Math1ubd

Situation 1A housewife goes to a supermarket to buy grocery

items. At the dairy section she took the can of the milk that is being advertised in the TV commercials to be creamy in taste. Way back home, she found that the milk she bought has less nutritional value than the other brands.

Situation 2Rina learned that calcium is good for the bones and

can be derived from milk. She heard about the daily calcium requirement that the body needs from a TV commercial. With this information, she scout for the most economical, creamy and rich in calcium milk at the grocery store.

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Training of Trainers for the Mass Training Training of Trainers for the Mass Training of First Year Teachers on the 2010 SEC of First Year Teachers on the 2010 SEC

Bureau of Secondary EducationCURRICULUM DEVELOPMENT DIVISION

Session 1

Session 2

Session 3

Session 4

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Session 1: Understanding the Math Curriculum Framework

• Explain the math framework as you understand it.

• Any misconceptions?• Share your thoughts on what you can do

and how you will deliver the desired results.

• Fill up the matrix “Something New, Something Better”.

• Answer this open-ended question: The 2010 curriculum in math should

_______________________________

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Functional Literacy for All

Problem SolvingCommunicatingMathematically

ReasoningMathematically

Making MathConnections andRepresentations

Computational skills and

Comprehension

Application toReal Life

Creative and Critical

ThinkingVisual Imagery

ExperientialLearning

ConstructivismCooperative

Learning

Integration withOther Disciplines

ICT IntegrationMath

Investigations/Games & Puzzles

Practical Work/Outdoor Activities

CONCEPTUAL FRAMEWORK OF SECONDARY

MATHEMATICS PROGRAM

VALUING

Session 1

PROBLEM SOLVING

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All students will...

Use multiple approaches to investigate and understand mathematical content.

Formulate problems from everyday and mathematical situations.Develop and apply strategies to solve a wide variety of problems, including multi-step and non-routine problems.

Verify and interpret results with respect to the original problem.

Generalize solutions and strategies to new problem situations.

Acquire confidence in using mathematics meaningfully.

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Recognize and formulate problems from situations within and outside mathematics.

Apply the process of mathematical modeling to real-world problem situations.Explore and use multiple strategies for solving problems.Determine, collect, and analyze appropriate data with respect to the original problem or in new problem-solving situations.Access and use appropriate problem-solving tools, including calculators, computers, and measurement devices.

Generalize problem-solving strategies to a wide range of adult oriented, real-world situations. framework

Communication of mathematical ideas will help students clarify and solidify their understanding of mathematics. By sharing their mathematical understandings in written and oral form with

their classmates, teachers, and parents, students develop confidence in themselves as mathematics learners and enable teachers to

better monitor their progress.

COMMUNICATING MATHEMATICALLY

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Relate physical materials, pictures, and diagrams to mathematical ideas.

Reflect on and clarify thinking about mathematical ideas and situations.

Relate everyday language to mathematical language and symbols.

Use the skills of reading, listening, and viewing to interpret and evaluate mathematical ideas.

Model situations by using oral, written, concrete, pictorial, graphical, and algebraic methods.

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Develop mathematical ideas, formulate mathematical definitions, and express generalizations discovered through investigations.

Appreciate the economy, power, and elegance of mathematical notation and its role in the development of mathematical ideas.

Develop the appropriate reading, writing, listening, and speaking skills necessary for communicating mathematically in a variety of settings.

Ask clarifying and extending questions related to mathematics students have read or heard about.

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Define everyday, work-related, or test-related mathematical situations by using concrete, pictorial, graphic, or algebraic methods.

Appreciate the value of mathematical language and notation in relation to mathematical ideas.

Discuss mathematics with others, reflecting and clarifying individual thinking about mathematical outcomes.

Make convincing arguments and informed decisions.

framework

M a the m a tica l re a soning is the c ritica l skill tha t e na ble s a s tude nt to m a ke use o f a ll o the r m a the m a tica l skills .

