Making (Informed) Mental Math Decisions: - PowerPoint Presentation

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Making (Informed) Mental Math Decisions: Four Factors for Appropriate UseICTM Annual MeetingSpringfield, IL10/16/10

Jim Olsen

Western Illinois University

JR-Olsen@wiu.edu

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

PurposeHelping 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. Slide3

OutlineThree broad goals.Why mental math.6 keys for helping students gain these skills.Making Informed Mental Math Decisions: Four Factors for Appropriate Use…including a storyRevisiting the issue of students showing their work.Two-part exams (with and without calculators)Slide4

Three Broad GoalsHelping students understand the importance and usefulness of mental math.Helping students make an informed decisions about which calculation method to use.Helping students develop mental math strategies.Why

mental math>>Cathy Seeley (04-06 NCTM President) Slide5

Six keys to helping our students “to be proficient with tools that include pencil and paper and technology, as well as mental techniques.” 1. Students see the importance and usefulness of mental math.2. Students make good decisions about the calculation method to use.*

3. Students

learn strategies

for mental

math.

4. Students practice the mental math strategies.

5.

Teachers

a

ssess students’

mental math

skills

and sans calculator paper-and-pencil procedures.*

6. Students have a

mindset of mental math

, in which they have an expectation of and belief in mental math.Slide6

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.Slide7

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.Slide8

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.”Slide9

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.Slide10

Making Informed Mental Math Decisions: Four Factors for Appropriate UseSlide11

1. Numbers/Strategies factor: Teachers and students need to consider the operation and the numbers and determine if 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? Slide12

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? Slide13

Take a BreakThe Parable of the BookshelfThe lesson to be learned:  When building something, consider its intended use.  Build the structure in such a way that it will be able to successfully be used for its intended purpose.The lesson to be learned for education:

When we are learning something, we need to consider how that knowledge will be used later.  We need to learn the concepts and procedures in such a way that they will be able to be applied later.Slide14

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? Slide15

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? Slide16

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

.Slide17

Revisiting the issue of students showing their workWhy do teachers have their students show their work? Slide18

Revisiting the issue of students showing their workWhy do students show their work? Slide19

Getting an appropriate policy regarding students showing their workAppropriate for reaching our goals of seeing work.Reasonable.Flexible. Slide20

The Showing-Your-Work ContinuumConsider having studentsd

o exercises here.

Do exercises that are normally

done with paper and pencil,

mentally.Slide21

Do exercises that are normally done with paper and pencil, mentally.Examples: Two-step equationsFinding x-intercepts of linear functionsPythagorean theorem to find an unknown side of a right triangle. Slide22

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.Slide23

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 methodPart 2: GCD using the ladder methodSlide24

Questions.Comments.Thank You.Jim OlsenWestern Illinois UniversityJR-Olsen@wiu.edu

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

I hope that you and your students can make good decisions regarding the use of mental math, pencil and paper, and calculators.