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Connecticut Mastery Test, Fourth Generation

Correlation Between Mathematics Objectives and the Instrumental Enrichment Thinking Skills Program

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
Identify rules for patterns	In several instruments, students must predict rules that summarize patterns
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.