DETAILING PROBLEM SOLVING August 8-9, 2013 “The most basic idea in mathematics is that mathematics makes sense!” Van De Walle (2001)

First. . . Let’s explore our own mathematical reasoning. . . Participants will be given this problem as the enter. Only direction is to solve it in whatever way they choose. Follow with a modified whip around: Everyone stands and one person shares their answer and the strategy they used to solve the problem. Everyone who got that answer and used that strategy sits down. Facilitator writes answer on the board. Continue until all different answers are written

The Changing Landscape of Elementary Mathematics Teaching and Learning 5 min Introduce article: “The Changing Landscape of Elementary Mathematics Teaching and Learning,” from Elementary Mathematics Pedagogical Content Knowledge by James Schwartz. Before reading ask: What is the most significant difference between these two strategies? How is this illustration a metaphor for mathematical thinking?

Mathematics Performance Translated to Real World Performance 78% of adults cannot explain how to compute interest paid on a loan 71% cannot calculate miles per gallon 58% cannot calculate a 10% tip 27% of 8th graders could not correctly shade 1/3 of a rectangle 45% could not solve a word problem that required dividing fractions Witzel, 2012 Ask this question first? Why is process (conceptual understanding) so important?

10 min Video Clip: 4th grade classroom in England where students are solving math problems on number operations. Focus questions: How is process being used to teach content? How are the tasks being differentiated? Give everyone a minutes to jot down a few observations and then share the answers in a table talk.

Process or Content? Dot has two quarters. Jim has three dimes. Hank has a nickel. How much money do they have altogether? I have coins worth 42 cents. What are two possibilities for the coins I might have? 2 min Read these two problems. Turn and talk to your neighbor and decide what is different between the two.

Process or Content? Draw a 6 sided polygon with a perimeter of 40 units. 2 min This time look at both problems, turn and talk again to a different person and decide which type of problem you think each would be.

Problem Solving Process Standards STAAR Content Standards It is only when a student can connect conceptual understanding and procedural understanding that efficient problem solving is possible. The TEA website gives information about what is assessed on STAAR for 3rd - 5th grade; it says that “75% of the questions will combine process standards and content standards.” Content Standards

Demonstration of Learning: Given a content-focused problem and the process standards, teachers will create a new process-focused problem that supports students’ mathematical reasoning. Pass out handout with content-focused questions.

Teachers will write a new process-focused question on chart paper and post it in the room. Then everyone will do a gallery walk to review the problems. Gallery Walk

3 . . . 2 . . . 1 !!! 3 - important points from today’s workshop 2 - things/ideas you will use at your campus 1 - burning question you still have

Thank you! Mark Broughton mbroughton@dallasisd.org Libby Sluder lsluder@dallasisd.org Linda Trujillo litrujillo@dallasisd.org

Resources http://nrich.maths.org excellent source of problems and games https://www.teachingchannel.org/ great source of video clips for all subject areas K-12