1 / 45

The use of technology in mathematics

A masters degree research presentation.

MathTechWiz
Télécharger la présentation

The use of technology in mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. + at the HIGH SCHOOL FOR

  2. A Field Work Project submitted in partial fulfillment for the Master of Science degree in Instructional Technology at the New York Institute of Technology Fall 2007.

  3. Research Project The use of interactive web sites and the HyperStudio software by Grade 11 Math B students, as a method of learning, will improve their performance in mathematics Dr. Robert S. Slotnick Milton B. Francis ProfessorNew York Institute of Technology EDPC 691MO1 (NYIT) MSIT Candidate

  4. Table of Contents 1. Introduction • Statement of topic and issues • Research Background/Review of Literature • Hypothesis 2. Method • Participants • Instruments – Test samples • Materials & Apparatus/Equipment • Project Design/Table and SBA Research • Procedure 3. Results – Tables and Graphs 4. Discussion (Results, Behavior) 5. Conclusions & Appendix

  5. Statement of topic and issues • The use of the Internet and HyperStudio software will be used to as the method to improve the Math B performance of a group of Grade 11 students in The High School for Teaching and The Professions (HSTnP). • These students are failing mathematics in the State’s Math B Regents Examination and need some remediation.

  6. Research Background

  7. Review of Literature • Mathematics – A discipline defined by the types of problems it addresses, the methods it uses to address these problems, and the results it has achieved.1 • Mathematics Education in high school is far reaching, as students have to rely heavily on the fundamental mathematics taught during their earlier years at Pre-Kindergarten, Elementary, and Junior High Schools.2 • Multimedia Technology can be associated with education to coin the term Educational Technology. This is the study and ethical practice of facilitating learning and improving performance by creating, using, and managing appropriate technological processes and resources. 3

  8. Hypothesis Grade 11 Math B students who use interactive websites and HyperStudio software as a method of learning will improve their performance in mathematics.

  9. Method • There are no real participants in the project, but if there were, it would be the 30 students in my Math B Regents class. • The lessons would be conducted in a regular classroom with wireless internet connection via the use of 30 laptop computers. Each period lasts for 48 minutes, with the teacher meeting the students 5 periods weekly.

  10. Instruments • The instruments to be used includes testing for measuring student achievement. • There will be two tests: – A Pretest, prior to the treatment to be administered. • A Posttest, given at the end of the treatment. • Sample questions from these tests follow in a timely manner.

  11. Test Samples ____ ___ 1. Subtract the following: √–125 – √–20 = (1) 5i√5 (2) 2i√5 (3) 3i√5 (4) i√5 2. Simplify the following: 12i + 20i + (–25i). (1) 7i2 (2)– 7i2 (3) 7i (4) –7i 3. Simplify 12 + 7i 6 – 2i (1) 2 + 7i (2) 12 + 7i (3) 10i (4) 29 + 33i 2 4i 20 __ _ __ 4. Multiply and simplify √–2 ( √6 + √10 ) ___ ____ _ _ ___ _ (1) √–12 + √–20 (2) 2i√3 + 2i√5 (3) √–32 (4) 10i√2

  12. Materials and Apparatus • The project will concentrate on the use of the software – HyperStudio. • In addition to this, and for the purpose of the project, the Internet will be deemed a software tool as well, exploring relative websites to the lesson unit. • In addition to accessing the various websites 1 during the unit of lessons, the students will refer to the HyperStudio player 2 when it’s necessary. • The main technology apparatus/equipment that would be used in the project is the computer (laptop). • Chalk, chalkboard, and chalkboard eraser would also be the other equipment to be used.

  13. Materials The students will use the hyperstudio software via the the Smartboard in the classroom, as only the teacher’s laptop has the HyperStudio Player. Intermitently, they would touch the screen to answer some questions during the lesson unit. The students are familiar with the use of this software, as well as the smartboard. The HyperStudio website is shown below. http://www.mackiev.com

  14. More Materials [Lessons] • In addition to HyperStudio, the students would use websites that are relative to each lesson in the unit. • Lesson 1 – Imaginary Numbers/Complex Numbers. (2 Days) http://www.regentsprep.org/Regents/mathb/mathb-topic.cfm?TopicCode=3c3 http://www.purplemath.com/modules/complex.htm http://www.webmath.com/cn_i.html http://regentsprep.org/Regents/mathb/3c1/SquareRootPrac.htm

  15. More Materials [Lessons] • Lesson 2 - Addition & Subtraction of Complex Numbers. (2 Days) http://www.webmath.com/cn_add.html http://www.webmath.com/cn_sub.html http://www.regentsprep.org/Regents/mathb/mathb-topic.cfm?TopicCode=3C2 • Lesson 3 -Multiplication & Division of Complex Numbers. (2 Days) http://www.webmath.com/cn_mult.html http://www.regentsprep.org/Regents/mathb/mathb-topic.cfm?TopicCode=3c4

