Teacher Profile

Name	JoAnn and Richard
Experience	Combined, 40 years
Grade & Subject	Grade 2; all subjects
Classroom	Elementary school in a suburb
Demographics	Combined, 40 students
Science Teaching	Daily
Curriculum	Specified by district
Other	Piloting integrated mathematics and science program; offering professional development to colleagues



Contents

• Module 1 Introducing the Case
• Module 2 Trying New Ideas
• Module 3 Reflecting and Building on Change



Module 1 -- Introducing the Case Following four weeks of intensive summer training in integrating mathematics with science and other subject areas, Jo-Ann and Richard implement what they have learned in their classrooms. Richard chooses to integrate literature, science, and mathematics by means of reading aloud the story of Johnny Appleseed and then asking students to describe and to classify four varieties of apples. Following a taste test, students record their favorite, predict the most popular, and then graph their results on a class picture graph. Jo-Ann decides to integrate the mathematics skill of recognizing coins and understanding their values with science in an activity where students estimate, then find the actual number of drops of water that will fill the surface of a coin without overflowing. Students compare their findings and propose ideas about the nature of water to explain what happened.  How Many Drops? Each student estimates how many drops of water the surface of a nickel and a penny will hold before the water overflows. Next, using an eyedropper, students find the actual number to check their estimates, always recording their data. A worksheet serves as a bar graph to compare the estimates with the actual number of drops for each coin.  Discussion Questions How would you compare the Apple Tasting activity and the "How Many Drops" activity with regard to the effective integration of science and mathematics?        Given the traditional practice of separating curriculum content areas, what do you think are the greatest challenges in integrating science and mathematics?        What criteria would you use to assess whether science and mathematics are integrated effectively in classroom activities?        

Module 2 -- Trying New Ideas "Secret formulas" activities provide students the opportunity to use both mathematics and science skills as they become inventors who are challenged to derive formulas, with given ingredients, for making paste and cola. In the process students develop their own problem- solving strategies, make decisions, and communicate findings. These young inventors discover for themselves the attributes of the different ingredients and carry out their own experiments. Jo-Ann and Richard meet with Dick Konicek of the University of Massachusetts, Amherst. He suggests that by being aware of the potential partnership between mathematics and science in answering questions and solving problems, teachers can help ensure that students realize the value of integrating both disciplines.  Secret Formulas Activities Students use given ingredients to derive formulas for making paste and cola. This involves making estimates, measuring ingredients, recording data, and graphing results. Students carry out experiments, adjusting formulas to make the best of each item. In the case of the cola formula, the young inventors conduct a taste test, decide upon the best formula, use mathematics to expand the quantities to create enough for the entire class, and then embark on "marketing" their product with a package design and advertising campaign.   Discussion Questions In the paste formula activity, how would you describe the mathematics component? The science component? The integration of the two disciplines? How would you compare this to the cola activity?        In your experience, how do mathematics and science "fit together?" Under what conditions do you think an "equal partnership" is possible?        What circumstances foster the effective integration of mathematics and science, as well as other subject areas?          

Module 3 -- Reflecting and Building on Change With summer vacation just around the corner, Jo-Ann and Richard sponsor a Bubble Festival. Parents are invited to assist in bubble activities with students. Stations feature many open-ended investigations of soap bubbles, several of which engage students in using their mathematical skills and understandings. Students rotate through several stations, making bubbles and observing their properties. As with other activities that are being piloted throughout the school year, Richard and Jo-Ann facilitate a professional development workshop with their colleagues. In critiquing the first Bubble Festival, teachers decide they will try to set up a different management system in the future, freeing up their time for more of those "teachable moments" that can act as catalysts to reaching goals for student understanding.  Bubble Festival Stations feature soap bubble activities that are designed for students to participate in open-ended, interactive investigations that explore the properties of bubbles.  Discussion Questions With regard to effective mathematics and science integration, how would you compare the Secret Formulas activities with the Bubble Festival?        Using content that is appropriate to your present or future teaching situation, how would you describe an activity that you feel shows effective integration of mathematics and science? Why do you feel this activity would be effective?        How can you envision involving colleagues in helping make changes in teaching and learning within your classroom? Within a school?      

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