Location: Tobaccoville, North Carolina

Tuesday, March 22, 2005

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.
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
High – Students should complete on daily basis
Medium – Students should complete on weekly basis
Low – Students should compete when time permits

Importance Difficulty Frequency
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
(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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