  16. More Materials [Lessons] • Review of Lesson Unit - Operations with Complex Numbers (Add, Subtract, Multiply, Divide). This review lesson would be done in 1 day. http://www.purplemath.com/modules/complex2.htm http://www.mecca.org/~halfacre/MATH/plesson31.htm http://www.uncwil.edu/courses/mat111hb/Izs/complex/complex.html http://www.edhelper.com/complex.htm http://www.tpub.com/math1/16d.htm http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut12_complexnum.htm http://tutorial.math.lamar.edu/Extras/ComplexPrimer/Arithmetic.aspx http://college.hmco.com/mathematics/larson/calculus_early/3e/shared/downloads/clc7eap0f01.pdf

  17. Apparatus • As previously mentioned, the main technology apparatus/equipment that would be used in the project is the computer (laptop). Each student will have access to a wireless internet connected laptop. • The teacher’s laptop would be connected, not only to the internet, but to the SmartBoard as well, to enable the students to be able to use the HyperStudio software. • Chalk, chalkboard, and chalkboard eraser would be the low tech equipment to be used.

  18. Research Project Design • If this was a real life project, the researcher would use the Pre-Experimental Design that uses the One-Group Pretest-Posttest Design O X O. • The independent variable, X, the treatment that would be administered, would see the students using the HyperStudio software and internet websites that should have helped them to improve their mathematics performance.

  19. Project Design Table Group Assignment Participants Pretest Treatment Posttest

  20. School-Based Action (SBA) Research • The HSTnP, even though a New Vision School, has used traditional methods in the teaching/learning process. • Many of the teachers used the antiquated method of ‘chalk and talk’ in their delivery to students. • The students, on the other hand, tried to learn in this manner, but for many of them it has proven futile, resulting in dismal results in the respective subject areas.

  21. Procedure • In trying to alleviate the problem of low grades, the researcher will take action by using technology in his classroom regularly. • This technology involves the - use of 30 laptop computers in his classroom. - use of the interactive websites on Complex Numbers. - use of the computer software program: HyperStudio.

  22. More Procedure The unit of study for the project will be ComplexNumbers. The concentration will be on the following: 1. Definition/Identification of the complex number, [√–1 = i], reads ‘the square root of negative 1 is i’. 2. Simplifying complex numbers. 3. Addition of complex numbers. 4. Subtraction of complex numbers. 5. Multiplication of complex numbers. 6. Division of complex numbers.

  23. Results • The results achieved were expected, as most of the students preformed incredibly well on the posttest as against their poor performance on the pretest. • The poor performance on the pretest was likely, as this unit – Complex Number – was not on the Math A curriculum (the prerequisite for Math B). • The students did well on the posttest because of the interactive behavior of the websites visited.1

  24. Pretest Results Posttest Results

  25. Discussion (Results) • The results obtained were not due to chance, as the students’ performance on both tests were expected. • Normally posttest results are better than pretest, as students are expected to learn from a treatment prior to doing the posttest. • These results are meaningful, as the treatment administered during the exercise played a significant role in the students’ learning behavior.

  26. Discussion (Behavior) • Due to the nature of the lessons - use of ‘handson’ technology - the students attendance to mathematics class improved greatly. • Using technology, and particularly the computer, the students enthusiasm for the lessons grew, as participation was at its peak. • Disruption was at its limit, as students had no time to waste because they were constantly on the pathway of learning.

  27. Conclusions • My predictions were materialized in my expectations. The results of the tests, particularly the posttest, and the behavior of the students, were overwhelming. • My learning experience as the teacher was also overwhelming. The rate at which the students accepted this style of teaching was amazing. The adaptation was quick. • The students learned that technology plays an integral role in the learning of mathematics, and that it is interactive to the learner not just in the short run, but for the future.

  28. Conclusions • If I had this to do again, I would better prepared in that research work would be done way in advance of the execution of the lessons. • This type of treatment can be used in my other mathematics classes, but at the level at which they would be able to master the content being presented. (Reference to the Math A classes). • This type of treatment can be disseminated to the wider school population, be it students (for learning) or teachers (for teaching).

  29. Appendix COMPLEX NUMBER PRETEST 1. Express √–9 in simplest form. (1) –3 (3) 3i (2) 3 (4) –3i 2. What is the sum of √–2 and √–18 ? (1) 5i √2 (3) 2i√5 (2) 4i√2 (4) 6i 3. Subtract the following: √–125 – √–20 = (1) 5i√5 (3) 3i√5 (2) 2i√5 (4) i√5 4. Multiply and simplify √–2 ( √6 + √10 ) (1) √–12 + √–20 (3) √–32 (2) 2i√3 + 2i√5 (4) 10i√2

  30. Appendix COMPLEX NUMBER PRETEST 5. Divide √–48 by √12 (1) 2i (3) i√2 _ (2) –2i (4) – i√2 6. Expressed in simplest form, i16 + i6 – 2i5 + i13 is equivalent to (1) 1 (3) i (2) -1 (4) -i 7. Simplify the following: 12i + 20i + (–25i). (1) 7i2 (3) 7i (2)–7i2(4) –7i

