Math Matters: Results that Add Up for Teachers and Students

1. Math Matters: Results that Add Up for Teachers and Students Presenters: Bonnie Warren-Kring, Deborah McAllister and John Graef, University of Tennessee at Chattanooga

2. Teacher Ed Faculty Partner with A & S Faculty • Math, Science, Social Science and English faculty devise lesson plans and learning strategies for students in low areas of performance on TCAP tests. • Faculty will focus on the thinking/reading skills needed for success in each of these areas.

3. Literacy Instruction in the Content Areas: Getting to the core of middle and high school improvement(Heller & Greenleaf, 2007) • Students need advanced literacy skills for the intellectual work that the academic disciplines require, • such as conducting and reporting scientific experiments, • analyzing historical sources, or • proving mathematical theorems.

4. Reading Difficult Text • If teachers want their students to be able to handle such assignments, they would do well to help them become more competent in reading difficult texts in general.

5. “For content area teachers, a key challenge is to articulate and make concrete the skills, knowledge, and concepts they may take for granted but that many students need to be shown explicitly… To become an expert is to internalize specific disciplinary standards and to learn how to do certain things more or less automatically…

6. Content area teachers need to understand what is distinct about reading and writing in their own discipline, and how to make those rules, conventions, and skills apparent to students…

7. They may need to help their students to see that such disciplinary styles exist, and that each discipline uses vocabulary, text structures, stylistic conventions, and modes of analysis and debate that are very different from the language students hear at home, or among their friends or elsewhere in school” (Heller & Greenleaf, 2007, p.22).

8. Partnering • Reading is thinking and problem-solving. Content area teachers (math, science, history, English) read, think and write about their discipline in a certain way. • These strategies that content area teachers employ can be translated into strategies to help their students understand the text they read, think and write about in their discipline.

9. Thinking/Reading in Content Areas • The challenge is to make these strategies explicit, first to yourself and then to your students. This process is known as metacognition. • Education and Arts & Science faculty will partner to think about their thinking processes in order to help middle schools students begin thinking in similar ways about the thinking in different content areas.

10. Beginning Stages of Process • Have asked the Hamilton County Director of Evaluation to share the 8th grade areas of lowest performance. • We will then develop thinking/reading processes to apply to those areas of weakness.

11. Possible Difficulties • Specific schools have specific areas of need. One size does not fit all. • Just because we come up with what looks like a good plan, doesn’t mean it will be successful when implemented in the classroom. Pilot lessons, implementation, and evaluation would be necessary.

12. Incongruencies between Curriculum & Testing • Students at this Title I school were all in Algebra I or Algebra 1a. • They were all being taught using the Cognitive Tutor and Carnegie Learning. • However, the TCAP tests other state standards not addressed in the Cognitive Tutor curriculum. Therefore, they would not do as well in those areas. • They also take the Algebra 1 Gateway test.

13. Sample Mathematics Lesson • 8th Grade TCAP - SPI 8.4.8 – Solve problems involving scale factors using ratios and proportions • Design supplemental instruction to address gaps in students’ knowledge not covered by the Cognitive Tutor but tested on the 8th grade TCAP.

14. Scale Factors • Begin the lesson with the motivational book, If You Hopped Like a Frog by David Schwartz. (Show book) • Using vivid pictures and concrete examples, this book captivates and engages students with its real-life examples of scale factors and begins the thinking processes related to ratios and proportions.

15. If You Hopped Like a Frog… • …you could jump from home plate to first base in one mighty leap! • Frogs are champion jumpers. A 3-inch frog can hop 60 inches. That means the frog is jumping 20 times its body’s length. Let’s suppose you are 4 ½ feet tall. If you, like a frog, could hop 20 times your body length (your height), you would be able to sail from home plate to first base, 90 feet in all!

16. Sample cont. • How tall are you? If you could jump 20 times your body length, how far could you go? Measure your height and multiply by 20 to find out! • The book goes on with many such intriguing examples. This hooks the students into thinking about using ratios and proportions.

17. Next you… • …use Chattanooga Math Trail: Community Mathematics Modules designed by Deborah McAllister to bring math concepts to life in the Chattanooga community. • Example: Carousel at Coolidge Park • In this math module, students explore the restored carousel to solve a variety of mathematics problems.

18. # 16. Measure the length, width, and height of one of the carousel animals. • Compare the measurements to those of a live animal (collect data or use resource material) or a porcelain figure or a plastic toy. What is the scale of the carousel animal, as compared to the live animal or figure/toy? Is the carousel animal in proportion to the actual animal (i.e., are all three dimensions at the same scale)?

19. Sample data

20. Connect to text: • After being given this introductory material to scale factors using ratios and proportions, students are then ready to connect what they have just experienced to the mathematics text that they are using in their classroom. • With math ratios and proportions made real to them, students are better able to begin thinking and reading about them from their text.

21. Partners will Develop • At this point, the A&S and Education partners will develop an explicit process of thinking about ratios and proportions that teachers can use to guide students in their understandings. • This thinking process could be used as an evaluation tool to verify the students’ understanding.

22. Community Mathematics • Found at this web site: • www.utc.edu/Faculty/Deborah-McAllister/ • Click on the Chattanooga Math Trail to find the Community Mathematics Modules

23. Geography Example • TCAP SPI 6.1 – Trace the stages of America’s westward growth through the analysis of maps and primary source accounts. • Thinking/reading about maps; reading/thinking about primary documents as they relate to America’s westward movement.

24. Faculty and Metacognition Developing metacognition • Notice what is happening in your mind in everyday situations • Identify various thinking processes you engage in a variety of everyday situations

25. Metacognition cont… • Notice where your attention is when you read • Identify all of the different processes going on while you read • Choose what thinking activities to engage in; direct and control your reading processes accordingly

26. Faculty Partners • Education and A&S faculty work together to make conscious their own reading/thinking processes concerning development of mapping skills in students. • As faculty become more aware of their own processes, they gain new appreciation for the reading/thinking difficulties students may face.

27. Scaffolding Students • Faculty can then begin to scaffold the students in their classes into the reading/thinking about maps and geography by making their own normally invisible comprehension processes (metacognition) visible to their students. • Faculty will develop concrete activities to make the students’ thinking/reading concerning map skills visible.

28. Additional Content Areas • Thinking/reading about English literature • Thinking/reading about areas of science.

29. Application of Lessons • Faculty can apply what they have learned about their own thinking processes to scaffolding students in their classes to become better thinker/readers in their content areas. • I will share the four lesson areas with my content area students to use as models for them when they teach.

30. THEC Application • These lessons can be further developed into units and used as workshops for teachers in public schools. A THEC grant proposal could be written to provide for materials, time, and money to accomplish these workshops for middle school teachers.

31. Areas of Possible Difficulties • Just a beginning. • These content lessons would need to be implemented within the classroom setting and TCAP given to see if the format of these lessons did increase the knowledge, understandings and skills in each of the four content areas tested on the TCAP. • THEC proposal would have to be accepted in order to further this study.

32. Reading Content Area Text Teacher’s for a New Era Mini-grant • Reading in the Content Area Course • Pre/post Preservice Teacher Attitude Survey • Education students tutor middle/high students in reading comprehension skills • Pre/post Bader Inventory with students they tutor • Comparison group tested but NOT tutored • Science and history trade books at CSAS and Orchard Knob Middle School libraries • *A&S and Education Faculty Partner*