Steve Krause – School of Materials Bob Culbertson – Physics

1. High School Teacher Change, Strategies, and Actions in a Professional Development Project Connecting Math, Science, & EngineeringFIE Conference, October 23, 2008 Steve Krause – School of Materials Bob Culbertson – Physics Marilyn Carlson & Mike Oehrtman – Mathematics Arizona State University This work was supported by NSF Grant # 0412537

2. Outline - Project Pathways: Opening Routes to Mathematics and Science for All Students • K-12 Education Issues in Arizona • Project Objectives • Project Courses & Prof. Learning Communities (PLCs) • Connecting Chemistry, Physics & Math (CPCM) Course • Engineering Course Linkages • Implementation of Objectives as Thrusts • End-of-Semester Summary Question for CPCM Course • Math and Science Teacher Sample Responses • Summary and Conclusions

3. Some K-12 STEM Education Issues in Arizona • 45% of K-12 students are persons of color • No HS diploma - 43% Hispanics, 30% Black, 48% Native American • Professional development HS math & science teachers - 2 days/year • 58% HS teachers lack degree in subject taught • Professional development critical for better student achievement

4. Project Pathways Objectives • Increase secondary student achievement in math and science • Close the achievement gap of minority students in each school by no less than 10% • Increase teachers’ ability to reflect on, monitor, and adjust their classroom practices • Deepen teachers’ math for understanding, connections, and science applications • Shift teachers’ practice to inquiry and project-based methods • Improve students’ strategies in problem solving, scientific inquiry and engineering design • Enhance teacher practice and student conceptual learning in ASU’s introductory STEM course • Improve the success rate in ASU introductory STEM courses by no less than 15%

5. Project Pathways Courses and PLCs Four Courses – Each a 3-hour class – one / week for 15 weeks • Functions and Modeling • Connecting Chemistry, Physics & Math (physical sciences) • Connecting Biology, Geology & Mathematics (natural sci.) • Connecting Mathematics, Science and Engineering Prof. Learning Communities (4-6 teachers)– 1-hour meeting each week • Report out on implementation of new pedagogy in own practice – Student understanding, thinking, difficulties, misconceptions • Discuss new pedagogy & content - From current MSP lecture/lab class • Discuss how to implement new pedagogy/content from MSP class – Approaches and issues for each teacher’s classroom practice • PLCs promoted culture of collaboration - Honest, well-facilitated discussions focused on teacher practice strategies, successes, difficulties & failures in implementing approach

6. Connecting Physics Chemistry & Math (CPCM)– Activities & Topics • Activities • Format - one 3-hour class linked with 1-hour PLC each week • Active learning pedagogy - mini-lectures + team-based activities • Data collection & analysis – characterizing physical phenomena with data from sensors recorded with computer data tables and plots • Multiple representations used to record, describe & analyze data - tables, graphs, verbal and written descriptions, sketches of concepts, plotting & equation fitting, characterization of function & phenomena • End-of-class reflection – teacher led about pedagogy and practice • Content understanding - module pre and post tests • Modules • Versions – teacher & student workbooks tying function & phenomena • Proportionality - kinetic motion & gas laws • Exponential decay - sound • Rate of change – Newton’s Laws & physics of motion • Trigonometric functions – vibrations and waves with light and sound

7. Topics – Connecting Science, Math, & Engineering • Introduction to Engineering • Introduction to the Design Cycle • STEM Processes Comparison – Math, Science, Engineering • Design Cycle: Problem Definition, Solution Generation, Decision, Implementation, Evaluation • Engineering Professions • Engineering in K-12 • Balloon Problem: Use of function and physical phenomena with physics of motion and gas laws in the design process

8. Project Pathways Thrusts • Creation of a sustainable culture of collaboration of math and science teachers in PLCs • Deepening knowledge and understanding of concept offunction to promote effective problem solving process skills • Integration of math and science through science and engineering contextualization of math content and processes • Development of classroom strategies and materials for inquiry-based learning activities • Promote teacher metacognition about student knowledge, thinking, and behavior during inquiry activities to better guide student learning

9. Project Pathways End-of-Semester Summary Question • Think back on all the lessons in this course. • What, from the things you learned, have you incorporated into your own teaching? • Include the following categories in your answer: • Concepts from opposite discipline (math teachers should state what science concept they are using, and vice versa), • Teaching methods, and • Reasoning strategies ("speaking with meaning").

