### Instructional Articulation

*Did the presenter/designer use the task analysis tool to identify and clearly name a holistic ‘job’ that learners will be able to perform as a result of having participated in their proposed instruction?*

Students job is to build connections between various courses and units within a single course. Worded another way, students’ job is connection building specifically in relation to mathematical understanding, i.e. to develop mathematical understanding.

This ties in with NCTM (National Council of Teachers of Mathematics) Learning Principle:

“Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge” (NCTM, Principles and Standards for School Mathematics, pg. 16).

Mathematics with understanding = mathematical understanding

Building new knowledge from experience and prior knowledge = connection building

For information regarding Mathematics Understanding see Blog entry (under construction) entitled “Meaning & Understanding in Mathematics”**Did they then articulate and list the component parts of the job –the tasks—and further select the ones to focus instruction on, based on a stated criteria such as DIF (difficulty, importance, frequency)?**

Through observations of students, informal interviews with students and teachers, and readings regarding mathematics curriculum; students who build connections (develop mathematical understanding) typically engage in the following tasks:

Reflection and Communication on course material regarding what was done and why

Reflection means consciously thinking about your experiences

· Evaluating own thinking

· Writing

· Regularly reviewing homework

Communication with others (social interaction)

· About concepts

· Strategies to solve Mathematical problems (i.e. homework)

· Talking

· Listening

· Writing

· Demonstrating (Projects)

· Watching

Criticality (Importance):

High – What should be implemented first.

Medium – Already implemented, but should be improved to increase effectiveness

Low – Good to do, but can be implemented as time permits.

Difficulty:

High – Logistics of implementation will be involved or Breaking students “beliefs” will be challenging or time issues.

Medium – Already implemented, but modifications are necessary to increase effectiveness

Low – Can be implemented relatively quickly with few if any difficulties

Frequency:

High – Students should complete on daily basis

Medium – Students should complete on weekly basis

Low – Students should compete when time permits

Importance Difficulty Frequency

Reflection

Writing about concepts Medium Medium Medium

Regularly reviewing homework High Low High

Listing question to discuss with classmates Low Low Low

Review of previous concepts Medium Medium Medium

Reading about concepts High High High

Communication (social interaction)

About Concepts

(Regular class Discussion) Medium Medium High

(Open Discussion Board on Website) High High High

Strategies to Solve Homework High Low High

Group Work/Co-operative Learning Medium Medium Medium

Projects

(Demonstration & Watching Classmates) Medium Medium Med/Low

Review of previous concepts Medium Medium Medium

Researching other Math-related Websites Low Low Medium

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