W ith the de ve lopm e nt o f m a the m a tica l re a soning, s tude nts re cogniz e tha t m a the m a tics m a ke s se nse a nd ca n be unde rs tood. T he y le a rn how to e va lua te

s itua tions , se le c t proble m -so lving s tra te gie s , dra w logica l conc lus ions , de ve lop a nd de sc ribe

so lutions , a nd re cogniz e how those so lutions ca n be a pplie d. M a the m a tica l re a sone rs a re a ble to re fle c t

on so lutions to proble m s a nd de te rm ine whe the r o r no t the y m a ke se nse . T he y a ppre c ia te the pe rva s ive use a nd powe r o f re a soning a s a pa rt o f m a the m a tics .

R ea s o n in g M a th em a tica lly

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A ll s tuden ts w ill...

D raw log ical conclusions abou t m athem atics.

U se m odels, know n facts, p roperties, and relationsh ips to exp lain m athem atical th ink ing .

Justify so lu tions and exp lain so lu tion p rocesses.

U se patterns and relationsh ips to analyze m athem atical situations.

B elieve that m athem atics m akes sense.

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R ecognize and app ly deductive and inductive reason ing .

M ake and evaluate m athem atical con jectu res and argum ents.

F o llow log ical argum ents.

Judge the valid ity o f argum ents.

A ppreciate the pervas ive use and pow er o f reason ing as a part o f m athem atics .

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U nderstand and app ly deductive, inductive and p roportional reason ing , w ith special atten tion to spatial and v isual reason ing w ith p roportions and graphs.

P ose m athem atical questions and evaluate argum ents.

Validate ind iv idual th ink ing and in tu ition .

S ee how m athem atics m akes sense.

D raw log ical conclusions from m athem atical situations, us ing concrete m odels and verbal sk ills.

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Making connections enables students to see relationships between different topics and to draw on those relationships in future study.

This applies within mathematics, so that students can translate readily between fractions

and decimals, or between algebra and geometry; to other content areas, so that

students understand how mathematics is used in the sciences, the social sciences, and the

arts; and to the everyday world, so that students can connect school mathematics to

daily life.

Mathematical Connections and Representations

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Representations are necessary to students' understanding of mathematical concepts and

relationships. Representations allow students to communicate mathematical approaches,

arguments, and understanding to themselves and to others. They allow students to recognize connections among related concepts and apply

mathematics to realistic problems.

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Link conceptual and procedural knowledge.

Relate various representations of concepts or procedures to one another.

Recognize and value the relationships among different topics in mathematics.

Use mathematics in other curriculum areas and in daily living.

Explore problems and describe results by using graphical, numerical, physical, algebraic, and verbal mathematical models or representations. next

Apply mathematical thinking and modeling to solve problems that arise in other disciplines.

Recognize equivalent representations of the same concept.

Relate procedures in one representation to procedures in an equivalent representation.

View mathematics as an integrated whole, which is connected to past learning, the real world, adult life skills, and work-related settings.

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create and use representations to organize, record, and communicate mathematical ideas;

Explore problems by using appropriate technology, and describe results by using a variety of mathematical models and representations.

select, apply, and translate among mathematical representations to solve problems;

use representations to model and interpret physical, social, and mathematical phenomena.

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Experiential learning is the process of making meaning from direct experience. It is learning

through reflection on doing.

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Constructivism is a theory of knowledge which argues that humans generate knowledge and

meaning from their experiences.

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Cooperative learning is an approach to organizing classroom activities into academic and social learning experiences. Students must work in

groups to complete the two sets of tasks collectively. Everyone succeeds when the group

succeeds.

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Write in the “Something New” column the new thrusts in your teaching that you commit to implement in light of the requirements of the Math curriculum. In the “Something Better” column, you will write the improvements in your teaching you commit to make.

Session 1

Something New Something Better

Session 2: Understanding Stage 1• What are the common elements of Stage 1

across quarters?• Analyze across quarters the relationship between

the elements and the purpose each of them serves.• Share your observations.• How is the Content Standard formulated?• Examine the Performance Standard and specify

the performance expected of learners.• In unpacking the Content Standards, write in meta

strips what students are expected to know (knowledge) and do (skills).

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• Content standardsContent standards What learners should know, understand and be able to do?

• Performance standardsPerformance standards What learners should create/ add value to/transfer?

