Momentum: Building Capacity for Change through Connections

1. Momentum: Building Capacity forChange through Connections Ann Assad and Lauren Wells Austin Peay State University Clarksville, Tennessee

2. Presented at the MTSU STEM Research Conference February 7, 2014 Murfreesboro, TN

3. Momentum: Building Capacity for Change through Connections was an 18-month professional development project funded by the Tennessee Higher Education Commission First to the Top Program, supported by Race to the Top.

4. Goal: To increase student achievement in mathematics by increasing elementary teachers’ capacity to teach mathematics in a STEM-centered environment.

5. Objectives • Deepen elementary teachers’ content knowledge of the Common Core State Standards for mathematics through problem solving. • Broaden elementary teachers’ pedagogical content knowledge by making connections to children’s literature and science and by incorporating appropriate technology. • Strengthen teachers’ understanding of the role of STEM in developing numeracy. • Deepen students’ understanding of the core concepts of algebraic thinking, measurement, and data analysis.

6. Children’s literature and stories provided engaging contexts in which to address these objectives.

7. Attention to numeracy guided task selection in the Momentum Project. Numeracy – The capacity for quantitative thought and expression • Practical numeracy – applications to daily life • Civic numeracy – ability to draw inferences from data related to issues that benefit society. • Professional numeracy – computational and analytical skills related to the workplace • Numeracy for leisure and cultural numeracy –understanding of the role of mathematics in games, puzzles, art, music, and dance

8. Components of Momentum • Eight Saturday workshops • Problem solving journals • Transitions to the classroom through development of lessons connecting literature, mathematics, and science. • Support through materials, professional memberships, and conference attendance • Online workshops • Weeklong summer academy

9. A Crow, half-dead with thirst, came upon a Pitcher which had once been full of water; but when the Crow put its beak into the mouth of the Pitcher he found that only very little water was left in it, and that he could not reach far enough down to get at it. He tried, and he tried, but at last had to give up in despair. Then a thought came to him …What did he do?

10. Common Core Content State Standards for Mathematical Practice1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.

11. In Saturday workshops, participants engaged in mathematics and science activities based on selections from children’s literature.

12. The boy said, “We’ve got a tree in our yard. It grows abut six feet every year. If I had grown at the same speed, I’d now be almost fifty feet tall!”How old is the boy?

13. Activities and problems were designed to deepen participants’ content knowledge as well as engage them in reading and writing about mathematics.

14. Participants kept journals of their own problem solving, reflecting on their own methods as well as the thinking of others in the class.

15. Based on their problem solving experiences, they created classroom lessons and shared student work samples with other participants.Their reflections were framed by a Mathematical Thinking Record based on the work of Mark Driscoll at the Education Development Center.

16. Mathematical Thinking Record The purpose of the Mathematical Thinking Record is to help you remember important mathematics aspects of this problem a year from now, when you might want to use this problem with your class or just refresh your own memory.1. Statement of the problem and your solution.

17. 2. What would you like to recall about the different strategies, solutions, and representations used by you and your colleagues? Record the mathematical approaches and strategies that you would like to remember.3. What would you like to recall about how the problem solving process affected your understanding of mathematical concepts? Record the specific topics or areas that this problem addressed in the different solutions and how your understanding was enhanced.

18. 4. What would you like to recall about the different strategies, solutions, and representations used by your students? Record the mathematical approaches and strategies that you would like to remember. ATTACH SAMPLE STUDENT SOLUTIONS.

19. Support • One Marilyn Burns math and literature kit – Grades K-1, 2-3, or 4-6 • Geometer’s Sketchpad ™ • Key Curriculum Tinkerplots™ software • Collection of four children’s books used in monthly workshops of summer academy. • NCTM membership • Mid-Cumberland Reading Association membership • Travel to Tennessee Mathematics Teacher’s Association Conference at which some participants presented sample lessons. • APSU STEM Center resources and a collection of research articles related to project goals.

20. Online workshops provided more in-depth studies of issues raised in the workshop. Example: In the middle of a lesson on creating scatterplots with Excel, a teacher asked how she could graph two sets of data on the same axes. We created an online workshop to address this topic through an example with a contextual problem.

21. In the weeklong summer academy, participants continued investigations of content and pedagogy and shared their ideas.

22. Example: Participants grew animals and measured length, area, and volume. They graphed the results.

26. Evaluation: Mathematics Content KnowledgeParticipants took a 25 question pre-test and post-test.

29. Sample Questions: Participants showed improvement on most questions, but there was little improvement on the following two questions. Problem 6: In the equation y = 4x, if the value of x is increased by 2, what is the effect on the value of y? Problem 12: Write a mathematics word problem for which 3 ÷ 1/2 would be the method of solution.

