should have learned when they come to us, but what understanding of these concepts do students actually bring with them? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Pretests One way to find out what understandings students have is to give a pretest. This is a very formal and popular approach, but what are some potential downsides? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Next… a video clip of Nick Branca leading a professional development session with middle school teachers. The focus of the session is on understanding what an equation is. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute As you watch the video, consider: How does Branca elicit and use evidence of what teachers know about equations in the video? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Two truths and a lie 1. a) The only correct answer for 4(x-6)-(x-6) is 3x-18 b) The right answer for 4(x-6)-(x-6) is x = 6. c) 3(x-6) is equivalent to 4(x-6)-(x-6). 2. a) All functions have inverses. b) sin(A+B) = sinA+sinB c) A linear function can have an average rate of change between two points on the line. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute 2 Truths & a Lie Any comments about this technique? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Another technique to figure out what students remember about a topic is “Write everything you know about …” What words do you think students will “remember” about lines? Talk at your table for a minute about what students might say. Reflecting on Practice Park City Mathematics Institute

Brainstorm – words about lines Reflecting on Practice Park City Mathematics Institute

Possible ways to organize ideas Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute In your own classrooms, how do you pre-assess or determine what your students remember? Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute “Unit starters” Short activities pushing students to mentally recall some specific content that will provoke a discussion enabling the teacher to draw and work with the students' previous understandings Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute “Unit starters” In pairs, choose one of the topics below, negotiating at your tables so each pair has a different topic. Law of Sines/Cosines Probability Exponential functions Proportional relationships Volume Identify a grade level, brainstorm the prerequisite knowledge for that grade level, and create a unit starter by modifying one of the examples or create one of your own. Provide a sample student response. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Unit Starters As a group come up with one thing that was really cool that you think the rest of the room needs to hear. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute Readings Read the common assigned section for next class. Then, choose one of the four options As you read, identify two key ideas and one thing you found surprising. Reflecting on Practice Park City Mathematics Institute

Park City Mathematics Institute References Boaler, J. https://www.youcubed.org/tour-of-mathematical-connections/ Meyer, D. https://www.ted.com/talks/dan_meyer_math_curriculum_makeover/transcript?language=en Frayer Model: http://www.adlit.org/strategies/22369/ KWL Chart (Know, Want to Know, Learned) http://www.nea.org/tools/k-w-l-know-want-to-know-learned.html National Research Council. (2000). How people learn. M. Suzanne Donovan, John D. Bransford, & James W. Pellegrino, (Eds.) Commission on Behavioral and Social Sciences and Education. Washington, D.C.: National Academy Press. Reflecting on Practice Park City Mathematics Institute

Other possible unit starters Write into your questions a "memory prompt" that reminds students of an important fact, i.e., use the name hypotenuse in comments before the lesson on right triangle trigonometry. What is the first question that comes to your mind? (Meyer) 3. KWL chart (what do you know, what do you want to know, what did you learn)/ Frayer model Reflecting on Practice Park City Mathematics Institute