Demonstrate

Demonstrate

understanding

understanding

PerformPerform

understanding

understanding

EssentialEssentialUnderstandingUnderstanding

(EU)(EU)

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Quarter I: Topic: Time Frame:

Stage 1

Content Standard: Performance Standard:

Essential Understanding(s):

Essential Question(s):

The learner will know: The learner will be able to:

Stage 2

Product or Performance Task: Evidence at the level of understandingLearner should be able to demonstrate understanding of _________________ using the six (6) facets of understanding:

Evidence at the level of performance

Stage 3

Teaching/Learning Sequence

Resources (websites, courseware, etc.)Materials/Equipment Needed

Session 2

Stage 1 – Desired ResultsEstablished Goals:• What relevant goals (e.g., content standards, course or program objectives, learning outcomes) will this design address?

Content Standards: What should students know and be able to do?

Performance Standards:How well must students do their work?At what level of performance would the student be appropriately qualified or certified?

Essential Understandings (EU):Students will understand that . . .• What are the big ideas?• What specific understandings about them are desired?• What misunderstandings are predictable?

Essential Questions (EQ):• What provocative questions will foster inquiry, understanding, and transfer of learning? Provocative questions-have no one obvious right answer-raise other important questions-address the philosophical or conceptual foundations of a discipline -recur naturally-are framed to provoke and sustain learner interest

Students will know. . .• What key knowledge and skills will students acquire as a result of this unit?• What should they eventually be able to do as a result of such knowledge and skills?

Students will be able to . . .

Session 2

MATHEMATICS IGeneral Standard: The learner demonstrates understanding of key concepts and principles of number and number sense as applied to measuring, estimating, graphing, solving equations and inequalities, communicating mathematically and solving problems in real life.QUARTER I (Real Number System, Measurement and Scientific Notation)

Stage 1: Results/Outcomes Stage 2: Assessment

STANDARDS ESSENTIALProduct/

Performance

At the Level of

Content Performance Understanding Question Understanding Performance

The learner demonstrates understanding of the key concepts of real number systems, measurements and scientific notation.

The learnerformulates real-life problems involving real numbers, measurements and scientific notation and solves these using a variety of strategies.

Daily tasks involving measurement, conversion, estimation and scientific notation make use of real numbers.

How useful are real numbers?

Problems formulated 1.are real life2.involve real numbers, measurement and scientific notation and3.are solved using a variety of strategies.

ExplanationExpress numbers in different ways and explain.Criteria:ThoroughCoherentExplain how to use the calibration model and find its degree of precisionCriteria:AccurateJustifiedExpress big and small quantities in scientific notationCriteria:AccurateJustifiedInterpretation“Tell a Story” of situations where numbers are used or how measuring devices are used.

Assessment of problems formulated based on the following suggested criteria:real-life problemsproblems involve real numbers, measurement and scientific notationproblems are solved using a variety of strategiesTools: Rubrics for assessment of problems formulated and solved

Physical quantities are measured using different measuring devices. The precision of the measurement is dependent on the measuring device used.

How are different measuring devices useful? How does one know when a measurement is precise? accurate?

Session 2

Which define what students should be able to know and do at the end of the program, course, or unit of study;

generally expressed in terms of overall goals, and specifically defined in terms of content and

performance standards.

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Which specify the essential knowledge (includes the most important and enduring ideas, issues, principles and concepts from the disciplines), skills and habits

of mind that should be taught and learned. They answer the question, “What should students know

and be able to do?”.

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Which express the degree or quality of proficiency that students are expected to demonstrate in relation to the

content standards. They answer the question, “How well must students do their work?” or “At what level of performance would the student be appropriately

qualified or certified?”

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Which are the big and enduring ideas at the heart of the discipline and which we want the children to remember even long

after they leave school.

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Which are open-ended, provocative questions that spark thinking and further inquiry into the

essential meanings and understandings.

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Which are expressed in terms of knowledge and skills that teachers can use as guide in formulating their own classroom objectives.

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Session 3: Understanding Stage 2• What is the relationship between the EU and assessment?• Analyze the following:

the relationship between the Performance Standards and the Products and Performances across quarters; what Products and Performances are for; and How Products and Performances may be differentiated.

• How would you link the Facets of Understanding to the assessment of the attainment of the Content Standard?• Formulate questions using the FUs.• Formulate assessment tools for Products and Performances.• Express orally or in writing your understanding of Stage 2.

