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Cognitive Assessments for Math

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Information about Cognitive Assessments for Math
Education

Published on November 21, 2008

Author: wyandersen

Source: authorstream.com

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Developing Cognitive Math Assessments for Daily Classroom Use : Developing Cognitive Math Assessments for Daily Classroom Use Maria H. Andersen Muskegon Community College AMATYC 2008, Washington DC Slide 2: *disclaimer I am not a cognitive psychologist (yet). I have only read some books. If you want more detailed information, you should probably do the same. Slide 3: *disclaimer There are at least five models for cognitive theory. I will talk about two of them in an instructional context. Slide 4: theory practice questions introduction Assessment of Student Learning : Assessment of Student Learning definition? ? Slide 6: 1. Provides information you need on your student’s learning. A participatory, iterative process that: (from Higher Learning Commission) ? Slide 7: 2. Engages you and others in analyzing and using this information to confirm and improve teaching and learning. A participatory, iterative process that: (from Higher Learning Commission) ? Slide 8: Suppose we center this assessment process on the students. ? Slide 9: 2A. Engages you in analyzing and using this information to confirm and improve teaching. A participatory, iterative process that: (modified from Higher Learning Commission) ? Slide 10: 2B. Engages students in analyzing and using this information to confirm and improve learning. A participatory, iterative process that: (modified from Higher Learning Commission) ? Slide 11: 3. Produces evidence that students are learning the outcomes you intended. A participatory, iterative process that: (from Higher Learning Commission) ? Slide 12: 3. Produces feedback to the student that they are learning the outcomes you intended. A participatory, iterative process that: (modified from Higher Learning Commission) ? We use information to confirm and improve learning goals. : We use information to confirm and improve learning goals. (from assessment) ? Students must learn cognitive monitoring to achieve learning goals. : Students must learn cognitive monitoring to achieve learning goals. (from cognitive theory) ? Cognitive Theory : Cognitive Theory Schema Theory Information Processing Theory What makes schemata? ? Schema (pl. schemata) : Schema (pl. schemata) a mental representation of what all instances of something have in common ? Schemata… : Schemata… 1. Categorize your experiences ? Schemata… : Schemata… 2. Help you remember what you are experiencing. ? Schemata… : Schemata… 3. Help you comprehend what you are experiencing. ? Schemata… : Schemata… 4. Are important in developing the ability to problem solve. ? Slide 21: Possible student scripts for factoring ? Slide 22: what happens? ? Slide 23: the problem here is that the student ran the wrong script ? Slide 24: Faulty Student script: Problem says factor Squared term in front? Three terms? Run trinomial factoring script. ? Slide 25: my hint ? Slide 26: what just happened? ? Slide 27: student “ran” trinomial factoring script ? Slide 28: ? Slide 29: now what happens? ? Slide 30: Student script: Problem says factor Four terms? Run factor by grouping script. ? Slide 31: ? Slide 32: Successful problem solvers have a large variety of flexible schemata. ? Information Processing Theory : Information Processing Theory Knowledge Declarative Procedural ? Slide 34: Knowledge Declarative Procedural ? Slide 35: How do we form procedural knowledge? ? Slide 36: Procedural knowledge is activated when the if of an if-then relationship is encountered. ? Slide 37: Students need to practice recognizing and categorizing problems into schemata. ? Slide 38: Students need to encounter problems that refine and revise their schemata. ? Slide 39: What makes schemata? abstraction gist-extraction interpretation ? Slide 40: ? Slide 41: Encountering objects in new ways revises and refines schemata. ? Slide 42: remember this? How can we change this in a way that helps students revise and refine their schemata? ? Slide 43: Why does this approach help to revise schemata? ? Slide 44: Initial script: If the problems are different, then the answers are different. ? Slide 45: Learners need to have multiple encounters with objects or events in different ways ? Slide 46: Learners need to have multiple encounters with objects or events in different ways ? Slide 47: that’s not repetition per se ? Slide 48: Repetition ? Slide 49: Abstraction ? Slide 50: Gist extraction ? Slide 51: The gist of what you saw: Cool poster Sing Uhr 06 Must stand back to read. ? Slide 52: the gist-extraction process revises your actual experience in order to store the memory ? Slide 53: Let’s say I teach my students to multiply polynomials in the following way.