Effective TeachingEffective Teaching::Examples in History, Math, Examples in History, Math,

& Science& Scienceby Michelle Brazealby Michelle Brazeal

Principles for the Design Principles for the Design of Learning Environmentsof Learning Environments

Learner-centered: teachers build on Learner-centered: teachers build on the knowledge students bring to the the knowledge students bring to the learning situationlearning situation

Knowledge-centered: teachers Knowledge-centered: teachers attempt to help students develop attempt to help students develop understanding of important concepts understanding of important concepts in each disciplinein each discipline

Principles for the Design Principles for the Design of Learning Environmentsof Learning Environments

Assessment-centered: teachers Assessment-centered: teachers attempt to make thinking visible so that attempt to make thinking visible so that ideas can be discussed and clarifiedideas can be discussed and clarified

Community-centered: teachers Community-centered: teachers establish classroom norms that establish classroom norms that learning with understanding is valued learning with understanding is valued and students feel free to explore what and students feel free to explore what they do not understandthey do not understand

Teaching is a generic skill Teaching is a generic skill and a good teacher can and a good teacher can

teach any subject.teach any subject.

This is a dangerous myth about This is a dangerous myth about teachingteaching

Any curriculum is mediated by a Any curriculum is mediated by a teacher’s understanding of the domainteacher’s understanding of the domain

You must have a deep understanding You must have a deep understanding and knowledge of your subject area and knowledge of your subject area before you can teach effectivelybefore you can teach effectively

What teachers know and believe about What teachers know and believe about a subject is closely linked to their a subject is closely linked to their instructional decisions and actionsinstructional decisions and actions

Why History, Math, & Why History, Math, & Science?Science?

To focus on similarities and To focus on similarities and differences of disciplines that use differences of disciplines that use different methods of analysisdifferent methods of analysis

To explore the knowledge required To explore the knowledge required to teach effectively in a diversity of to teach effectively in a diversity of disciplinesdisciplines

TinkertoyTinkertoy Derby Derby

Effective Teachers Need:Effective Teachers Need:

Extensive knowledge of their subject Extensive knowledge of their subject mattermatter

To understand barriers likely to hinder the To understand barriers likely to hinder the studentsstudents

Knowledge of children as learnersKnowledge of children as learners Pedagogical content knowledge (knowledge Pedagogical content knowledge (knowledge

about how to teach in their subject)about how to teach in their subject) Provides teachers with cognitive roadmaps that Provides teachers with cognitive roadmaps that

guide the assessments they give students to gauge guide the assessments they give students to gauge student progress and questions they askstudent progress and questions they ask

Example of an Effective Example of an Effective TeacherTeacher

Barb Johnson – 6Barb Johnson – 6thth grade teacher grade teacher AsksAsks students what students what questionsquestions they have they have

about themselves and the worldabout themselves and the world They then narrow the questions in groups They then narrow the questions in groups

and this guides the curriculum for the yearand this guides the curriculum for the year With only the question, “Will I live to be With only the question, “Will I live to be

100 years old?” students explored 100 years old?” students explored genetics, family history, actuarial science, genetics, family history, actuarial science, statistics/probability, heart disease, statistics/probability, heart disease, cancer, & hypertension cancer, & hypertension

Barb Johnson’s teaching requires wide Barb Johnson’s teaching requires wide range of disciplinary knowledge because range of disciplinary knowledge because she begins with student questions rather she begins with student questions rather than a fixed curriculumthan a fixed curriculum

““It would not work to simply arm new It would not work to simply arm new teachers with general strategies to teachers with general strategies to mirror how she teaches; they must have mirror how she teaches; they must have the subject knowledge and knowledge of the subject knowledge and knowledge of how students learn as well.” how students learn as well.”

HistoryHistory

Many times taught as clusters of Many times taught as clusters of fixed names and dates fixed names and dates

If taught in this way, students only If taught in this way, students only master concepts and facts instead of master concepts and facts instead of being able to use them to form being able to use them to form conclusions or interpretations of conclusions or interpretations of eventsevents

Examples of Effective Examples of Effective History TeachersHistory Teachers

Bob Bain – 9Bob Bain – 9thth grade History grade History Starts class by Starts class by asking questionsasking questions about about

what they think are the most important what they think are the most important artifacts from the past and tell whyartifacts from the past and tell why

Responses are pooled and go on a Responses are pooled and go on a posterposter

The responses are revised and The responses are revised and elaborated on throughout the yearelaborated on throughout the year

Examples of Effective Examples of Effective History TeachersHistory Teachers

Ms. Sterling – AP History teacherMs. Sterling – AP History teacher Begins school year by Begins school year by asking asking

questionsquestions such as: such as: ““What is history?”, “How do we know the What is history?”, “How do we know the

past?”past?” Goal: to show students that history is more Goal: to show students that history is more

than names and dates; bring students to a than names and dates; bring students to a place where they can reason and draw place where they can reason and draw meaningful conclusionsmeaningful conclusions

FeedbackFeedback

Your topic sentence is weakYour topic sentence is weak More factual detail would improve More factual detail would improve

your essayyour essay Note spelling and grammar Note spelling and grammar

correctionscorrections

FeedbackFeedback

The greatest strength of this essay is its The greatest strength of this essay is its outstanding effort to grapple thoughtfully with outstanding effort to grapple thoughtfully with the question, why did the colonists rebel? Keep the question, why did the colonists rebel? Keep thinking personally, “What if I were here?” It is thinking personally, “What if I were here?” It is a great place to start.a great place to start.