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MATHEMATICS IGeneral Standard: The learner demonstrates understanding of key concepts and principles of number and number sense as applied to measuring, estimating, graphing, solving equations and inequalities, communicating mathematically and solving problems in real life.QUARTER I (Real Number System, Measurement and Scientific Notation)

Stage 1: Results/Outcomes Stage 2: Assessment

STANDARDS ESSENTIALProduct/

Performance

At the Level of

Content Performance Understanding Question Understanding Performance

The learner demonstrates understanding of the key concepts of real number systems, measurements and scientific notation.

The learnerformulates real-life problems involving real numbers, measurements and scientific notation and solves these using a variety of strategies.

Daily tasks involving measurement, conversion, estimation and scientific notation make use of real numbers.

How useful are real numbers?

Problems formulated 1.are real life2.involve real numbers, measurement and scientific notation and3.are solved using a variety of strategies.

ExplanationExpress numbers in different ways and explain.Criteria:ThoroughCoherentExplain how to use the calibration model and find its degree of precisionCriteria:AccurateJustifiedExpress big and small quantities in scientific notationCriteria:AccurateJustifiedInterpretation“Tell a Story” of situations where numbers are used or how measuring devices are used.

Assessment of problems formulated based on the following suggested criteria:real-life problemsproblems involve real numbers, measurement and scientific notationproblems are solved using a variety of strategiesTools: Rubrics for assessment of problems formulated and solved

Physical quantities are measured using different measuring devices. The precision of the measurement is dependent on the measuring device used.

How are different measuring devices useful? How does one know when a measurement is precise? accurate?

Session 3

What is evidence of understanding? Learners truly understand when they:• can explain• can interpret• can apply• have perspective• can emphatize• have self-knowledge

Session 3

Provides thorough, supported, and justifiable accounts of phenomena, facts and data.

(Describe – Express – Justify – Predict - Synthesize)

Facets

Tells meaningful stories, provides a revealing historical or personal dimension to ideas and events; makes it personal or accessible through images, anecdotes, analogies, and models.

(Be aware of – Realize – Recognize – Reflect -- Self-assess)

Facets

Effectively uses and adapts what is known in diverse context.

(Build –Create – Design – Perform – Solve)

Facets

Can see and hear points of view through critical eyes and ears, sees the big picture.

(Analyze – Argue – Compare – Contrast – Infer)

Facets

Finds value in what others might find odd, alien, or implausible; perceives sensitively on the bases of prior direct experience.

The ability to get inside another person’s feelings and worldview.

(Assume role of – Consider – Imagine – Relate – Role play)

Facets

Perceives the personal style, prejudices, projections, and habits of mind that both shape and impede their own understanding.

The wisdom to know one’s ignorance and how one’s patterns of thought and action inform as well as prejudice understanding.

(Be aware of – Realize – Recognize – Reflect -Self-assess)

Facets

ExplanationInterpretation

Application

PerspectiveEmpathy

Self-Knowledge

Session 4: Understanding Stage 3Session 4: Understanding Stage 3• Interpret your ideas about the following;Interpret your ideas about the following;

WHERETO design principles; and design principles; and 4-phase teaching/learning sequence.teaching/learning sequence.

• Do a micro teaching of each phase of the lesson Do a micro teaching of each phase of the lesson in Quarter 1 (4 teachers, i.e., 1 teacher for each in Quarter 1 (4 teachers, i.e., 1 teacher for each phase).phase).

• Give your comments and observations about Give your comments and observations about the micro teaching.the micro teaching.

• What are your enrichment(s)/ modification(s) What are your enrichment(s)/ modification(s) you would propose to make on the lesson? you would propose to make on the lesson?

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• ExploreExplore

• Firm UpFirm Up

• DeepenDeepen

• TransferTransfer (Create, add

value)

U n

d e r s t a n

d i n

g U

n d

e r s t a n d

i n

g

C o

n t e n

t S t a n

d a r

dP

erform

ance

Stan

dard

A s s e s s m

e n

A s s e s s m

e n

tt

W H

E R

E T

O

Session 4

WW H E R E T OH E R E T O

WW - How shall we help learners know wherewhere they are headed (the learning goals) and why they are going there (reason for learning the content)?