* *I don’t do it this way, but let’s just say I do. ? Slide 54: ? Slide 55: ? Slide 56: ? Slide 57: After the student leaves class, what is retained in their memory? ? Slide 58: gist of today’s class: If you have to multiply polynomials, use FOIL (first, outer, inner, last). ? Slide 59: Even worse, an interpretation has been made: All multiplication involves FOIL. ? Slide 60: Let’s say (instead) I teach my students this way. ? Slide 61: ? Slide 62: ? Slide 63: ? Slide 64: After the student leaves class, what is retained in their memory? ? Slide 65: gist of today’s class: If you have to multiply polynomials, multiply each term in the first expression by each term in the second expression. Cues: Draw arcs to help, line up like terms. ? Slide 66: interpretation: filling in things that were not said or seen ? Slide 67: ? One common interpretation: Slide 68: ? One common interpretation: Put it inPractice : Put it inPractice Revise and Refine Metacognitive Skills Diagnostic Tools Assess Understanding Slide 70: Diagnostic Tools ? Slide 71: Students undergo imperfect gist-extraction, and the flawed schemata they form must be identified. We need to be able to identify where the false schemata are. ? Building a Diagnostic Tool : Building a Diagnostic Tool Think back to the last time you gave a test on lines. Write down some examples of mistakes that students made. ? Slide 73: Misapply the negative on a fraction. Difficulty evaluating expressions with x and y. Don’t know the difference between vertical and horizontal. Mistakes in subtracting signed numbers in the slope expression. Incorrectly solve equations with negative coefficients. Simplifying point-slope form when it involves fractions. Can’t plot points involving fractions. ? Slide 74: Can’t plot points involving fractions. Incorrectly solve equations with negative coefficients. Difficulty evaluating expressions with x and y. Misapply the negative on a fraction. Mistakes in subtracting signed numbers in the slope expression. Simplifying point-slope form when it involves fractions. Don’t know the difference between vertical and horizontal. ? Slide 75: ? Slide 76: But now you have one more thing to grade, right? ? Slide 77: nope ? Slide 78: ? Slide 79: ? Slide 80: ? Slide 81: ? Slide 82: Summary: Diagnostic Tool Identify false schemata Purpose: How to construct: Think about past student behavior, write short questions that target common errors at end of chapter. How to assess: Tally sheet. Students self-assess. ? Slide 83: Revise and Refine ? Slide 84: ? Slide 85: ? Slide 86: ? Slide 87: ? Slide 88: ? Slide 89: ? Slide 90: ? Slide 91: Summary: Revise & Refine Revise & Refine existing schemata to improve learning. Purpose: How to construct: Think about what gets muddled when a new concept is added. How to assess: You monitor progress and students self-assess. Simple answer-checking is key. ? Slide 92: Assess Understanding Categorize this Picture ? Slide 93: Does this help? ? Slide 94: ? Slide 95: ? Slide 96: ? Slide 97: ? Slide 98: ? Slide 99: Summary: Assess Understanding Improve Information Processing and gist-extraction. Purpose: How to construct: Work with “first-steps” and categorization of problem types. How to assess: Student or group makes first attempt, then go over assessment as a class. ? Slide 100: Metacognitive Skills ? Slide 101: ? Slide 102: ? Slide 103: 5 Bring it on!!! 4 I know I will pass, grade? Not sure. 3 Well, we’ll see how it goes. 2 I think I should have attended more class. 1 Not a clue. ? Slide 104: Summary: Metacognitive Skills Improve metacognitive skills. Purpose: How to construct: Look at learning objectives and look where objectives overlap. How to assess: Student makes initial assessment prior to studying for exam. Second assessment after studying. Reflection after exam. ? Slide 105: Recommended Reading: Cognitive Development and Learning in instructional Contexts, by James P. Brynes Presentation at: www.tcmtechnologyblog .blogspot.com (right-hand side) Workbooks of Assessments and Activities: Cengage Learning, author: Maria H. Andersen ?

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