Elementary ACT meeting

1. Elementary ACT meeting Mathematics DepartmentSeptember 26, 2013

2. Mathematical literacy

3. Warm up Please justify that 25 / 5 = 14

4. Justifying work

5. “revision is where the real mathematics happens” • Dr. Ravi Vakil, 2012

6. Warm up response

7. Clear Learner Objectives • Gain an understanding of why mathematical writing is critical. • Tools for incorporating mathematical writing in class

8. Why write in math class?

9. Research says…

10. In the Texas Essential Knowledge and Skills A(2) “…. in Kindergarten-Grade 2, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use numbers in ordering, labeling, and expressing quantities and relationships to solve problems and translate informal language intomathematical language and symbols. Students use objects to create and identify patterns and use those patterns to express relationships, make predictions, and solve problems as they build an understanding of number, operation, shape, and space. Students progress from informal to formal language to describe two- and three-dimensional geometric figures and likenesses in the physical world. Students begin to develop measurement concepts as they identify and compare attributes of objects and situations. Students collect, organize, and display data and use information from graphs to answer questions, make summary statements, and make informal predictions based on their experiences ” (K-2, Texas Education Agency, 2012)

11. In the Texas Essential Knowledge and Skills • A(2) “…. in Grades 3-5, students build a foundation of basic understandings in number, operation, and quantitative reasoning; patterns, relationships, and algebraic thinking; geometry and spatial reasoning; measurement; and probability and statistics. Students use algorithms for addition, subtraction, multiplication, and division as generalizations connected to concrete experiences; and they concretely develop basic concepts of fractions and decimals. Students use appropriate language and organizational structures such as tables and charts to represent and communicate relationships, make predictions, and solve problems. Students select and use formal language to describe their reasoning as they identify, compare, and classify two- or three-dimensional geometric figures; and they use numbers, standard units, and measurement tools to describe and compare objects, make estimates, and solve application problems. Students organize data, choose an appropriate method to display the data, and interpret the data to make decisions and predictions and solve problems. • (3-5, Texas Education Agency, 2012)

12. It’s in the College and Career Readiness Standards (Texas College and Career Readiness Standards, 2009)

13. It’s part of Mathematics “it centers on proof, argumentation, and perspective, convincing people, making them understand it is central to mathematics…..as a result it’s probably the only subject where elegance in the writing is essential to how we see the subject” - Dr. Ravi Vakil, 2012

14. It matters to mathematicians

15. It supports the development of Academic Language Knowing where the they stand within the content is important, but learning how they acquired the knowledge is relevant to continuing comprehension (D’Ambrosio, 1997) • “There is no one-to-one correspondence between the words and symbols they represent.” • “Mathematics text are conceptually packed, have high density.” • “Require left-to-right as well as up-and-down eye movement.” • “Use numerous symbolic devices such as charts and graphs.” • (Wright, 2008)

16. It enriches teaching practice • Identify student misconception. • Improve delivery of instructions • Deepen classroom questioning

17. Quick Glance Writing is essential in mathematics as it: • Increases and deepens content understanding • Helps Identify misconceptions • Improves lesson planning and delivery of instruction “Writing is nature’s way of letting us see how sloppy our thinking is” (Wolfe, 2001)

18. What should math writing look like?

19. Types of writing • Opinion:Support a choice. The writer must use evidence to clearly argue his/her opinion. • Content: Provide descriptive information about a topic. • K-2 The student uses mathematical (oral) language to express understanding by using words, sentence stems, and full sentences to express and label mathematical content. (progress) • 3-5 The writer must use vivid details to paint a picture for the reader. • Process: Explain the steps or procedures of something. • K-2 The student translates informal language to mathematical language and symbols. By developing summary statements. • 3-5 The writer must provide a clear coherent explanation of problem solving and procedure (Burns 2004, Russek 1998, Schmidt 1985)

20. Example 1a: Mathematics Content Writing

21. Example 1b: Mathematics Content Writing

22. Example 2a: Mathematics Process Writing

23. Example 2b: Mathematics Process Writing

24. Exemplars Word problems that focus on specific math content

25. Betty’s Blocks Betty loves blocks. First she made a tower 2 blocks high. Next to it she made a tower 4 blocks high. Next to those she made a tower 6 blocks high. If she continues this pattern, how many blocks in all will she have used after she has completed a tower 10 blocks high? Elementary School Level Exemplar K-2

26. Betty’s Blocks Student “A” response

27. Betty’s Blocks Student “B” response

28. To the Detail Mike was born on February 20, 1988, at 11:05 a.m. His birthday falls on a Friday this year, but he will be celebrating it with a party on Saturday, February 21, 1998, at 3:00 p.m. On the birthday cake she made, his mom wants to write the exact age he will be at the start of his party. How could she write it? Elementary School Level Exemplar 3-5

29. To the Detail Student “A” response

30. To the Detail Student “B” response

31. Make sure your Math writing includes: • Complete response with mathematical notations. • Clear, coherent explanation. • Clear and labeled diagrams when used. • Shows understanding of the question • Identifies the elements of the question. • Includes examples and/or counter examples. • Combines words with symbols. • Uses correct mathematical notation • Provide details. • Submit neat work (AVID 2008, Lee 2010, Crannell 2008) “elegance in the writing is essential to how we see the subject” Dr. Vakil

32. Writing Practice time

33. Most Importantly… Providing descriptive feedback allows students to learn and understand their mistakes, it also influences and molds the way a teacher conducts instruction. (Barry, 2008)

34. Some Feedback methods

35. Type of feedback

36. FEEDBACK Practice timE

37. Mathematical Writing Frequency * Provide students opportunities to use their notes during a test to encourage good note taking.

38. Please Remember that… “Teachers incorporate writing in math class to help students reflect on their learning, deepen their understanding of important concepts by explaining and providing examples of those concepts, and make important connections to real-life applications of the math they are learning.” (Mathwire.com, 2013)

39. Final Thought “Every year, we buy ten cases of paper at $35 each; and every year we sell them for about $1 million each. Writing… well… is very important to us” Bill Browing, President of Applied Mathematics, Inc.