Learning comes aliveusing MODSIM

Presenters:

Janet Hammer- MathematicsAlgebra I, Algebra II

Sabrina Shumate- ScienceBiology, Earth Science

“When you can do common things in an uncommon way, you can command the

attention of the world”- George W. Carver

How we began

• We initially met over the summer to determine where our curriculums overlapped.

• We explored different technologies that would support those topics using a MODSIM approach.

• We set initial goals of what we wanted to accomplish, both individually and collaboratively.

Ways to incorporate MODSIM

• Introduction – Before a student has knowledge of a unit.

• Exploring – Enrichment during a unit.

• Reviewing – To enforce what has already been covered in the unit.

How We Approach MODSIM Lessons

• Janet’s approach- While putting together a unit plan, search available MODSIM resources that could be used to introduce a concept.

• Sabrina’s approach- determine a topic students struggle with every year and explore the internet for MODSIM resources that will help students “SEE” the concept.

MODSIM and Math

• Modeling and Simulation occurs often in a math classroom but not as a “stand alone” more like a tool.

• By incorporating MODSIM into an otherwise teacher directed routine, students have the opportunity to grasp more efficiently what it is that we are trying to teach them.

Before Data is enteredI nvestigating the height of a stack of cookies - Your measurements in centimeters!

Enter your data in the appropriate yellow cells in the table on the lef t.

number height

of cookies of stack

0 #DI V/ 0! #DI V/ 0! The regression line (blue)

1 #DI V/ 0! #DI V/ 0! or the line of best-fi t, its

2 #DI V/ 0! #DI V/ 0! equation, and r2 will appear

3 #DI V/ 0! #DI V/ 0! #DI V/ 0! when data are entered.

4 #DI V/ 0! #DI V/ 0!

5 #DI V/ 0! #DI V/ 0! I f you don't have data

6 #DI V/ 0! #DI V/ 0! f or a certain number

7 #DI V/ 0! #DI V/ 0! of cookies, leave the

8 #DI V/ 0! #DI V/ 0! cell blank.

9 #DI V/ 0! #DI V/ 0!

10 #DI V/ 0! #DI V/ 0!

Simulation

Using the regression equation f rom the graph, the f ollowing can be calculated: change average thickness (the green line appears)

enter number of cookies = predicted height of stack = new slope 1 increase

Predictions #DI V/ 0! 10

measured stack height = predicted number of cookies = decrease

NOTE: The #DI V/ 0! error will be removed when data is entered!

Sinex 2006

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10number of cookies

hei

ght

of s

tack

, cm

Student resultsI nvestigating the height of a stack of cookies - Your measurements in centimeters!

Enter your data in the appropriate yellow cells in the table on the lef t.

number height

of cookies of stack

0 0.0 0.2 0.3 The regression line (blue)

1 3.8 3.7 4.9 or the line of best-fi t, its

2 7.2 7.3 9.4 equation, and r2 will appear

3 10.9 10.8 14.0 1.000 when data are entered.

4 14.4 14.3 18.6

5 18.0 17.8 23.1 I f you don't have data

6 21.3 21.3 27.7 for a certain number

7 24.9 24.8 32.3 of cookies, leave the

8 28.2 28.3 36.8 cell blank.

9 31.8 31.9 41.4

10 35.3 35.4 46.0

Simulation

Using the regression equation f rom the graph, the f ollowing can be calculated: change average thickness (the green line appears)

enter number of cookies = 50 predicted height of stack = 175.9 new slope 1.3 increase

Predictions 4.567 13

measured stack height = 75 predicted number of cookies = 21.3 decrease

NOTE: The #DI V/ 0! error will be removed when data is entered!

Sinex 2006

y = 3.513x + 0.236

R2 = 1.000

0.0

10.0

20.0

30.0

40.0

50.0

0 2 4 6 8 10number of cookies

hei

ght

of s

tack

, cm

Cookie Stack Lesson Summary

• This activity is designed to be an introduction to the mathematical modeling of experimental data.

• Sandwich cookies tend to have a relatively consistent thickness; hence, a good fit of the data occurs on performing a linear regression. The interactive Excel spreadsheet produces the best-fit line and its equation.

• Once the linear equation is determined, you have the mathematical model. This gives the students the opportunity to recognize what represents the slope (thickness of the cookies) and also the variations of the y-intercept (errors in measurement and actual cookie thickness variation cause this small value).

• The students write the equation in terms of the variables and define them as: H = tn.

• You can use the model to make predictions too.

Students Response

• The students were receptive to beginning a unit with an investigative approach.

• They were eager to work as a group to answer questions. This created a more competitive environment. One where they were eager to get it right, not just for a grade.

• This approach required them to think at a higher level. Making it possible for them to answer questions that I normally would not ask this level of student.

MODSIM and Science

• Biology is the study of life• Before the school year began, I made a list

of concepts students never truly “SEE”• Difficult topics-predator/prey relationships,

cell structure, cell division, etc.• Labs- funding? availability of equipment?• I explored MODSIM technologies that

would aid in students understanding difficult topics

Lesson Plan Outline

1) Objective-what are the main concepts?

2) Introduction/review sites3) Reference sites4) Computer-user interactive sites5) Conclusion/wrap up

Sample Biology Lesson Plan• Ecology Lesson plan• Introduced energy flow (food chain/food

web) and had students work on handouts for review

• Students were not grasping predator/ prey relationships

Sample Biology Lesson Plan

• http://www.sciencebob.com/lab/q-web-chain.html• http://www.ecokidsonline.com/pub/eco_info/topics/frogs/chain_reaction/index.cfm• http://puzzling.caret.cam.ac.uk/game.php?game=foodchain• http://www.quia.com/rr/53234.html

To prevent headache:http://tinyurl.com/

•Developed MOSIM activity to concrete topics they have learned and had them explore predator/prey relationships to develop a deeper grasping of topic

Sample Earth Science Lesson Plan• Density lesson plan

• Introduced density and relationships between variables

• Students can memorize the equation but have trouble really “seeing” the concept of density

• Students completed a lab in class where they recorded mass and volume of different substances and determined the density

• Developed MODSIM activity to guide students through an online Density Demo

Sample Earth Science Lesson Plan

• Density Gizmo• www.explorelearning.com• Explore, Engage, Review

Math and Science Connections• Probability/ratio

• Scientific notation • Solving single variable equations• Graphing- coordinates, accuracy,

functions, etc.

Sample Math and Science Lesson Plan

Mapping/Coordinate Planewww.explorelearning.com

Gizmos that could be used to teach or review graphing and mapping.

City Tour (Coordinates)Points in the Coordinate Plane

Activities A, B, & C.

MODSM Reflections

• Increase in student engagement• Increase in student understanding• Increase in technological literacy• Increase in test scores• Increase in motivation to learn• MODSIM development takes time

Future MODSIM

• Continue trying to find connections between math and science

• Develop more MODSIM lessons to include different areas of the Math and Science curriculum.

• http://modsim.wikispaces.com/