Bridging the Gap Between Middle/High School

Physics and Mathematics

Hector Lopez, Eugenia Etkina, Suzane Brahmia, Jim Flakker, Jeff Goett, Alan Van Heuvelen

July 21, 2008AAPT Summer MeetingEdmonton, Alberta

Problem

•We reform college physics courses but PER focuses less on secondary level

•Possible barriers to the direct dissemination of techniques

•Not enough scaffolding•Weak math•Lack of non-traditional resources•Lack of non-traditional support network

To solve the problem we started working on a new curriculum

PUM

Physics Union Mathematics

•differentiated so can be adapted to diverse classroom and learning levels.

•based on ISLE (active learning; mirrors science processes, emphasis on developing scientific abilities)

•focused on mathematical literacy.

•physics curriculum for middle school and high school in its pilot phase.

Scientific abilities + mathematical reasoning

What is Physics Union Mathematics?

•middle - high school continuum

Improved learning of both physics and mathematics

Investigative Science Learning Environment, college physics

Etkina and Van Heuvelen (2001; 2007)

+

yes

no

My observations(data)

RevisionMultiple explanations,

mechanisms or relations between physical quantities

Assumptions

More + Applications

Testing experiments:Does outcome match prediction based on explanation/relation?

check

different

Project Goals

+

My observations(data)

RevisionMultiple explanations,

mechanisms or relations between

physical quantities

More + Applications

Testing experiments

Scientific abilities and rubrics; mathematical

reasoning

Provide different levels of professional development and study the reenactment

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PUM People

PILOT Modules

High SchoolKinematicsDynamicsWork & EnergyElectrostatics

Middle SchoolKinematicsDynamicsWork & EnergyMatter

ALG original activity1.3.7 Three statements about motion and force are provided below. Use any of

the equipment listed at the beginning of Section 1.3 to disprove the statements.

• (a) An object always moves in the direction of the unbalanced force exerted on it.

• (b) If the unbalanced force exerted on an object is zero, the object is at rest.

• (c) The arrows on a motion diagram for the object and the unbalanced force on the free body diagram are in the same direction.

Which statement couldn’t you disprove?

Δrv

Changing the ALG activities

• Provide more scaffolding

• Simplify the language

• Emphasize, infuse, and strengthen mathematics reasoning

Revised PUM activity (middle school)5.1 Test a hypothesis: motion and unbalanced force

• Aaron has a hypothesis that objects always move in the direction of the unbalanced force exerted on them by other objects.

• (a) Design an experiment in which an object will move in the direction of the unbalanced force. Describe carefully what you are going to do, draw a force diagram.

• (b) Make a specific prediction about the object’s motion based on Aaron’s hypothesis. A prediction is a statement of what will happen in your experiment if the hypothesis is correct. The prediction can only be made if you have an experiment in mind. Use the steps below.

• if _____________(hypothesis) is correct

• and I do ________(description of the testing experiment)

• Then___________(prediction: description of the outcome) should happen.

• (c) Perform the experiment and record the outcome. Did it match the prediction? Can you say that you proved Aaron’s hypothesis? Think how the prediction is different from the hypothesis.

• (d) Now think of an experiment in which you can exert a force on an already moving object in the direction that is different from the direction of its motion. Draw a force diagram. Now use Aaron’s idea to make the prediction about the object’s motion. IT IS VERY IMPORTANT TO USE AARON’S IDEA TO MAKE A PREDICTION EVEN IF YOU DISAGREE WITH IT. Then perform the experiment and record the outcome. Did it match the prediction? Now what can you say about Aaron’s idea?

PUM module structure

Test questions

Mark says that a bathroom scale measures the force that the Earth exerts on a person standing on the scale. What experiment can you design to test his hypothesis?

For questions 19-24, a rope pulls a sled exerting a force of 50 N to the left. The snow exerts a friction force of 30 N on the sled to the right. The mass of the sled with the passenger is 50 kg.

- Is the sled speeding up or slowing down? How do you know? Explain.

- What integer statement(s) represent the forces exerted on the sled in the horizontal direction? You may choose more than one answer.

a. +30 + (-50)

b. -30 + (+50)

• -30 + (-50)

• +30 + (+50)

- What integer statements represent the forces exerted on the sled in the vertical direction?

a. +50 + (-50)

b. +500 + (-500)

c. -500 + 500

• Next 2 talks - the process of module development and testing and infusion of mathematics

• For more information– http://pum.rutgers.edu– http://www.islephysics.net– http://paer.rutgers.edu/scientificabilities– http://paer.rutgers/pt3

16.1. Equation jeopardy:Four mathematical statements are listed below. For each statement describe the problems for which this statement could be a solution. Then represent the statement using a force diagram and a motion diagram.

a) Funbalanced on object = 9.8N/kg x 3 kg.

b) 7m/s – 2m/s = 3s x a

c) 35 N – 9.8 N = 1 kg x a

d) Frope on sled – FJake on sled = 35 kg x 0m/s2

Title of lesson Class work Homework Assessment NJCCS Forces as interactions 1.1, 1.2,

1.3 1.4, 1.5, RE 1

A1 5.1.8.b, 5.3.8.c, 5.7.8.a, 4.3.8.c, CCWR 3

Can a table push? 2.1, 2.4, 2.2

2.3, 2.5, RE 2

A2 5.1.8.a/b, 5.3.8.a, 5.7.8.a, 4.4.8.a, CCWR 3

Combining math and physics RS 1, 3.1, 3.2

3.3 A3 5.3.8.c, 5.7.8.a, 4.3.8.c, CCWR 4

Relating motion diagrams and force diagrams

4.1, 4.2, 4.3

4.4 A4 5.1.8.b, 5.3.8.c, 5.7.8.a, 4.3.8.c, CCWR 3

Testing ideas 5.1 5.2, 5.3 A5 5.1.8.a/b, 5.7.8.a, CCWR 3/4

16 lessons + test

Middle school dynamics excerpt from a planning table