  31. Appendix COMPLEX NUMBER PRETEST 8. Subtract 4 + 3i from 12 – 8i. (1) –8 – 5i (3) 8 – 5i (2) 8 – 11i (4) –8 + 11i 9. Multiply:   (3 + 5i)(3 – 5i) (1) 9 – 25i (3) 25 (2) 34 (4) 9 + 25i 10. Simplify 12 + 7i 6 – 2i (1) 2 + 7i (3) 10i 2 (2) 12 + 7i (4) 29 + 33i 4i 20

  32. Appendix Lesson #1 Aim: What are complex numbers and their properties? (2 Days) • Students will be able to • 1. define an imaginary number and a complex number. • 2. simplify powers of i. • 3. differentiate between complex and imaginary numbers. • 4. plot points on the complex number plane. • 5. identify a complex number as a vector quantity. • 6. compute the absolute value of a number. • Writing Exercise: The history of imaginary numbers is much like that of the irrational number. Use the resources of the Internet or the local library to find out about the early discovery of imaginary numbers. Why do you think that they were called "imaginary numbers?"

  33. Appendix • Lesson #2 Aim: How do we add and subtract complex numbers? (2 Days) • Students will be able to • 1. add and subtract complex numbers algebraically and express answers in a + bi form. • 2. add and subtract complex numbers graphically and express answers in a + bi form. • 3. find the additive inverse of complex numbers. • Writing Exercise: Complex numbers are a new group of numbers yet they behave like variables or radicals under binary operations. Describe these similarities.

  34. Appendix • Lesson #3 Aim: How do we multiply complex numbers? (2 Days) • Students will be able to • 1. multiply and combine expressions that involve complex numbers. • 2. write the conjugate of a given complex number. • Writing Exercise: What are conjugate pairs? What makes them special?

  35. Appendix • Lesson #4 Aim: How do we divide complex numbers and simplify fractions with complex denominators? (2 Days) • Students will be able to • 1. write the conjugate of a given complex number. • 2. find the quotient of two complex numbers and express the result with a real denominator. • 3. express the multiplicative inverse of a complex number in standard form. • Writing Exercise: How do conjugate pairs help to simplify fractions with complex denominators?

  36. Appendix COMPLEX NUMBER POSTTEST 1. Express √–9 in simplest form. (1) –3 (3) 3i (2) 3 (4) –3i 2. What is the sum of √–2 and √–18 ? (1) 5i √2 (3) 2i√5 (2) 4i√2 (4) 6i 3. Subtract the following: √–125 – √–20 = (1) 5i√5 (3) 3i√5 (2) 2i√5 (4) i√5 4. Multiply and simplify √–2 ( √6 + √10 ) (1) √–12 + √–20 (3) √–32 (2) 2i√3 + 2i√5 (4) 10i√2

  37. Appendix COMPLEX NUMBER POSTTEST 5. Divide √–48 by √12 (1) 2i (3) i√2 _ (2) –2i (4) – i√2 6. Expressed in simplest form, i16 + i6 – 2i5 + i13 is equivalent to (1) 1 (3) i (2) -1 (4) -i 7. Simplify the following: 12i + 20i + (–25i). (1) 7i2 (3) 7i (2)–7i2(4) –7i

  38. Appendix COMPLEX NUMBER POSTTEST 8. Subtract 4 + 3i from 12 – 8i. (1) –8 – 5i (3) 8 – 5i (2) 8 – 11i (4) –8 + 11i 9. Multiply:   (3 + 5i)(3 – 5i) (1) 9 – 25i (3) 25 (2) 34 (4) 9 + 25i 10. Simplify 12 + 7i 6 – 2i (1) 2 + 7i (3) 10i 2 (2) 12 + 7i (4) 29 + 33i 4i 20

  39. Appendix Completion Certificate • This is to certify that • Milton Francis • has completed the Human Participants Protection Education for Research Teams online course, sponsored by the National Institutes of Health (NIH), on 09/14/2007. • This course included the following: • key historical events and current issues that impact guidelines and legislation on human participant protection in research. • ethical principles and guidelines that should assist in resolving the ethical issues inherent in the conduct of research with human participants. • the use of key ethical principles and federal regulations to protect human participants at various stages in the research process. • a description of guidelines for the protection of special populations in research. • a definition of informed consent and components necessary for a valid consent. • a description of the role of the IRB in the research process. • the roles, responsibilities, and interactions of federal agencies, institutions, and researchers in conducting research with human participants.

  40. Appendix

  41. Appendix • My Math B page at HSTnP (click below) • http://hstnp.newvisionsk12.org/class_profile_view.aspx?id=e85aa936-737a-4f8e-897c-2786cbda3994

  42. THE END

  43. I Received a Grade of A for this, the final project for my Masters of Science(MS) degree in Instructional Technology(IT) at the New York Institute of Technology (NYIT).

More Related