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Making (Informed) Mental Math Decisions: Making (Informed) Mental Math Decisions:

Making (Informed) Mental Math Decisions: - PowerPoint Presentation

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Uploaded On 2019-03-04

Making (Informed) Mental Math Decisions: - PPT Presentation

Four Factors for Appropriate Use AllDay Workshop Jim Olsen Western Illinois University JROlsenwiuedu wwwwiueduusersmfjro1wiu Purpose To help 712 students develop mental math skills and understandings These skills and understandings are beneficial in their own right but add ID: 754956

making students mental decision students making decision mental part factor paper calculation math pencil time decisions factors numbers method

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Slide1

Making (Informed) Mental Math Decisions: Four Factors for Appropriate UseAll-Day Workshop

Jim Olsen

Western Illinois University

JR-Olsen@wiu.edu

www.wiu.edu/users/mfjro1/wiu/Slide2

PurposeTo help 7-12 students develop mental math skills and understandings. These skills and understandings are beneficial in their own right, but additionally enhance students’ achievement and success throughout nearly all areas of mathematics and in everyday life.Slide3

Based on the 5 Keys for Learning Mental Math

FocusSlide4

Making Informed DecisionsThe decision by teachers, students, and citizens to use mental math, paper-and-pencil, or

technology

to arrive at an answer.

…who decides?

Sometimes the teacher decides (!)

Ultimately, we want students and citizens to make good decisions.Slide5

Making a good decision is harder than one might thinkThe extremes of Use all the available technology all the time ORNO more calculators !! ….are not appropriate.The policy of allowing (or not allowing) calculators according to the grade level or course is short sighted.Making decisions based on the size of the numbers or number of digits is not appropriate.We need to send the right message about calculator use.Slide6

Consider adding language similar to the following in your course information:“In this course, the xyz [e.g., scientific] calculator will be used at times. In addition to performing calculations with a calculator, students will be expected to perform calculations mentally and with paper and pencil. All three methods of calculation are important and students will learn to make good decisions when choosing which method of calculation to use.”Slide7

The Teacher Making DecisionsThe decision to have the students do a process or calculation mentally, with paper and pencil, or with technology is a very important decision. These important decisions are made numerous times in each lesson. A decision that requires thought based on at least 4 factors.Slide8

Making Informed Mental Math Decisions: Four Factors for Appropriate UseTeachers need to: Model the decision-making process.Teach the four factors (next slides) to consider when making a decision. Some of the time, “decide for the students.”

Help

students make the decision as a regular course of action in class. Slide9

1. Numbers/Strategies factor: Teachers and students need to consider the operation and the numbers to determine if the calculation can be done with known strategies. If an efficient mental math or paper-and-pencil strategy is known, it should be used.Q:

Do I have a mental math or paper-and-pencil strategy that would work well on these numbers?

Slide10

2. Purpose factor: Here, teachers and students consider the purpose of the activity, exercises, or lesson in making the determination. Q: Would it be informative, instructional, or enlightening to carry out a mental or hand calculation? Slide11

3. Distraction factor: The teacher and student needs to consider the level to which the use of a method is distracting to the overall process.Q: Would it be distracting to carry out a hand calculation or use technology? Slide12

4. Accuracy/Time/Resources factor: Here the user considers practical issues such as the required accuracy of the task, available time, and available resources. Q: Do available resources, time constraints, or required accuracy dictate my method of calculation? Slide13

A Look At The Three Groups Of People Making The Decision

Teacher

Student

Citizen

Available Strategies/Numbers factor

#2

#1

#1-tie

Purpose factor

#1

#2

(#4)

Distraction factor

#3

#3

#1-tie

Accuracy/Time/Resources factor

#4

#4

#2

The #1-4 factors are in the order they are because

students should consider the factors in this order

.Slide14

Revisiting the issue of students showing their workWhy do teachers have their students show their work? Slide15

Revisiting the issue of students showing their workWhy do students show their work? Slide16

Getting an appropriate policy regarding students showing their workAppropriate for reaching our goals of seeing work.Reasonable.Flexible. Slide17

The Showing-Your-Work Continuum

Consider having students

d

o exercises here.

Do exercises that are normally

done with paper and pencil,

mentally.Slide18

Do exercises that are normally done with paper and pencil, mentally – good way to practice fluency objectives.Examples: Two-step equationsFinding x-intercepts of linear functionsPythagorean theorem to find an unknown side of a right triangle. Slide19

Two-part ExamsThere is a No Calculator partCalculator partUsually one page each on different colors.First part tells the total number of problems and recommended amount of time for part 1.Slide20

Two-part Exams continuedWhen writing the test, some questions can go on either part, giving you flexibility.Each part is about half the test.Usually I do not have the “same question” on both parts of the test (with different numbers). Similar questions yes. E.g.,Part 1: GCD using the prime factorization method

Part 2: GCD

using the ladder method