Effective Teaching : Examples in History, Math, & Science

1. Effective Teaching:Examples in History, Math, & Science by Michelle Brazeal

2. Principles for the Design of Learning Environments • Learner-centered: teachers build on the knowledge students bring to the learning situation • Knowledge-centered: teachers attempt to help students develop understanding of important concepts in each discipline

3. Principles for the Design of Learning Environments • Assessment-centered: teachers attempt to make thinking visible so that ideas can be discussed and clarified • Community-centered: teachers establish classroom norms that learning with understanding is valued and students feel free to explore what they do not understand

4. Teaching is a generic skill and a good teacher can teach any subject.

5. This is a dangerous myth about teaching • Any curriculum is mediated by a teacher’s understanding of the domain • You must have a deep understanding and knowledge of your subject area before you can teach effectively • What teachers know and believe about a subject is closely linked to their instructional decisions and actions

6. Why History, Math, & Science? • To focus on similarities and differences of disciplines that use different methods of analysis • To explore the knowledge required to teach effectively in a diversity of disciplines

7. Tinkertoy Derby

8. Effective Teachers Need: • Extensive knowledge of their subject matter • To understand barriers likely to hinder the students • Knowledge of children as learners • Pedagogical content knowledge (knowledge about how to teach in their subject) • Provides teachers with cognitive roadmaps that guide the assessments they give students to gauge student progress and questions they ask

9. Example of an Effective Teacher • Barb Johnson – 6th grade teacher • Asks students what questions they have about themselves and the world • They then narrow the questions in groups and this guides the curriculum for the year • With only the question, “Will I live to be 100 years old?” students explored genetics, family history, actuarial science, statistics/probability, heart disease, cancer, & hypertension

10. Barb Johnson’s teaching requires wide range of disciplinary knowledge because she begins with student questions rather than a fixed curriculum • “It would not work to simply arm new teachers with general strategies to mirror how she teaches; they must have the subject knowledge and knowledge of how students learn as well.”

11. History • Many times taught as clusters of fixed names and dates • If taught in this way, students only master concepts and facts instead of being able to use them to form conclusions or interpretations of events

12. Examples of Effective History Teachers • Bob Bain – 9th grade History • Starts class by asking questions about what they think are the most important artifacts from the past and tell why • Responses are pooled and go on a poster • The responses are revised and elaborated on throughout the year

13. Examples of Effective History Teachers • Ms. Sterling – AP History teacher • Begins school year by asking questions such as: • “What is history?”, “How do we know the past?” • Goal: to show students that history is more than names and dates; bring students to a place where they can reason and draw meaningful conclusions

14. Feedback • Your topic sentence is weak • More factual detail would improve your essay • Note spelling and grammar corrections

15. Feedback • The greatest strength of this essay is its outstanding effort to grapple thoughtfully with the question, why did the colonists rebel? Keep thinking personally, “What if I were here?” It is a great place to start. • To make the essay work, however, you need to refine your organization strategies significantly. Remember that your reader is basically ignorant, so you need to express your view as clearly as you can. Try to form your ideas from the beginning to a middle and then an end.

16. Feedback • In the beginning, tell what side you’re on: What made the colonists rebel? • In the middle, justify your view. What factors support your idea and will convince your reader? • In the end, remind your reader again about your point of view. • Go back and revise and hand this in again!

17. Effective Teaching • Debates • Presentation skills • Students defend their own ideas/beliefs • Leads to a deeper understanding of the context • Not just memorized facts, but students begin to articulate what they know

18. What about Math? Which seems easier to you: to be an effective teacher in history or math? Why?

19. How most people see math: Computation

20. How mathematicians see math: Computation is a tool in the “real stuff” of math (problem solving and characterizing and understanding structure and patterns)

21. Popcorn Drop

22. What all the effective math teachers seemed to be doing: • Discover what the students already know and what is interesting/meaningful to them • Have the students verbalize their thinking on the subject • Guide discussions/arguments, leading to reasonable ideas while mentally making notes about what students are understanding • Bring in new information, but have students use their own ways of deciding whether something was mathematically reasonable by doing the work

23. Example: How Many Altogether? Teacher: Can anyone give me a story that could go with this multiplication…12 x 4? Jessica: There were 12 jars, and each had 4 butterflies in it. Teacher: And if I did this multiplication and found the answer, what would I know about those jars and butterflies? Jessica: You’d know you had that many butterflies altogether.

24. Example: How Many Altogether? • Teacher illustrates Jessica’s story using stars in the jars • Teacher & students give pictorial representation of grouping 10 sets of four butterflies and having 2 jars not in group • This helped students recognize that 12 x 4 can be thought of as 10 x 4 plus 2 x 4. Students then grouped the jars as 6 x 4 plus 6 x 4 and saw this was the same…this surprised students.

25. Example: How Many Altogether? • The surprise of students was a sign to the teacher that students needed more activities involving different groupings • Lesson continued with students developing and defending procedures for problems with two-digit numbers in the multiplication (28 x 65) • Eventually students are lead to using only written symbols for their procedures

26. Example of Guided Discussion/Instruction Annie Keith - combo 1st/2nd grade teacher • Word problems are basis for almost all instruction and used during activities • Spends a lot of time in discussions on strategies for solving problems • Uses activities as opportunities for her to learn what individual students know and understand • Her instruction is carefully orchestrated

27. Modeling What is a model-based approach to a problem? • Inventing (or selecting) a model • Exploring the qualities of the model • Applying the model (to answer the question) • Useful in Math (spatial visualization, geometry, data structure, measurement, & uncertainty) • Largely missing from school instruction

28. Science Physicists (Experts in Science) – generally discuss principles and procedures Novices – tend to discuss specific equations that could be used in solving the problem

29. Expert Skills in Science • Ability to describe a problem in detail before attempting a solution • Ability to determine what relevant information should enter the analysis of a problem • Ability to decide which procedures can be used to generate problem descriptions and analyses Unfortunately, these are rarely taught in science courses!

30. Example of Effective Science Teaching Which water tastes better? (handout)

31. Green Thumbs

32. Conceptual Change • Before learning new scientific concepts, students often need to re-conceptualize deeply rooted misconceptions that interfere with learning • Bridging – attempts to bridge from students correct beliefs to their misconceptions through a series of intermediate analagous situations • Interactive lecture demonstrations • Ex: Collision between air carts on an air track

33. Science for All ChildrenWhat is important and why? • Class discussions • To develop a language for talking about scientific ideas • Makes students’ thinking visible to the teacher and the rest of the class • Helps students develop a line of argumentation using what they have learned to solve problems and explain observations

34. Science for All ChildrenWhat is important and why? • Building and arguing theories • Students explore their own questions and beliefs, design studies, collect information, analyze data, construct evidence, then debate conclusions they derived from their evidence

35. Science for All ChildrenWhat is important and why? • Teacher Guidance/Community of Practice • Guide as students explore problems and define questions of interest to them • Community of practice – students share the responsibility for thinking and doing • They challenge each other’s thoughts, learn to be explicit about their meanings, negotiate conflicts in evidence, and share their knowledge to achieve understanding

36. Conclusion Effective teaching requires: • Deep understanding of the subject matter • Equally thorough understanding of kinds of teaching activities that help students understand the subject matter • Knowledge of conceptual barriers that students face in learning about a discipline

37. Conclusion Effective teaching requires: • Knowledge of effective strategies for working with students • Focus on understanding rather than memorization and routine procedures to follow • Engaging students in activities that help them reflect on their own learning and understanding

38. Jaime Escalante