To make the essay work, however, you need to To make the essay work, however, you need to refine your organization strategies significantly. refine your organization strategies significantly. Remember that your reader is basically Remember that your reader is basically ignorant, so you need to express your view as ignorant, so you need to express your view as clearly as you can. Try to form your ideas from clearly as you can. Try to form your ideas from the beginning to a middle and then an end.the beginning to a middle and then an end.

FeedbackFeedback

In the beginning, tell what side you’re In the beginning, tell what side you’re on: What made the colonists rebel?on: What made the colonists rebel?

In the middle, justify your view. What In the middle, justify your view. What factors support your idea and will factors support your idea and will convince your reader?convince your reader?

In the end, remind your reader again In the end, remind your reader again about your point of view.about your point of view.

Go back and revise and hand this in Go back and revise and hand this in again!again!

Effective TeachingEffective Teaching

DebatesDebates Presentation skillsPresentation skills Students defend their own ideas/beliefsStudents defend their own ideas/beliefs Leads to a deeper understanding of the Leads to a deeper understanding of the

contextcontext Not just memorized facts, but students Not just memorized facts, but students

begin to articulate what they knowbegin to articulate what they know

What about Math?What about Math?

Which seems easier to you: to Which seems easier to you: to be an effective teacher in be an effective teacher in history or math? Why?history or math? Why?

How most people see How most people see math:math:

ComputationComputation

How mathematicians see How mathematicians see math:math:

Computation is a tool in the Computation is a tool in the “real stuff” of math “real stuff” of math

(problem solving and (problem solving and characterizing and characterizing and

understanding structure understanding structure and patterns)and patterns)

Popcorn DropPopcorn Drop

What all the effective math What all the effective math teachers seemed to be teachers seemed to be

doing:doing: Discover what the students already know and Discover what the students already know and

what is interesting/meaningful to themwhat is interesting/meaningful to them Have the students verbalize their thinking on Have the students verbalize their thinking on

the subjectthe subject Guide discussions/arguments, leading to Guide discussions/arguments, leading to

reasonable ideas while mentally making reasonable ideas while mentally making notes about what students are understandingnotes about what students are understanding

Bring in new information, but have students Bring in new information, but have students use their own ways of deciding whether use their own ways of deciding whether something was mathematically reasonable by something was mathematically reasonable by doing the workdoing the work

Example: How Many Example: How Many Altogether?Altogether?

Teacher: Can anyone give me a story Teacher: Can anyone give me a story that could go with this multiplication…that could go with this multiplication…12 x 4?12 x 4?

Jessica: There were 12 jars, and each Jessica: There were 12 jars, and each had 4 butterflies in it.had 4 butterflies in it.

Teacher: And if I did this multiplication Teacher: And if I did this multiplication and found the answer, what would I and found the answer, what would I know about those jars and butterflies?know about those jars and butterflies?

Jessica: You’d know you had that many Jessica: You’d know you had that many butterflies altogether.butterflies altogether.

Example: How Many Example: How Many Altogether?Altogether?

Teacher illustrates Jessica’s story using Teacher illustrates Jessica’s story using stars in the jarsstars in the jars

Teacher & students give pictorial Teacher & students give pictorial representation of grouping 10 sets of representation of grouping 10 sets of four butterflies and having 2 jars not in four butterflies and having 2 jars not in groupgroup

This helped students recognize that 12 x This helped students recognize that 12 x 4 can be thought of as 10 x 4 plus 2 x 4. 4 can be thought of as 10 x 4 plus 2 x 4. Students then grouped the jars as 6 x 4 Students then grouped the jars as 6 x 4 plus 6 x 4 and saw this was the same…plus 6 x 4 and saw this was the same…this surprised students. this surprised students.

Example: How Many Example: How Many Altogether?Altogether?

