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8/12/2019 CUNY_Mathematics 2014 Conference presentation - Effective Teaching Strategies with Computer Algebra Systems - VThompson

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Effective Teaching Strategies with Computer Algebra

SystemsBy Virginia L. Thompson, York College

May 9th

, 2014


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IntroductionOver the past decade, the use of Computer Algebra Systems

(CAS) in the mathematics classrooms has spread widely.Studies have shown it to be beneficial to students whereas

they are able to understand mathematical concepts at amore advanced level.

A CAS is a software package that can be used to performalgebra manipulations, such as solving equations, graphingfunctions, finding limits, derivatives and more.

Popular CASs includes Maple, Mathematica, MathLab andMathCad. Some handheld calculators such as the TexasInstruments 89 or TI-Inspire editions also have CASabilities.


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IntroductionThe use of Mathematica is particularly helpful tostudents in my precalculas class when learning topicslike:

graphing functions, transformation of functions,

compressing and stretching functions,

reflection,

obtaining information from the graph of a functionincluding domain and range,

asymptotes,

modeling our world with functions and more.


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What does Mathematica look like?


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What does Mathematica look like?


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Benefits of Teaching with MathematicaResearch studies found that the effective use of the CAS

can:

free students from having to work out mathematicalprocedures by hand, affording them more time to examinethe output in order to make interpretations (Zbiek, 2007)

allow more time to be spent on problem solving and lesstime on pencil and paper procedures

enable instructors to present a wider range of examplesand visualize results immediately.


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However However, to accomplish such great results is not so

simple. The very presence of a CAS in a classroomdoes not automatically produce positive results.

Teachers must know how to efficiently integrate thetechnology into the learning process, because not allstudents adapt to this type of learning well.


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..This rest of my talk will

consider effective strategies on teaching with CASs,

propose some new ways this powerful tool can beintegrated in mathematics courses, and

student and faculty experience using CAS in theundergraduate mathematics classroom


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Effective StrategiesBeginner learners of Mathematica may find it difficult to

understand the commands at the start. This difficultycan be overcome by first focusing on the syntax of theMathematica language. Students should beencouraged to think about what the desired resultshould before executing the statement. (Husain, 1997)


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Introduction to Mathematica


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Introduction to Mathematica


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Effective StrategiesWith Mathematica, students are able to manipulatefunctions quickly and, from this, can easily see theresults by changing a parameter, or by adding anumerical value to a function. (Zbiek, 2007)

Students are able to focus on and make assumptions

about common attributes shared by a family offunctions.


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Effective Strategies


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Effective StrategiesStudents can discover the rules of horizontal and vertical

shifting of a function.


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Effective StrategiesStudents discover other techniques on graphing, and at its

end, student can answer questions on their own like isbelow:

Plot the absolute value function shifted to the right by 5units and upward 20 units from the origin.

Plot a parabola function that has the vertex (-3, 2), concavedownward.

Plot the reciprocal function that is shifted 3 units to the leftfrom the origin.

Plot a parabola that had the vertex (-2,4) and intercepts thex and y axis at zero.


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Effective Strategies The use of computer algebra systems in our lessons

requires us to think more carefully about the problemswe give our students.

A CAS must be seen as more than a computationaltool.

Students should view the CAS as a valuable tool, not a

crutch.

Using a CAS, more time to be spent on problem solvingand less time on pencil and paper procedures.


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Modeling our World with Functions


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Effective Strategies Make your materials, worksheets and demonstrations

available to your students. (http://www.math.tamu.edu/~dallen/papers/strategies.pdf)


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New ways this powerful tool can be

used in Mathematics courses.Hybrid!!!

Blending face to face (f2f) and online learning wouldin a Computer Algebra Systems course would bebeneficial to students.


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used in Mathematics courses.A hybrid course

offers flexibility and convenience to the students enabling themto learn somewhat at their own paste.

Students cannot sit back and hide in class or not show up class(as in traditional classes) but they must be responsible for theirwork.

Students are forced to participate in discussions.

Students can network with their classmates through blogging,chatting in order to understand concepts.


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used in Mathematics courses.In my Computer Algebra Systems Hybrid Course

Students can access video recorded lessons Students read weekly readings (ebook or other

materials)

Students participate in discussion questions

Students complete individual and group projects


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Discussion board

The discussion board can provide an area for students tocompare problem solving methods or have other

conversations regarding the course with peers or theinstructor so students do not feel isolated when

encountering difficulties

Example of a DQ: Explain to me as if you were to a friend howyou would go about finding the domain and range of afunction. Give some examples of your own (at least 3).Provide some equations, and ask your classmates todetermine the domain and range.

Wh i i d d


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What are instructors attitudes towards

implementing mathematics using the

CAS?Overall,

The instructors pointed out advantages the CAS has to offer, which went along withwhat was found in the Literature Review, such as:

the ability to give immediate calculations and feedback on answers.

They saw that students are able to learn mathematics without being an expert atthe manipulation.

The disadvantages were as follows:

If the student doesnt use the software appropriately, it wont work for them

the course class time (which is 50 minutes / per week) is just not enough time toteach the course effectively.

due to the small amount of time the course meets (50 minutes / per week),students are not able to properly learn what is being taught, the amount ofmaterial covered is limited, and topics cannot be learning in depth.


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Student and Faculty experience

teaching and learning with a CAS Some teachers experience difficulties achieving

aspects of the curriculum, having to change theirteaching methods and styles to incorporate the CAS

into the lesson.

Integrating the CAS is perceived by some teachers astime consuming and a burden. (Barzel, 2007)

Some teachers lack training on how to use the CASproperly and therefore are discouraged from using it


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Student and Faculty experience

teaching and learning with a CASDifficulties students face, learning mathematics

with a CAS: CASs are not flexible, do not allow informal

language. A user must input the data with notypographical errors. Students have difficulties entering algebraic

expressions properly.

For example:The student enters instead of

or instead of .

)(6

100 alvf

)(6

100

al

vf

2x 2x


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Conclusion Teachers should:

learn effective ways of integrating technology into the lesson.

review influential research on methods of teaching with

technology. work with educators who have already went on that path, who are

able to guided them successfully.

Access their students ability to use to technology effectively.

Structure mathematical questions so that the CAS is not just being

used to compute answers, but providing opportunities for studentsto explore mathematics.


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The EndFeel free to contact me at:

Virginia L. Thompson, Ed.D.Doctoral Lecturer

School of Arts and Sciences

Department of Mathematics and Computer Science York

College, City University of New [email protected]

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