WhatWhat is expected (unit goal and performance requirements)?

In whatwhat ways will learners be evaluated (evaluation criteria)?

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Questions to consider for WGoals:

• Where are we going in this unit or course?• What are the goals or standards toward which we

are going?• What will students be learning?

• What resources and learning experiences will help us get there?

Relevance & Value:• Why is this worth learning?

• In what ways will this knowledge or these skills benefit students in school? In the future?

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Examples for W

Goals:• Directly state the desired results at the beginning of the unit.

• Present unit & course goals, syllabus, & schedule on first day.• Post and discuss EQs at the start of the unit.

• Invite students to generate questions.• Ask students to identify personal goals.

Relevance & Value:• Present the rationale for the unit & course goals.

• Discuss the benefits to students.• Identify people & place beyond the classroom where this

knowledge & these skills are applied.• Use K-W-L to have students identify things they want to learn.

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Questions to consider for WExpectations:

• What is expected of students?• What are key assignments and assessments?

• In what ways will students be expected to demonstrate learning? Understanding?

• What criteria and performance standards will be used for assessment?

Diagnosis:• From where are students coming?

• What prior knowledge, interests, learning styles, talents do they bring?

• What misconceptions may exist?

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Examples for W

Expectations:• Present the culminating performance task requirements.

• Review scoring rubrics.• Show models and exemplars for expected products &

performances.• Involve students in identifying preliminary evaluation

criteria.

Diagnosis:• Give a pretest on content knowledge.

• Give a diagnostic skills test.• Use K-W-L to see what students already know (or think they

know).• Have students create a visual organizer to reveal their initial

knowledge & understandings.• Check for possible & probable misconceptions.

WHERETO

W W HH E R E T O E R E T O

HH - How shall we help hookhook and engage learners’ interest through thought- provoking experiences at the beginning of instructional episode

(digging into the EUs thru inquiry, research, problem-solving, experimentation)?

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Hooking and Holding StudentsHooking and Holding Students

Brainstorm on how will you hook & hold Brainstorm on how will you hook & hold student interest?student interest?

• Odd fact, anomaly, counterintuitive exampleOdd fact, anomaly, counterintuitive example• Provocative entry questionProvocative entry question

• MysteryMystery• ChallengeChallenge

• Problem or issueProblem or issue• Experiment – predict outcomeExperiment – predict outcome

• Role play or simulationRole play or simulation• Personal experiencePersonal experience

• Allow student choice forAllow student choice for• Emotional connectionEmotional connection

• HumorHumor

WHERETO

W H W H EE R E T O R E T O

EE - What experiencesexperiences shall we provide to help learners make their understandings real?

How shall we equipequip them for success throughout the unit or course?

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Equipping StudentsEquipping Students

Experiencing & Inductive LearningExperiencing & Inductive Learning • What experiential or inductive learning will

help students to explore the EUs and EQs?

Direct Instruction• What information or skills need to be taught

explicitly to equip students?

Homework & Other Out-of-Class Experiences

• What homework & other out-of-class experiences are needed to equip students?

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Examples of Equipping StudentsExamples of Equipping Students

Experiencing & Inductive LearningExperiencing & Inductive Learning • Concept attainment

• Research/I-Search project• Historical investigation

• Scientific experimentation• Problem-based learning

• Creative expression• Artistic or production• Exploration of issues• Construction project

• Socratic seminar• Simulation

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Direct InstructionDirect Instruction To help students:

• Compare ideas & information• Find information (e.g. research)

• Evaluate information & ideas• Generate & test hypothesis

• Communicate ideas• Manage their time

• Monitor their understanding• Organize information

• Persuade• Review each other’s work

• Revise their own work• Use problem-solving strategies

• Self-evaluate• Summarize key ideas

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Homework & Other Out-of-Class ExperiencesHomework & Other Out-of-Class Experiences

• Practicing Skills

• Reading with a purpose

• Working on project or performance task

• Studying & synthesizing information (e.g. create a concept map)

• Reflecting on ideas, process, or product (e.g. journal entry)

• Revising work

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Equipping Students for PerformanceEquipping Students for PerformanceHistorical Role-PlayHistorical Role-Play

Performance Task or Other Evidence:Performance Task or Other Evidence:Assume the role of a historical character & role-play her participation Assume the role of a historical character & role-play her participation

in a debate on a current issue.in a debate on a current issue.

