Developing Developing the the

TechMath TechMath Instructional Instructional

ModuleModule

““Imagine a Imagine a classroom, …classroom, …

NCTM, 2000. PSSM, p.3.NCTM, 2000. PSSM, p.3.

where all where all students have students have access to high-access to high-quality, engaging quality, engaging …instruction.”…instruction.”

““[where] there are [where] there are ambitious ambitious expectations for all, expectations for all, with accommodation with accommodation for those who need for those who need it.”it.” NCTM, 2000. PSSM, p.3.NCTM, 2000. PSSM, p.3.

“…“…[where students] [where students] learn important learn important mathematic[s] with mathematic[s] with understanding.”understanding.”

NCTM, 2000. PSSM, p.3.NCTM, 2000. PSSM, p.3.

““Technology is an Technology is an essential essential component of the component of the environment.”environment.”

NCTM, 2000. PSSM, p.3.NCTM, 2000. PSSM, p.3.

““Students Students confidently engage confidently engage in complex in complex mathematical mathematical tasks…” tasks…” NCTM, 2000. PSSM, p.3.NCTM, 2000. PSSM, p.3.

“…“…[and] draw on [and] draw on knowledge from a knowledge from a …variety of …variety of mathematical mathematical topics, topics,

[and] [and] approach… approach… the same the same problem… in problem… in different waysdifferent ways…”…”

NCTM, 2000. PSSM, p.3.NCTM, 2000. PSSM, p.3.

““……students students make, refine, make, refine, and explore and explore conjecturesconjectures … …

and use a variety of and use a variety of reasoning and proof reasoning and proof …to confirm or …to confirm or disprove [their]… disprove [their]… conjectures.”conjectures.”

NCTM, 2000. PSSM, p.3.

NCTM, 2000. NCTM, 2000. PSSMPSSM, p.3., p.3.

““Students are Students are flexible and flexible and resourceful resourceful problem solvers.”problem solvers.”

““Alone or in Alone or in groups and with groups and with access to access to technology,technology,

NCTM, 2000. NCTM, 2000. PSSMPSSM, , p.3.p.3.

[students] work [students] work productively and productively and reflectively,reflectively,

with the skilled with the skilled guidance of guidance of their teachers.” their teachers.”

““Orally and in Orally and in writing, students writing, students communicate their communicate their ideas and results ideas and results effectively.”effectively.” NCTM, 2000. NCTM, 2000. PSSMPSSM, p.3., p.3.

““Students value Students value mathematics and mathematics and engage actively in engage actively in learning it.” learning it.” NCTM, 2000. NCTM, 2000. PSSMPSSM, ,

p.3.p.3.

Imagine.Imagine.

Imagine your Imagine your TechMath module TechMath module as the curriculum as the curriculum for the classroom in for the classroom in our vision.our vision.

Central to the Central to the module and the key module and the key to module to module development is the development is the essential question. essential question.

The essential The essential question---question---

A problem…A problem…

……a “puzzlement.”a “puzzlement.”

Something that is not Something that is not obvious, not clear, that obvious, not clear, that is challenging, engaging, is challenging, engaging, something that the something that the student wants to know.student wants to know.

But is the problem But is the problem instructionally instructionally rich?rich?

Does it Does it engage students in engage students in important mathematics?important mathematics?

enable students to make enable students to make connections?connections?

promote communication?promote communication?support different entry levels support different entry levels & different approaches? & different approaches?

Example of NCTM Example of NCTM “Instructionally Rich Task” is “Instructionally Rich Task” is

generalizing a geometric generalizing a geometric pattern.pattern.

How do we pose the How do we pose the problem?problem?

Tell a story of the business; show a Tell a story of the business; show a video; project pictures; share some video; project pictures; share some quotes from your business partner.quotes from your business partner.

Engage the students.Engage the students.

Pose the question. Use Polya’s advicePose the question. Use Polya’s advice—don’t say too much.—don’t say too much.

Developing InstructionDeveloping InstructionUse Polya’s stages or Use Polya’s stages or 5E Lesson Structure or 5E Lesson Structure or a curriculum approach of a curriculum approach of

posing the question, posing the question, exploring some exploring some mathematics, and then mathematics, and then returning to the question.returning to the question.

Don’t forget closure.Don’t forget closure.How can we ensure our How can we ensure our

students’ reflections—their students’ reflections—their “looking back,” making sense “looking back,” making sense of new knowledge? of new knowledge?

Ask students to write a business Ask students to write a business report, create and share report, create and share similar problems, construct a similar problems, construct a concept map… concept map…

TechMath ModuleTechMath ModuleI. I. Title PageTitle Page

II. Overview/prefaceII. Overview/prefaceIII. Table of ContentsIII. Table of Contents

If mini-unitIf mini-unit

Daily Lesson Daily Lesson PlansPlans

Assessment of Assessment of Student Student LearningLearning

If student If student projectproject

Teacher NotesTeacher Notes

Task DescriptionTask Description

Sample SolutionsSample Solutions

Rubric for Rubric for EvaluationEvaluation

Lesson PlansLesson PlansWrite your lesson plans for novice Write your lesson plans for novice

teachers.teachers.

Title your lesson plans.Title your lesson plans.

Write clear statements of learning Write clear statements of learning objectives.objectives.

Include a list of materials needed.Include a list of materials needed.

Include all directions. Include all directions.

Include questions to be posed.Include questions to be posed.

Include solutions.Include solutions.

Attach all black-line masters.Attach all black-line masters.

Where are we going?Where are we going?June 18, 2009June 18, 2009: a complete module draft : a complete module draft

that you submit to Kathleen. that you submit to Kathleen. June 26, 2009June 26, 2009: a complete module, : a complete module, version version

11 Fall 2009Fall 2009: Pilot Module in Your Classroom : Pilot Module in Your Classroom

[notify Kathleen and Bethany of times and [notify Kathleen and Bethany of times and dates], Reflect, & Revise Module, dates], Reflect, & Revise Module, version 2version 2

Spring 2010Spring 2010: Share your module with : Share your module with another teacher, who teaches the module another teacher, who teaches the module and provides you with an assessment [using and provides you with an assessment [using a rubric]. Revise your module, complete the a rubric]. Revise your module, complete the module overview and submit to Bethany, module overview and submit to Bethany, version 3version 3. .