PowerPoint Presentation

Utilizing Mathematica as an Effective Teaching Tool for an Honors Calculus Course at a Community CollegeCUNY 2014 Mathematics ConferenceEffective Instructional Strategies (May 9, 2014) Ruslan Flek, Ph.D. & Tanvir prince, Ph.D.mathematics departmentHostos Community CollegeCITY UNIVERSITY OF NEW YORK

Why Mathematica? The purpose of the lab component The introductory lab Sample notebooks (labs) Students opinions Instructors reflections

Why Mathematica?

Why Mathematica?

1.Both of us have substantial previous knowledge and teaching experience using Mathematica2.Free to all CUNY students3.Used by many universities and colleges4.Very user-friendlyThe Role of the Mathematica Lab

The main idea is similar to a Physics or Chemistry course that has a lab componentThe Role of the Mathematica Lab

The main idea is similar to a Physics or Chemistry course that has a lab componentStudents are encouraged to experiment and make their own discoveries modelling discovery-based learningThe Role of the Mathematica Lab

The main idea is similar to a Physics or Chemistry course that has a lab componentStudents are encouraged to experiment and make their own discoveries modelling discovery-based learningThe main scripts of the labs are developed by the instructors to enhance the understanding of the underlying theoretical concepts being taught that weekThe Role of the Mathematica Lab

The main idea is similar to a Physics or Chemistry course that has a lab componentStudents are encouraged to experiment and make their own discoveries modelling discovery-based learningThe main scripts of the labs are developed by the instructors to enhance the understanding of the underlying theoretical concepts being taught that weekMany books include exercises suitable for a Mathematica lab, usually located close the end of a section that have a CAS tag The Role of the Mathematica Lab

The Introductory Lab

Basic CommandsSyntaxTerminologyHands-onExercisesVisualizationsTrial and ErrorApplicationsTo AlgebraReview of FunctionsAnother Example of a Lab

This lab facilitates discovery learning through experimentation at the previous lecture meeting students learned the definition of the derivativeIntroduce the simple command for the derivative:

D[f(x),x]Another Example of a LabMathematica View:

D[x3,x]3 x2

D[x4,x]4 x3Mathematica View:

Another Example of a LabMathematica View:

Answer the following questions:

Are these three patterns same or different?Can you summarize all into one formulae?Are there any exceptions to this formulae?Another Example of a LabFinding Equations of Tangent Lines

Finding Equations of Tangent Lines

How the slopes of tangent lines change along a curve. (Animations are very easily created in Mathematica to further visualize the concepts)

How the slopes of tangent lines change along a curve. (Animations are very easily created in Mathematica to further visualize the concepts)

How the slopes of tangent lines change along a curve. (Animations are very easily created in Mathematica to further visualize the concepts)

How the slopes of tangent lines change along a curve. (Animations are very easily created in Mathematica to further visualize the concepts)

How the slopes of tangent lines change along a curve. (Animations are very easily created in Mathematica to further visualize the concepts)

How the slopes of tangent lines change along a curve. (Animations are very easily created in Mathematica to further visualize the concepts)

Finding and graphing the y-intercepts, turning points and points of inflection of a polynomial function

Riemann SumsBy increasing the magnitude of n, users can observe how partial Riemann sums approach the true area bounded by the curve and the x-axis

Riemann SumsBy increasing the magnitude of n, users can observe how partial Riemann sums approach the true area bounded by the curve and the x-axis

Riemann SumsBy increasing the magnitude of n, users can observe how partial Riemann sums approach the true area bounded by the curve and the x-axisStudent Opinions

Use them in other classes. This is in fact one of the main goal of lab once students see the potential of mathematica, they will use them throughout their students life.

Student Opinions

Use them in other classes. This is in fact one of the main goal of lab once students see the potential of mathematica, they will use them throughout their students life.Tend to use this in their homework to check their solutions, draw pictures etc.

Student Opinions

Use them in other classes. This is in fact one of the main goal of lab once students see the potential of mathematica, they will use them throughout their students life.Tend to use this in their homework to check their solutions, draw pictures etc.Most students generally like discovery lab more than lab using lectured materials

Student Opinions

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