A Fourth Year Course

 North Salem Middle High School  Teaching and learning since 1985  You name it …. I probably taught it!  Been searching for ways to make mathematics meaningful, and to put the meaning into mathematics.

 Problem Based Learning ◦ Involvement that leads to questioning and comprehending. ◦ Investigations and meaningful tasks ◦ Construct Knowledge through meaningful tasks ◦ Culminates and a real life task or problem to solve  5 E’s ◦ Engage, explore, explain, elaborate, evaluate. I forget, I remember, I understand !

 A person gathers, discovers or creates knowledge in the course of some purposeful activity set in a meaningful context.  Improve understanding.

Provide meaning to mathematics through activities that have a real purpose- Provide an answer to the question: When am I ever going to use this? Solve problems in a STEM context. Bring meaning through purposeful activities

Provide the background and knowledge students will need to solve their problem.

“They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.”

FOCUS LOSS of : Width, Motivation, Applications Loss of: Depth Efficiency Elegance

Designed to reveal a learner's understanding of a problem/task and her/his mathematical approach to it. Can be a problem, project, or performance. Individual, group or class-wide exercise.

A good performance task usually has eight characteristics (outlined by Steve Leinwand and Grant Wiggins and printed in the NCTM Mathematics Assessment book). Good tasks are: essential, authentic, rich, engaging, active, feasible, equitable and open.

 Investigations and meaningful tasks.  Construct knowledge through inquiry.  Culminates in a realistic hands –on project.  5 Es Instructional Model. 5 Es Instructional Model

 Problem  Problem: When will this particular species be delisted from endangered to threatened? Will it happen in your life time?  Exponential Functions.  Model population decay and growth of the Kemp Ridley Sea Turtle with technology.  Data provided by a turtle demographer from Duke University- Dr. Selina Heppell.  Construct an internet scavenger hunt to find details about the Kemp Ridley Sea turtle.

A Scatter Plot of the data Point of intersection represents the solution.

-Satellite tracking of Sea Turtles allowed students to follow the behavior of a particular turtle for as long as data was available. -As the project evolved pieces like this were added to improve the overall experience. -It made it real.

Students predicted that in the year 2013 the Kemp Ridley would be delisted.

How can I make this topic more meaningful to students and relevant to other disciplines?  An Idea.  Started with a question concerning the use of exponential functions to study population of endangered animal species. Just thought that studying animals would be more fun than the growth of cell phones.  My Research.  Extensive use of the internet led me to sea turtles and an obscure posting on a website led me to Dr. Heppell. Great sources :  Some Issues.  Students did not initially expect to be spending time in a math class learning about a particular sea turtle as extensively as they did. And did not expect to be writing as much as they were expected to.

 Problem:  Problem: You and your partner are surveyors and are asked to provide an accurate survey of a plot of land of your choosing.  Geometry- Polygons, convex and concave, parallel lines, alternate interior angles.  Orienteering  Using a compass to create the plot and test the region.  Trigonometry  Pythagorean Theorem, Right Triangle Trig, Law of Sines and Cosines, Area and Triangulation.

To test their orienteering skills, we go out into the wild! Surveying their plot of land.

A great real-life application of trigonometry.

Applying the trig.Reflecting on the results

 Pythagorean Thm  Alternate int. angles, corresponding angles  Triangle-Angle_Sum Thm  Parallel lines  Soh Cah Toa  Law of Sines  Law of Cosines  Area of triangles  Non right triangles-icky ones too!  Measurement and measuring tools  Dimensional analysis  ?

 Problem: Design and build a car so as to determine its acceleration using a variety of methods.  Functions  Constant, Linear, Quadratic. Function notation as it applies to physics.  Technology  Authentic Data Collection, graphing calculators, motion detectors.  Physics  1-Dimensional Kinematics

Kelvin.com is a wonderful source for technology and finding cool things to build. You can get great ideas there too! Building the Car

It’s a team effort. After data is collected students decide through applying their new skills and knowledge if the data is “good” data. The Set Up

 How do you know you have “good” data?  The following are from student reports.

Acceleration GraphDistance time graphVelocity time graph Constant graph, as time increases, acceleration remained the same. As time increases on a distance time graph, so does the distance, quadratically. Linear graph, when time increases, velocity does also at a constant rate.

D(T)= ½aT^2 + V 0 T + D 0 a (lead coefficient) = acceleration V 0 = initial velocity T = time D 0 = initial distance My Data D(T)= (.31)T^2 + (-.51)T +.62 Acceleration =.62 m/s/s Doubled lead coefficient to find this.

V(T) = aT + V 0 a = acceleration V 0 = initial velocity T = time My Data V(T) =.63T + (-.534) Slope =.63 m/s/s Acceleration = change in velocity/change in time

 _ X = ave acceleration  Constant function  Average Acceleration =.62 m/s/s

 Look at the next slide carefully…  What do you notice?  What do you think happened?

D(T)= -.312T T-.993 Quadratic Equation Acceleration = a(2) = m/s

 What math Do YOU see?  ?

 Who is your audience?  What are your topics?  Integrate STEM activities  Modify!  ELA

 Mathematical Modeling can answer the age old question… “When am I ever going to use this?”  Mathematical Modeling can generate new questions. “Why didn’t this work?” or “ Why did this work?”

 Dan Meyer-math class needs a makeover. Dan Meyer  RSA Animate-Ken RobinsonAnimate-Ken Robinson  Hans Rosling : Population Growth over 200 years. Hans Rosling : Population Growth over 200 years.  David McCandless turns complex data sets (like worldwide military spending, media buzz, into beautiful, simple diagrams that tease out unseen patterns and connections. David McCandless turns complex data sets (like worldwide military spending, media buzz,  Taylor Mali- just because Taylor Mali- just because