Correlation Between Mathematics Objectives and the Instrumental Enrichment Thinking Skills Program

Connecticut Mastery Test, Fourth Generation

Overview

The Connecticut Mastery Test, Fourth Generation Mathematics Handbook, provides a specific list of both teaching strategies and student-skill outcomes for mathematics up through grade 8. The Thinking Skills Program, known as “Instrumental Enrichment” provides direct teaching of a significant number of those skills along with the use of a number of the same strategies. Instrumental Enrichment consists of 14 different units or “instruments”, each designed to directly teach one or more specific cognitive skills, and involves in-depth teacher-training in the methodology of how to enable students to acquire these skills.

Below is a listing of the teaching strategies and skill outcomes from the CMT on the left column, and opposite on the right are the particular parts or “instruments” of the Instrumental Enrichment program which address those CMT strategies and skills. It is proposed that this program provides a strong and high-quality method by which to enable students to acquire these critical outcomes and to succeed on both the CMT as well as in other applications of mathematics. The numbering of the items in the CMT left column for mathematics content matches the numbering system used in the CMT Fourth Generation Handbook.

C.M.T. Practical Instructional Strategies
Instrumental Enrichment Strategies

Asking Why
Methodology involves regular teacher questioning about why, in classroom group dialogues

A Language-Rich Classroom
Methodology centers on discussion

Creating Mental Pictures
Several instruments involve creating mental images before discussing or drawing

Focus on Sense-Making
Student responses are evaluated regularly by peers and teacher for how sensible they are in problem-solving scenario’s

C.M.T. Content Areas
Instrumental Enrichment (I.E.) Content

Solve Word Problems with Multistep Problems
All instruments involve multiple-step problems within each exercise page

Determine a reasonable estimate
I.E. problems are posed and students estimate solutions before beginning a strategy and finding a solution

Describe the strategy
Students are asked to explicitly describe the steps used, during the metacognitive discussion after every I.E. episode

Time
An entire I.E. instrument, Temporal Relationships, deals with all aspects of time (estimation, perception, past-present-future, sequence, causation of events)

Spatial Relationships
The first instrument, Organization of Dots, deals with geometric shapes and figures which are similar and different; students draw data on grids in several instruments; students identify transformations of shapes in Organization; students classify shapes in Organization

Graphing
Students work with graphs in Numerical Progressions, both decoding and encoding data in various tabular forms

Draw reasonable conclusions
Students use summarized data in instruments such as Categorization to develop and defend conclusions

Probability
Students deal early with probability problems, such as in chart form in Orientation in Space, Part I

Make predictions
In Numerical Progressions, students make predictions about patterns that are emerging

Patterns
In several instruments ( Organization of Dots, Categorization, Numerical Progressions, Temporal Relationships) students must identify patterns which are present but not immediately obvious

Algebraic Concepts-Use Formula’s
In Numerical Progressions, students first invent formula’s from given data, and then apply them to new data

Algebraic Concepts-Write expressions
In several instruments, students encode data into expressions (Temporal Relationships, Numerical Progressions, Transitive Relations)

Classification
Three instruments teach the classification – Comparisons, Categorization, and Syllogisms; emphasis is on numerous criteria for categorizing different forms of data (numerical, pictorial, geometric, and verbal)

Logical Reasoning
Strategies related to Logic are explicitly taught through both Transitive Relations and Syllogisms instruments, representing data graphically and symbolically

Venn Diagrams
The Syllogisms instrument  makes direct use of Venn Diagrams to show how data sets interact logically

Permutations and Combinations
Permutations and Combinations are involved in an early instrument, Orientation in Space, Part 1.

Applications: Spatial problems
Two instruments deal explicitly with spatial orientation—Orientation in Space Part 1, which deals with orientation in personal space and point-of-view, and Orientation in Space Part 2, which deals with orientation in geographic space