To successfully perform, the student will have to know:

Rules of devate

Debate procedure

and be able to:

Succinctly state a position

Use rebuttal techniques

THEN, what teaching & learning experiences will be needed to equip him/her for a successful performance?

• Review the rule of debate• Show videotape excerpts of

debates to illustrate the procedure & effective debating strategies

• Teach rebuttal techniques

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Equipping Students for PerformanceEquipping Students for Performance

Performance Task or Other Evidence:Performance Task or Other Evidence:

To successfully perform, the student will have to know:

__________________________

__________________________

and be able to:

__________________________

__________________________

THEN, what teaching & learning experiences will be needed to equip him/her for a successful performance?

• _______________________• _______________________

• _______________________

• _______________________

WHERETO

W H E W H E RR E T O E T O

RR - How shall we cause learners to rehearse, reflectreflect, revisitrevisit, reviserevise, refine, and rethinkrethink based upon based upon timely feedbacktimely feedback?

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Questions to Consider for Questions to Consider for RRRethinkRethink

• What EUs do we want students to rethink?What EUs do we want students to rethink?• How will your design challenge students to revisit important How will your design challenge students to revisit important

ideas?ideas?

Revise or RefineRevise or Refine• What skills need to be practiced & rehearsed?What skills need to be practiced & rehearsed?

• How might student products & performances be improved?How might student products & performances be improved?

ReflectReflect• How will you encourage students to reflect uponHow will you encourage students to reflect upon

their learning & thinking?their learning & thinking? The evolution of their understanding?The evolution of their understanding? Their use of strategies?Their use of strategies?

• How will your design help students to become more How will your design help students to become more metacognitive?metacognitive?

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Examples of Examples of RR

RethinkRethink

Help students rethink by having them:Help students rethink by having them:• Shift perspectiveShift perspective

• Reconsider key assumptionsReconsider key assumptions• Confront alternative versionsConfront alternative versions

• Take the roles of …Take the roles of …• Play devil’s advocatePlay devil’s advocate

• Reexamine the argument and evidenceReexamine the argument and evidence• Conducts researchConducts research

• Consider new informationConsider new information• Rethink the naïve idea that …Rethink the naïve idea that …

• Argue & debateArgue & debate• Confront surprises & anomaliesConfront surprises & anomalies

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Examples of Examples of RRRevise or RefineRevise or Refine

Provide opportunities for students to revise & Provide opportunities for students to revise & refine their work through:refine their work through:

• Drafting & editing sessionsDrafting & editing sessions

• Peer critiquesPeer critiques

• RehearsalsRehearsals

• Peer response groupsPeer response groups

• Practice sessionsPractice sessions

• Self-assessmentSelf-assessment

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Examples of Examples of RR

ReflectReflect

Encourage students to reflect through the use of:Encourage students to reflect through the use of:

• Reflective journals & think logsReflective journals & think logs

• Regular self-assessmentsRegular self-assessments

• Metacognitive promptsMetacognitive prompts

• Think aloudsThink alouds

• I – Search papersI – Search papers

WHERETO

W H E R W H E R EE T O T O

EE - How shall learners expressexpress their understandings and engageengage in meaningful self-evaluationevaluation of their of their

workwork?

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Encouraging Self-Evaluation – Encouraging Self-Evaluation – EE• What do you really understand about _____________________?

• What questions & uncertainties do you still have about _________?• What was most effective in _________________________________?• What was least effective in _________________________________?• How could you improve ___________________________________?• What are your strengths in _________________________________?• What are your deficiencies in _______________________________?• How difficult was _________________________________________?• How does your preferred learning style influence ______________?

• What would you do differently next time ______________________?

• What are you most proud of? Why?___________________________• What are you most disappointed in? Why? ___________________?• What grade or score do you deserve? Why? __________________?• How does what you’ve learned connect to other learnings?______?• How has what you’ve learned relate to the present & future?_____?• What follow-up work is needed? ____________________________?

