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**2006 School Science & Mathematics Annual Convention,**

Write is Right: Improving Students' Problem Solving Using Graphic Organizers Dr. Alan Zollman Northern Illinois University Graphic Organizers to Help Students Communicate, Connect, Reason, Problem Solve, and Represent Mathematics Thursday, October 26, :30 pm 2006 School Science & Mathematics Annual Convention, Missoula, Montana

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question: What’s the new national law that states corporal punishment should only be applied to the right side of a child’s buttocks?

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question: What’s the new national law that states corporal punishment should only be applied to the right side of a child’s buttocks? No Child’s Left Behind

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**Assessing the Curriculum Content Needs of the Students**

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**SURVEYS OF ENACTED CURRICULUM (SEC) Council of Chief State School Officers (CCSSO)**

Surveys of Enacted CurriculumTools for Aligning Instruction, Standards, and Assessments Correlations of teacher-reported enacted curriculum vs. the Illinois State Achievement Test (ISAT)

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**MSTD Teachers vs. ISAT Exam Correlations**

Left side slides Grades 3-5 Teachers’ Enacted Curriculum in Math Right side slides Illinois ISAT Exam 2003 Grade 5 Math

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GRAPHIC ORGANIZER One way to assist students in problem solving, communicating, reasoning, making connections, and showing representations in mathematics

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**Four Squares Graphic Organizer 1 + 4 + 3 + T + V**

ONE TOPIC FOUR MAIN POINTS (LAST IS CLOSURE) THREE SUPPORTING IDEAS FOR EACH POINT TRANSITION STATEMENTS BETWEEN MAIN POINTS VIVID DESCRIPTORS OF SUPPORTING IDEAS

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**NCTM Process Standards**

Communications Problem Solving Reasoning and Proof Representation Connections

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**Adapting for Extended Response Questions**

Thinking like a Mathematician Adapting for Extended Response Questions

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**Brainstorm ways to solve this.**

What do I know? Brainstorm ways to solve this. What do I want to find? Try it here. Things I need to include in my extended-response write up Dr. Alan Zollman, Northern Illinois University Four-Corners Extended Response

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**Write what you know from the problem. **

Second Paragraph Write what you know from the problem. “What I know from the problem is …” Third Paragraph Show your strategies you will try. “So what I first tried to do was …” Fourth Paragraph Show your solution. “Using numbers this is …” First Paragraph Write what you are to find. “First, what I want to find is ..” Fifth Paragraph Explain your answer. “Therefore, what I did was …” Dr. Alan Zollman, Northern Illinois University Four-Corners Extended Response

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**Two extended-response**

example problems

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MARTY’S SANDWICHES

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**MARTY’S SANDWICHES Marty loves sandwiches**

MARTY’S SANDWICHES Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them!

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**MARTY’S SANDWICHES Marty loves sandwiches**

MARTY’S SANDWICHES Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them! He always puts exactly one type of topping on his sandwich: either ketchup, mustard, mayo, or even taco sauce!

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**MARTY’S SANDWICHES Marty loves sandwiches**

MARTY’S SANDWICHES Marty loves sandwiches. He likes hamburgers, hot dogs, and fish sandwiches. He loves sandwiches with anything on them! He always puts exactly one type of topping on his sandwich: either ketchup, mustard, mayo, or even taco sauce. Marty says that for lunch he can eat a different one-topping sandwich everyday for 2 weeks without having the same thing. Can this be true? Explain why.

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Oil is gushing out of an oil rig leak on the ocean, radiating outward in a circular film on the surface of the water.

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Oil is gushing out of an oil rig leak on the ocean, radiating outward in a circular film on the surface of the water. If the radius of this circular film is increasing at the rate of 2 meters per minute, how fast is the area of the oil film growing when the radius reaches 100 meters?

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**Helping students use multiple representations to solve extended response problems**

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**TEAM Alice: Always works a problem using algebra**

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**TEAM Alice:. Always works a problem using algebra TEAM Cheryl:**

TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart

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**TEAM Alice:. Always works a problem using algebra TEAM Cheryl:**

TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture

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**TEAM Alice:. Always works a problem using algebra TEAM Cheryl:**

TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture TEAM Thomas: Always works a problem guessing & testing

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**TEAM Alice:. Always works a problem using algebra TEAM Cheryl:**

TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture TEAM Thomas: Always works a problem guessing & testing TEAM Marvin: Always works a problem using manipulatives

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**TEAM Alice:. Always works a problem using algebra TEAM Cheryl:**

TEAM Alice: Always works a problem using algebra TEAM Cheryl: Always works a problem making a chart TEAM Darrell: Always works a problem drawing a picture TEAM Thomas: Always works a problem guessing & testing TEAM Marvin: Always works a problem using manipulatives TEAM Gwen: Always works a problem graphing it

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**Assessing for mathematical knowledge, strategy, and explanation in problem solving**

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Before

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Same student after!

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Before Before

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Same student after!

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Before

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Same student after!

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Before

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Same student after!

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student favorites

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later in the semester …

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**Helping students self-reflect**

In cooperative groups have students: Design an abbreviated rubric that includes mathematical knowledge, strategy, and explanation Assess “student” work using rubric Give recommendations to the “student”

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Results

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**PRETEST SCORES 27% average N=186 Students**

OPEN-ENDED RESPONSE QUESTIONS PRETEST SCORES 27% average N=186 Students POSTTEST SCORES 70% average N=183 Students Using ISAT Scoring Rubric

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PRETEST State meets or exceeds 4% in Math Knowledge, 19% in Strategic Knowledge 8% in Explanation N=186 Students POSTTEST State meets or exceeds 75% in Math Knowledge, 68% in Strategic Knowledge 68% in Explanation N=183 Students Using ISAT Scoring Rubric

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references: “Four Square Writing Method for Grades 1-3” written by Judith S. and Evan Jay Gould published by Teaching and Learning Company, Carthage, Illinois. (1999). “Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, NIMS Mathematics-Science Partnership. (2004). “Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, MSTD Mathematics-Science Partnership. (2005). “Four Corners Graphic Organizer for Open-Ended Mathematical Problem Solving” Alan Zollman, Raising The MEANs Mathematics-Science Partnership. (2005). “Four Corners is Better Than Four Squares in Math” Alan Zollman, ICTM 57th Annual Meeting, Springfield, IL. (Oct. 14, 2005). Illinois Assessment web site: Council of Chief State School Officers;Surveys of EnactedCurr.(SEC) “Simmons Middle School Results: East Aurora District 131” Karen Lopez, MEANs Partnership Showcase, DeKalb, IL. (Apr. 6, 2006).

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Dr. Alan Zollman Dept. of Mathematical Sciences Northern Illinois University Dekalb, IL /

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