The surprise of students was a sign to The surprise of students was a sign to the teacher that students needed more the teacher that students needed more activities involving different groupingsactivities involving different groupings

Lesson continued with students Lesson continued with students developing and defending procedures for developing and defending procedures for problems with two-digit numbers in the problems with two-digit numbers in the multiplication (28 x 65)multiplication (28 x 65)

Eventually students are lead to using Eventually students are lead to using only written symbols for their only written symbols for their proceduresprocedures

Example of Guided Example of Guided Discussion/InstructionDiscussion/Instruction

Annie Keith - combo 1Annie Keith - combo 1stst/2/2ndnd grade teacher grade teacher Word problems are basis for almost all Word problems are basis for almost all

instruction and used during activitiesinstruction and used during activities Spends a lot of time in discussions on Spends a lot of time in discussions on

strategies for solving problemsstrategies for solving problems Uses activities as opportunities for her Uses activities as opportunities for her

to learn what individual students know to learn what individual students know and understandand understand

Her instruction is carefully orchestratedHer instruction is carefully orchestrated

ModelingModeling

What is a model-based approach to a What is a model-based approach to a problem?problem? Inventing (or selecting) a modelInventing (or selecting) a model Exploring the qualities of the modelExploring the qualities of the model Applying the model (to answer the Applying the model (to answer the

question)question) Useful in Math (spatial visualization, Useful in Math (spatial visualization,

geometry, data structure, measurement, & geometry, data structure, measurement, & uncertainty)uncertainty)

Largely missing from school instructionLargely missing from school instruction

ScienceScience

Physicists (Experts in Science) – Physicists (Experts in Science) – generally discuss principles and generally discuss principles and proceduresprocedures

Novices – tend to discuss specific Novices – tend to discuss specific equations that could be used in equations that could be used in solving the problemsolving the problem

Expert Skills in ScienceExpert Skills in Science

Ability to describe a problem in detail before Ability to describe a problem in detail before attempting a solutionattempting a solution

Ability to determine what relevant information Ability to determine what relevant information should enter the analysis of a problemshould enter the analysis of a problem

Ability to decide which procedures can be Ability to decide which procedures can be used to generate problem descriptions and used to generate problem descriptions and analysesanalyses

Unfortunately, these are rarely taught in Unfortunately, these are rarely taught in science courses!science courses!

Example of Effective Example of Effective Science TeachingScience Teaching

Which water tastes better?Which water tastes better?

(handout)(handout)

Green ThumbsGreen Thumbs

Conceptual ChangeConceptual Change

Before learning new scientific concepts, Before learning new scientific concepts, students often need to re-conceptualize students often need to re-conceptualize deeply rooted misconceptions that deeply rooted misconceptions that interfere with learninginterfere with learning

Bridging – attempts to bridge from Bridging – attempts to bridge from students correct beliefs to their students correct beliefs to their misconceptions through a series of misconceptions through a series of intermediate analagous situationsintermediate analagous situations

Interactive lecture demonstrationsInteractive lecture demonstrations Ex: Collision between air carts on an air trackEx: Collision between air carts on an air track

Science for All ChildrenScience for All ChildrenWhat is important and why?What is important and why?

Class discussionsClass discussions To develop a language for talking about To develop a language for talking about

scientific ideasscientific ideas Makes students’ thinking visible to the Makes students’ thinking visible to the

teacher and the rest of the classteacher and the rest of the class Helps students develop a line of Helps students develop a line of

argumentation using what they have argumentation using what they have learned to solve problems and explain learned to solve problems and explain observationsobservations

Science for All ChildrenScience for All ChildrenWhat is important and why?What is important and why?

Building and arguing theoriesBuilding and arguing theories Students explore their own questions Students explore their own questions

and beliefs, design studies, collect and beliefs, design studies, collect information, analyze data, construct information, analyze data, construct evidence, then debate conclusions evidence, then debate conclusions theythey derived from their evidencederived from their evidence

Science for All ChildrenScience for All ChildrenWhat is important and why?What is important and why?

Teacher Guidance/Community of Teacher Guidance/Community of PracticePractice Guide as students explore problems and Guide as students explore problems and

define questions of interest to themdefine questions of interest to them Community of practice – students share Community of practice – students share

the responsibility for thinking and doing the responsibility for thinking and doing They challenge each other’s thoughts, learn They challenge each other’s thoughts, learn

to be explicit about their meanings, to be explicit about their meanings, negotiate conflicts in evidence, and share negotiate conflicts in evidence, and share their knowledge to achieve understandingtheir knowledge to achieve understanding

ConclusionConclusion

Effective teaching requires:Effective teaching requires: Deep understanding of the subject Deep understanding of the subject

mattermatter Equally thorough understanding of Equally thorough understanding of

kinds of teaching activities that help kinds of teaching activities that help students understand the subject matterstudents understand the subject matter

Knowledge of conceptual barriers that Knowledge of conceptual barriers that students face in learning about a students face in learning about a disciplinediscipline

ConclusionConclusion

Effective teaching requires:Effective teaching requires: Knowledge of effective strategies for Knowledge of effective strategies for

working with studentsworking with students Focus on understanding rather than Focus on understanding rather than

memorization and routine procedures to memorization and routine procedures to followfollow

Engaging students in activities that Engaging students in activities that help them reflect on their own learning help them reflect on their own learning and understandingand understanding

Jaime EscalanteJaime Escalante