30. Question 2. The graph at the left shows distance versus time for a race between runners A and B. The race is already in progress, and the graph shows only the portion of the race that occurred after 11 A.M. In the space below, describe everything you know about the situation. Show your work or explain your answers (modified from NAEP 2011 question samples). Throughout the project, the participants joked about Runner A and Runner B and what they could have been doing. Because of participant interest, several problems were introduced related to this concept.

32. Score on the following problems increased significantly. • Questions 19: A rectangular pool 24 feet long, 8 feet wide, and 4 feet deep is filled with water. Water is leaking from the pool at the rate of 0.30 cubic foot per minute. At this rate, how many hours will it take for the water level to drop 1 foot? • Question 20: Suppose the pool in the previous problem is twice as long, twice as wide, and twice as deep. Will it take twice as long for the water level to drop 1 foot? Explain your answer.

33. Question 22: A machine for producing choco-nuts gives 5 choco-nut hearts for every 4 • chocolate bars and ½ cup of nuts put into the machine (nothing is lost in the • machine). Solve the following by reasoning. • (A) How many hearts would the machine give for 18 bars and the right amount of nuts? • How many cups of nuts would be the right amount for 18 bars? • Question 23: In the previous problem, an order comes in for 48 hearts. How many bars and how many cups of nuts would be needed to fill the order?

34. 24. In an experiment, the number of organisms on a plate had the following growth pattern. At the end of three days, how many organisms will be on the plate? • 25. For the above problem, write a general rule that will give the number of organisms on the plate after n days.

35. Some comments from Participants I really liked the hands-on activities. They allow us to experience the activity as our students might. It allows for discussion about possible modifications needed depending on the level you teach. It also promotes discussion about problem solving strategies. Meeting with our grade levels and sharing experiences from teaching the activities from the previous session gives us the opportunity to share experiences. It helps us to see how to tailor the same story to different levels and skills… Integrating literature and math allows the student to see the relevance of the learning. Teaching math in isolation is a futile task if you expect the student to apply the information in real life settings. The math was a great refresher for me in upper level math (above 2nd grade).

36. Today I learned that you can gain so much from including more literature in your math lessons. As a K-2 teacher I already use many books to teach lessons. This session today has shown me many great ideas that I can adapt to use in my classroom. I also had a refresher course on some of the math that I don’t often use in my teaching small children. This is a great workshop that I have really been enjoying especially the tangrams from the last story Grandfather Tang’s Story. There were a variety of ideas that I took away from the activities with The King’s Chessboard. I loved the hands-on with the chessboard and the rice allowing for discovery! I am finding that using the materials and ideas in the Momentum project are enjoyable for me and beneficial for my students.

37. I know I am stronger algebraically, and it surely showed with the cutting of the tangrams. I couldn’t set it aside until I got it. It makes me hate the fact that too often I am forced to move on when I have some who ant to get it and probably could if given enough time. The book, Who Sank the Boat, was a great math and science link. To introduce subjects like buoyancy and relate it to weight and surface area was a great experience for my students. I really enjoyed the sharing of the activities for Who Sank the Boat. The other fourth-grade teachers had some fantastic ideas. I liked the idea of using Each Orange has 8 Slices to teach fractions of a whole number. My students always seem to struggle with that on standardized tests and I believe the literature will help their understanding greatly.

38. Contact us: Ann Assad assadd@apsu.edu Lauren Wells wellsl@apsu.edu

39. Selected References Used in the ProjectAllen, Pamela (1996). Who Sank the Boat? ISBN 10: 069811373X Anderson, Gavin, Dailey, Stone, & Vuolo (2005). Navigating through Measurement in Grades 3-5 (NCTM). ISBN: 0-87353-544-8 Birch, David (1993). The King’s Chessboard. ISBN-10: 0140548807Clement, Rod (1994). Counting on Frank. ISBN-10: 039570393XCronin, Doreen (2004). Duck for President. ISBN 978-0-689-86377-6Dee, Ruby (1999). Two Ways to Count to Ten. ISBN 10: 0833543121 DiPucchio, Kelly (2008). Grace for President. ISBN:978-1-4231-3999-7 Driscoll, M. D., Ellis, J., Hammerman, J., Zawojewski, J., Humez, A. & Nikula, J. (2000). Algebraic Thinking Toolkit. Newton, MA: Education Development Center, Inc. (An update of this is available through Heinemann: ISBN 978-0-325-02865-1 / 0-325-02865-6 / 2009 / bundle.) 

40. Grifalconi, Ann (1986). The Village of Round and Square Houses. ISBN 0-316-32862-6 Mozelle, Shirley (1994). Zack’s Alligator Goes to School. ISBN 13: 978-0-06-44248-0Thaler, Mike (2003). The Class Election from the Black Lagoon. ISBN 13: 978-0-439-55716-0Van Dyke, Frances (2002). A Visual Approach to Fractions. ISBN: 1-55953-537-7Winters, Kay (2004). My Teacher for President. ISBN: 0-439-69995-9