Using Maplets for Teaching Calculus & Precalculus SCCMT Fall Conference October 25, 2013

Using Maplets for Teaching Calculus & Precalculus SCCMT Fall Conference October 25, 2013

Using Maplets for Teaching Calculus & Precalculus

SCCMT Fall ConferenceOctober 25, 2013Ray Patenaude, South Pointe High School, Rock Hill, SCDoug Meade, University of South CarolinaSession OutlineIntro & Examples of Maplets for CalculusCurrent Uses of MapletsResearch using Maplets with ContinuityImplications/Advice for using AppletsSummary and Q&A

What are they?

Set of over 200 applets designed using Maple software

Provide examples and exercises

Cover topics from Precalculus, Calc. I, II, & IIIExample Reflections of Functions

Example The Chain Rule

Example Max/Min Application

Current Instructor Uses of M4CDemonstration visualize concepts during lectureProvide Examples for InstructionSimilar to Chain Rule aboveHomework ExercisesAssign number of exercises to be completed

Current Student Uses of M4CLab ExercisesInstructor assign Maplets to be completed prior to, or after lecturePracticeMany Maplets make student complete one step prior to anotherHints and check feature allow students opportunity to correct Use of Applets for Developing Understanding in Mathematics: A Case Study Using Maplets for Calculus with Continuity Concepts

ObjectivesDetermine the features of Maplets for Calculus that promoted understanding of continuity concepts.And,Determine student actions, and strategies developed, while using M4C that promoted understanding of continuity concepts.

Collecting Data

*Image used with permission of student and guardian.Collecting Data

QuestionsWhat understanding did this student demonstrate?

What features of this Maplet did the student use to gain this understanding?Continuity using a Piecewise FunctionSecond Maplet used in research study.

axiomatic-formalproceptual-symbolicblending embodiment& symbolismdefinitions based on known objectsTheres no holes or jumps in the graphFrom the left and from the right, the graph goes to two different points.The limit from the left and from the right have the same valueLeft/right continuity described by open/closed points on graphIts not continuous from the left because the limit does not equal the value of fIts continuous because from the left, right, and the value of f all meet at this point on the graphIts continuous because the values of the left and right limits and the value of f(x) are all the sameBasic description of - to describe discontinuity on graph exercise: If you draw these epsilon lines here and here, that other point [open] isnt in there Picture approximates student drawing

Primarily discuss continuity in terms of limit definition and function values.Students level of understanding of continuity within David Talls Three Worlds model. Describe continuity naturally using points and endpoints visually or embodied on a graph.Able to describe continuity using limits, graph, and/or bothconceptual-embodiedformal objects based on definitionsLessons Learned from M4C ResearchTen take-aways that can be applied to using applets in teaching mathematics in the classroom.Lessons Learned from M4C ResearchTeaching/instructing is still necessary.- M4C and most applets are supplemental.- Some students need guidance on use of applets to get the most out of them.- Model the use of applet.Lessons Learned from M4C Research2. Maplets kept students engagedCCSSM practice calling for persistence in problem solving

Lessons Learned from M4C Research3. Overt features students found/reported most helpful: - Check Answer- Change Answers - Hints- Graphs

Lessons Learned from M4C Research4. Subtle features also contributed to understanding:- Layout/organization of problems- Directions- Variety of problemsLessons Learned from M4C Research5. Some features were not useful to students:

Lessons Learned from M4C Research6. Field test applets/Maplets with students before using with entire classStudents will find trouble spots with appletsHelp with your decision to use, modify, or omit from instructionLessons Learned from M4C Research7. Students enjoyed working with Maplets for Calculus applets- expressed desire to do these exercises as opposed to textbook exercisesLessons Learned from M4C Research8. Use Thinking Aloud while tutoring students.

9. Especially when starting, allow students to work in pairs.

10. Start small.

ReferencesMeade, D. B. & Yasskin, P. B. (2008, December). Maplets for calculus: Tutoring without the tutor. Paper presented at the Asian Conference on Technology in Mathematics, Bangkok, Thailand. Retrieved from http://maple.math.sc.edu/maplenet/M4Cfree/pages/publications.html

Nez, R. E., Edwards, L. D., & Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39, 45-65.

Patenaude, R.E. (2013). The use of applets for developing understanding in mathematics: A case study using Maplets for Calculus with continuity concepts. (Doctoral dissertation, University of South Carolina).

Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20(2), 5-24.

Maplets for Calculus: http://m4c.math.tamu.edu/