• Other: __________________________________________ WHERETO

W H E R E W H E R E TT O O

TT - How shall we tailortailor (differentiate) our instruction to address the unique

strengths and needs of every learner (flexible to interests & learning styles)?

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Tailoring the Design for Diverse LearnersTailoring the Design for Diverse Learners

ContentContent• At the beginning of a unit, assess prior

knowledge & skills, & develop differentiated activities to accommodate different knowledge & skill levels.

• Provide students with open-ended questions, activities, assignments that enable students to give different but equally valid responses.

• Appeal to various modalities (e.g. present information orally, visually, & in writing).

• Use a variety of resource materials (e.g. multiple reading materials at different levels) to help students understand a difficult concept.

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ProcessProcess

• Accommodate students with different learning styles by providing opportunities for them to work alone and in groups.

• Encourage students to develop their own research questions for in-depth exploration of a key idea or question.


ProductProduct

• Allow students choices of products (e.g. visual, written, oral) for activities & assignments.

• Provide students with options for demonstrating understanding through various products and performances without compromising the goals or standards.

WHERETO

W H E R E T W H E R E T OO

OO - How shall we organizeorganize learning experiences so that learners move from teacher-guided and concrete activities to independent applications that emphasize growing conceptual understandings (sequenced to

maximize engagement & effectiveness)?

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Organizing the LearningOrganizing the Learning

The Logic of “Coverage”The Logic of “Coverage” What is most appropriately and effectively

covered in a linear & didactic fashion?• Present information in a logical, step-by=step fashion

(Teacher as tour guide).• Follow the sequence of the textbook.

• Move from the facts & basic skills to the more advanced concepts & processes.

• Expose students to a breadth of material dictated by established goals.

• Use hands-on & other experiential activities selectively because these can make considerable time.

• Teach & test the discrete pieces before having students apply what they are learning.

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Organizing the LearningOrganizing the Learning

The Logic of “Uncoverage”The Logic of “Uncoverage” What is most appropriately and effectively

“uncovered” in an inductive, inquiry-oriented experiential manner?

• Begin with a hook and teach on an as-needed basis. Don’t front load all of the information before application.

• Make the sequence more surprising & less predictable.• Ensure that there are ongoing cycles of model, practice,

feedback & adjustment built into the unit.• Focus on transferable, EUs

• Move back & forth between the whole & the parts rather than teaching all the little bits first, out of context (Think of

sports, the arts, and vocational/technical projects.

Session 4

Learning/Instructional PlanLearning/Instructional Plan

I. ExploreExplore

• Diagnose.

• Activate prior knowledge.

• Clarify expectations and how learning shall be assessed: standards; products/performances; criteria; tools.

• Hook and engage learner interest.

• Ask EQ; encourage learner questions; welcome tentative responses as guide to further exploration.

WHERETO


II. Firm UpFirm Up

• Provide variety of learning resources (books, videos, readings/documents, web-based resources, etc) and differentiated activities to validate responses to EQ; process learners’ meanings and check these against the EU.

• Encourage learners to reflect, revise, or rethink their understanding.

• Check for understanding; provide feedback; check against content standard.

WHERETO


III. DeepenDeepen

• Provide variety of learning resources and differentiated activities/learning experiences in similar contexts to further validate learner understanding.

• Encourage learners to reflect, rethink, revise their understanding.

• Have learners express their understanding.

• Check for mastery of EU; provide feedback; check against content standard.

WHERETO


IV. TransferTransfer

• Provide for transfer of learning to a new or different context.

• Evaluate product/performance; check against performance standard.

WHERETO

Quarter I: Topic: Time Frame:

Stage 1

Content Standard: Performance Standard:

Essential Understanding(s):

Essential Question(s):

The learner will know: The learner will be able to:

Stage 2

Product or Performance Task: Evidence at the level of understandingLearner should be able to demonstrate understanding of _________________ using the six (6) facets of understanding:

Evidence at the level of performance

Stage 3

Teaching/Learning Sequence

Resources (websites, courseware, etc.)Materials/Equipment Needed Session 4

Thank you and MABUHAY!Thank you and MABUHAY!

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Math1ubd