10. Professional Learning Community Collaborative Culture Mary, Scottsdale math teacher, in her PLC and CPCM course discovered differences in presentation of math and science now converses to better connect with her students taking physics and chemistry. "A big comparison of math education and science education is that, in science and the real world, nothing is exact or perfect. In math we like to work with exact numbers and measurements. ....What I learned about significant figures has also been very helpful in the math classes I’ve taught. Knowing these concepts has made me a better math teacher because it has given me some real world connections to the math concepts that I teach. It opens up the dialogue between students that are taking physics and chemistry and me. The class has also inspired me to do some experimental activities to teach math concepts.“ Christine, Scottsdale science teacher, learned in the PLC how pedagogy from the CPCM course could be used in her classroom, such as multiple representations data as tables, graphs, bar charts, and equations. ""In Chemistry, we deal with energy of a system all the time. I have started to have my students use bar charts to represent the changes in energy for a system. The visual depiction of the energy really helps them to understand what is happening as the reaction or physical process proceeds forward. ."

11. Deepening Understanding of Concept of Function Paula, Mesa math teacher, found that math could be better explained through using the context of physics of motion. "I have gained so much deeper understanding of concepts that I truly am a better teacher. With the physics background I am planning to incorporate "labs" into my math classes. . . seeing how distance, time, and rate were related and discovering those relationships helped me understand so much more.“ Barb, Scottsdale science teacher, takes advantage of math-science integration because, for some science phenomena, it is only possible to understand it through the use of mathematics. "To understand the science of EM waves and light one needs to comprehend the mathematics behind it. The wavelength is inversely related to the wave frequency. Waves are “in phase” when they coincide peak to peak and trough to trough, and produce a bright spot. These can be produced when the difference in path length is an integer multiple of the wavelength of light. The math formula can be manipulated to receive the result you want in science or the science can be explained by understanding the math."

12. Integrating Math & Science Through Context Hannah, Tempe special education math teacher, contextualized her math with science by using graphs to tell a story of Archimedes taking a bath. “Students could just draw a line showing increase, constant, and decreasing volume of water in the tub, as we filled the tub, turned off the water, put a man in and out of tub….. In doing this lesson, students were able to speak in meaning with terms of speed, average speed, velocity, average velocity, acceleration, and distance, and displacement." Rhonda, Scottsdale science teacher, shifted teaching of Gas Laws from formulaic to a deeper conceptual approach using the proportionality concept to better describe and explain molecular behavior of gasses. “I try to show them what they learn in math has practical applications in science. I also plan on trying to teach gas laws differently next year. I have always taught gas laws by talking about the proportions between the variables in Boyle’s and Charles’ law. We also graph the data so that they can see why one of the gas laws is a direct relationship and the other is an inverse."

13. Strategizing for Teaching by Inquiry Learning May, Tempe math teacher, developed an inquiry "math" lab with graphing calculators to develop an expression for describing the function for position-time relationship for a vertically tossed ball. "I incorporated the use of vertical motion as a real world phenomenon represented in math by a quadratic function. Students experimented and collected data to find how high a ball was thrown into the air. This motivated the students and they were actively engaged in the lesson." Christine, Scottsdale science teacher, uses inquiry experiements to study proportionality concepts to mathematicize the Gas Laws. "Now that I am teaching the Gas Laws, I will require my students to show proportional reasoning as well as the gas law equation approach to solving the problems. I really like the fact that setting up the various ratios will help me confirm whether or not they have grasped the relationship between the different variables (volume, temperature, pressure, and amount) for a gas."

14. Teacher Metacognitively Mediated Student Learning Peggy, Mesa math teacher, says she is focusing more on the students thinking and expression in their learning. "I am more cognizant of 'speaking with meaning'. I do not think I really paid attention to this before these classes. Also, being a student in a frustrating situation has taught me to really pay attention to my student's facial expressions and body language. Through the past two semesters I have been constantly reminded of the importance of modeling my expectations for my students." Frieda, Scottsdale science teacher, probes students' thinking on what data say about the mathematics of the science in classroom experiments. "As a science teacher, the concepts I have tried to use more often in my class include: truly understanding what the mathematical data is saying about the experiments conducted in class, knowing that there is more that one way to solve an equation and allowing the students to know all ways to "attack" a problem, and finally using the mathematical calculations to support or not support the hypotheses (where applicable)."

15. Summary and Conclusions • CPCM course a common hands-on learning experience for math & science teachers • PLCs created a community of collaboration with shared goals, experiences, values, and approaches to facilitate implementing reform in their own practice. • Cultural change promoted with classroom strategies such as using concept of function as a key to understanding math and quantification of science phenomena. • Math teachers integrated math & science through the contextualization of math. • Math teachers promoted inquiry learning through context due to familiarity, relevance & usefulness of context to learner to help clarify the math application. • Science teachers new use of function connected better to physical phenomena. • Science teachers deepened understanding of concept of function allowed them to use more math and new ways to use math in their teaching of science. • Math and science teachers both described ways in which reflections helped devise strategies for integrating math and science for promoting inquiry learning. For additional information contact Steve Krause at skrause@asu.edu OR Go to the web site for the MSP at: http://cresmet.asu.edu/msp