1

Problem

Students are not successful in developmental math courses.

Students are not successful in subsequent math courses.

Students don't know how to learn.

2

Observations

■ Placement scores■ Completion, attrition rates■ Program requirements■ Student demographics■ Math in society and workplace

3

Placement Scores in the past: MAT090 level: ~70 %MAT095 level: ~15%

----------Placement Scores Fall 2007:MAT090 level: ~55 %MAT095 level: ~30% 80% of 55% score < 40

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Data: Fall 2003 – Spring 2006

■ EnrollmentsMAT090 – 2nd highestMAT095 – 3rd highest

■ Success RatesMAT090 – 34% (lowest)MAT095 – 35% (2nd lowest)MAT195 – 61% (3rd lowest)

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6

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Data: Fall 2001 – Summer 2006

~37%20%~43%MAT095~41%19%~40%MAT090

Do not continue

Repeat (may or may

not pass)

Pass first time

80% of MAT090 students■ CPT scores in the 20 - 40 range■ Skill level of grades 1- 4■ Success rate of 34%.

8

■ Many programs had no “college level” math requirement

----------

■ Most programs now require two “college level” math courses

Program Requirements

9

Student Demographics

■ Median age was about 26----------

■ Median age now about 20

10

Math in Society and Workplace

■ Math formerly used by select few

----------

■ Math now required for entry to many fields■ Math literacy needed for informed citizens

11

MAT090/MAT095“dead horse”

■ New vehicle required to meet today's needs

■ Goals of new sequence

■ 100% Math recommendations

12

GOAL: Students learn math

■ Success in developmental math courses■ Success in subsequent college level math courses■ Quantitative reasoning outside the classroom

13

Goal: Students learn how to learn

■ Generic study skills and learning strategies■ Math specific study skills and learning strategies■ Lifelong learning in the community and workplace

14

100% Math Recommendations

■ More contact time

■ Student study skills and learning strategies

■ Instructional approaches

15

New Sequence

■ MAT091–Fundamentals of Math■ MAT092–Prealgebra■ MAT094–Fundamentals of Algebra

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New Sequence

■ More instructional time for math content■ Time for study skills and math learning objectives■ Implementation of recommended best practices

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New SequenceData Collection

Instructors■ Classroom Practices Inventory Summer 2008 -> December 2008

Students ■ Successful Students Strategies Sept. Pretest -> Dec. Posttest

■ Exit Test Data Test format to be determined

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100% Math #15

… contact time should be sufficient to enable instructors to implement all aspects of effective instruction and active learning … including the integration of study skills into classroom activities.

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New Sequence – Math Content

■ Math content comparison: MAT090/095 <-> MAT091/092/094

■ Math content objectives: MAT091 MAT092 MAT094

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Math ContentDevelopmental ≠ Remedial

Developmental■ Build on concepts previously learned.■ Introduce and develop concepts never learned.■ Replace misconceptions.■ Prepare for future math.

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Math ContentMATHEMATICS LEARNING CUBE

DIMENSIONS

Cognitive

Representational

Content

Musser, G.L. and Burger, W.F. Mathematics for Elementary Teachers, Macmillan (1994).

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New Sequence – Successful Student Objectives

■ Generic study skills and learning strategies

■ Math specific study skills and learning strategies

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STUDENT PROFILE-COMPOSITE

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Math Success Objectives

STRANDS

SELF-AWARENESS personal strengths/weaknesses/attitudes

GENERIC STUDY SKILLS classroom, homework, test preparation

MATH LEARNING PROCESS math models and multiple representation, problem solving, math language

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MAT091/092/094Successful Student

Objectives

■ Study Skills ObjectivesSS1 – SS14

■ Math Learning ObjectivesML1 – ML11

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100% Math #6

Skills and understandings related to learning process should be integrated directly into course curriculum and classroom activities

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Portfolios

■ Portfolio Content

■ Portfolio Logistics

■ Portfolio Assessment

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Portfolio Content

■ 15 worksheet activities corresponding to objectives from 6 study skills areas

■ 3 worksheet activities corresponding to objectives from 3 math learning areas

■ 2 written reflections

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Portfolio Logistics■ Classroom file cabinet will contain student folders

■ Each student folder label will showcourse number, section number and student number

■ Each student folder will include the portfolio index page and completed worksheets collected over the semester

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Portfolio Assessment

Evaluating student work:

■ Worksheets graded by instructor

■ Portfolio weighted 5-15% of semester grade

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Portfolio AssessmentEvaluating portfolio process:

■ Portfolio Index Page for each student

■ Complete portfolio folder for randomly selected students

--- submitted to portfolio committee --- evaluated using portfolio rubric

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Materials – August 2008

■ Sample course policies■ Pretests – math objectives■ Pretest/posttest – success objectives■ Practice Final Exams■ Portfolio rubric■ Electronic versions of all materials

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100% Math #6

Skills and understandings related to learning process should be integrated directly into course curriculum and classroom activities

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Success Activities

Discussion Before Activity

■ Establish baseline■ Motivate■ Describe activity

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Success Activities

Three criteria

■ Introduce information■ Apply immediately to math context or individual needs■ Use multiple learning channels

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Success Activities

Discussion After Activity

■ Summarize information■ Describe how helpful■ Extend to other contexts

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100% Math #3

Adjust instructional approach to accommodate different learning styles

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Learning Styles

ReadingWritingVisualizingHearingSpeakingManipulating

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Learning Pyramid*Average

Retention Rateafter 24 Hours

5%

10%

20%

30%

50%

75%

90%

* National Training Laboratories of Bethel, Maine Sousa, David A. How the Brain Learns, NASSP (1995).

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100% Math #1

Instructors should incorporate active learning approaches into their classroom methodology. Students learn best by active involvement, so it is important to allow students the opportunity to do hands-on work in every class.

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Classroom Methodology

Classroom StructuresLecture/Whole Group Small Group

Individualized Self-paced

Instructional Approaches Active Learning

Multiple Learning Channels Multiple Representations

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Instructional Approaches ■ LEARN BY DOING (Active Learning)

Act Observe Interpret Connect Apply

■ LEARN THROUGH MULTIPLE LEARNING CHANNELS

Manipulate Visualize Hear Speak Read Write

■ LEARN THROUGH MULTIPLE REPRESENTATIONS

Use concrete models to understand abstract ideas

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Learn by DoingAction-Consequence-Reflection

■ Perform math actions on math

objects

■ Observe math consequences

■ Reflect on meaning

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Change in Mindset

introduce build show observe

explain explore

practice interpret

connect

apply

Replace … With …

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Learn through Multiple Representations

SEQUENTIAL PROCESSconcrete -> connecting -> abstract level levels level

example:REAL OBJECT--> VISUAL MODEL--> VERBAL DESCRIPTION--> SYMBOLIC FORM

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Models

Modelling and technology facilitate a deeper understanding of mathematics content.

Physical models -> -> Symbolic ModelsConcrete -> -> Abstract

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Models

■ Everyday objects■ Math manipulatives■ Diagrams/sketches■ Overhead manipulatives■ Smart Notebook objects■ Virtual models ■ Math models

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Math ModelsRule of Three:Geometric – Numeric – AlgebraicGraph - Table - Expression

Rule of Four:Geometric – Numeric – Verbal - AlgebraicGraph - Table - Words - Expression

Rule of Five:Concrete - Geometric – Numeric – Verbal – AlgebraicPhysical Object -Graph - Table – Words - Expression

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Math Language Structure

■ Elements words, symbols, diagrams, graphic devices■ Syntax conventions for combining elements

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thinking //// xx ---> idea of four xx

listening and speaking hearing "four" saying "four"

reading and writing reading four,4,

writing four,4,

Learning Math Language

8

2

3

3

m

m

8

2

3

3

m

m

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The Role of Technology

■ Create action/consequence scenarios

■ Ask good questions

■ Emphasize “sense” making

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Technology As a Learning Tool

User controls technology.User makes inquiries; technology responds.

--> User asks questions, makes conjecture | Software provides information <-- User verifies or modifies conjecture

Process repeats until ideas are clarified.

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Technology As a Learning Tool

Student is actively involved in the learning process

Visual Models for: concepts

symbolsrelationshipsalgorithmsformulas

Course Policy■ Math content objectives■ Study skills and math learning objectives■ Portfolio content■ Tentative schedule■ Exit test■ Grading policy to include math content grade, portfolio grade, (5-15%) and final exam grade

Summary

Classroom activities should integrate successful student strategies with math content objectives in order to implement all aspects of effective instruction and active learning.

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“Teaching is a long distance event. It is more than just today’s lesson, since students return tomorrow, the next day, and the next. ... Your teaching is influential. It shapes and influences what students know today, tomorrow, and in years to come.”

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