MEDU2010 Technology in Math Education

Fall 2017 - Professor Kate Poirier

Month: November 2017 (Page 1 of 2)

Project #4: Research Article – due Thursday, December 14

November 30, 2017 / / 16 Comments

For project #4, you will report on an academic journal about technology in math education.

Instructions

  1. Choose an article from one of the journals listed below. The article should be around 10-20 pages long and should have been published between 2007 and 2017.
  2. Your article must be approved by me. Comment on this post with your choice; include the title and author(s) of the article, the journal name, and year of publication. Each pair must choose a different article, so make sure to check others’ posts before you claim yours. Post your claim by midnight on Tuesday, December 5.
  3. Submit an OpenLab post with the following:
    1. The title and author(s) of the article, the journal name, and year of publication.
    2. A 1- or 2-paragraph summary of the article.
    3. Details about one important point made by the article. Write this as a question with a short essay response. (The reason for writing it as a question and response is that these questions will serve as inspiration for one of your final exam questions.) Make your question and essay response as clear as possible as it will serve as a study guide for your peers.
    4. One discussion question about the important point from the item 3 above (or more discussion questions, if you like).
    5. Add the category “Project #4: Research Article” to your post.
  4. Prepare a 15-20 minute presentation based on your OpenLab post and prepare to lead a short discussion with the class about the important point you chose to report on above.

Due date: Thursday, December 14

Journals

  • Journal for Research in Mathematics Education

  • Educational Studies in Mathematics

  • Mathematics Teacher

  • Mathematics Teaching in Middle School

  • For the Learning of Mathematics

  • Research in Mathematics Education

  • Mathematics Education Research Journal

  • The Australian Mathematics Teacher

  • College Mathematics Journal

  • Journal of Mathematics Education at Teachers College

Journal access

These journals may be accessed through the CityTech library. You can view them online from anywhere by following the directions here.

Reviewing the Report and the Article

November 28, 2017 / / 0 Comments

The report discusses the benefit of using calculators in classrooms. As the report states, calculators help students to do their computations quickly and more effectively. They make students more confident about their mathematical understanding and make mathematics more fun to work with. Because calculators help students to do their work faster, that means students can spend their time to develop their reasoning and mathematical skills. calculators help students to be more active learners and to spend more time to improve their solving problem skills. Also calculators are inexpensive so almost everyone can have them. Even though there are research which showed that calculators are effective in math education, there are still some people who believe that they are harmful and that is because of the circulation of misinformation regarding their use.

According to “Why Johnny Can’t Add Without a Calculator” article by Konstantin Kakaes, the article states that the calculators are harmful tools that discourage students’ mathematical understanding. It says that a study proved that technology do not show measurable effect on students’ test score which means, technology is not effective in teaching. The article also mentions that technology cost a lot money that better to be spend on teachers’ training specially in math and science.

I agree more with the report than the article even though I was not comfortable reading the repetitive phrase/word the report has, such as paper and pencil and tedious. Also I feel that the report is advertising calculators which make me a little skeptical about it. Even though I don’t totally agree with the article, there are some points that I agree with.

The report states “…the National Council of Teachers of Mathematics (NCTM) and various other organizations and individuals recommend that appropriate calculators be made available for use by students at every grade level from kindergarten through college”, students should use calculators when they really need them, however, it is too early for lower grades to use them because they need to understand the basic arithmetic and computation without using calculators. When they understand how to deal with basic arithmetic then they can use calculators not to depend on them, but to save time and spend the other time to explore, sharp, and understand mathematical concepts.

The author in the article complains about the electric circuit situations where students were shown it technologically instead of making them manipulate the real batteries and wires to create the real electric circuit. In this point, I agree with him because if students manipulate real materials, they understand more and become creative. That reminds me with tangrams and pattern blocks that we are working with in my other education class where we explore many things that cannot be clear without manipulating these materials. Also, it reminds me with the physics class I took, where I feel more comfortable working in the lab because I can explore a given situation.

The article indicates that there is more money that spend on technology more than on programs to train teachers to be effective. I am not sure if there is an evidence in this point. However, I think there should be a balance between both because we need technology and we need to have well-trained teachers as well. Also, if we think about technology and kids these days, we better make our kids to use it as an educational tool instead of using it for playing games because they are using it anyway.

The second myth in the report says “Because calculators do all of the work for the student, he/she will not be stimulated or challenged enough”. Similar idea is addressed by the article where the author explains that if a student can multiply two numbers it does not mean they know how calculators work. He also explains that there cannot be a technological tool that substitute a teacher.

 

 

Myth #2 about calculators

November 27, 2017 / / 0 Comments

Because calculators do all of the work for the student he/she will not be  stimulated or challenged enough  . both report and article expose to this which is not true at all  Calculator only do the low level tasks of computation they don`t think  calculators can speed up the leaning process calculators permit student to work enough problems to discover and observe patterns in mathematics student will also be able to focus on useful particular applications  for theories and concept they learn in class which is absolutely true.  This myth is not true at all because as the report say calculators do the low level task of the math problem and instead accelerate their work and  it let them achieve.

the report about calculator using

November 27, 2017 / / 0 Comments

I really agree with the report every things in this report convinced me , from the beginning when it mention its calculator make the low level math until the time when the report discuss those myths which is really make me think more clear its really wasting of time if we depending on pencil and paper to finish our work and we will never finish or progress.

home work about the beneficial of calculators

November 27, 2017 / / 0 Comments

I read the report and its really a great report  shows how the calculator benefit the students and the teachers as well , this report and also the article discuss the benefit of the calculators also shows some of the bad side affect both some parents and some teachers think , especially those old parents and the teachers they  not use to these technology , also some of the new generation think that calculators prevented student from progress which is not true the report has mention many myths about the use of calculators. which really convinced me a lot, calculators meant to  be helpful for student in computation which is the low level part of math , its true we all knows how to compute but when the student reach to a higher level need time to think and explore more than  wasting the time for computation.

Graphing Calculators Project #3 due Monday, November 28

November 14, 2017 / / 5 Comments

One of the most familiar technological tools in the classroom is the last we’ll discuss in this class: the graphing calculator. You are probably already aware of at least the basic functions of whatever calculator you have used in your own classes, but you might not have thought about the calculator as a pedagogical tool.

I’m of two minds about graphing calculators. On one hand, they are surprisingly powerful machines and, when used the right way, they can help a student understand a concept or an example without being distracted by rote computation. On the other, they’re clunky and old fashioned; we have much more powerful and user-friendly tools available now (for example, the software we’ve discussed in this class).

In addition to the benefits of using the calculator as a pedagogical tool (see the graphing calculators homework), you should become familiar with the pitfalls as well. There is a nice chapter on Lies My Calculator and Computer Told Me from Stewart’s Calculus book. The examples listed in it aren’t the most relevant for us (many of them deal with rounding errors) but the chapter contains a nice quote:

Computers and calculators are not replacements for mathematical thought. They are just replacements for some kinds of mathematical labor, either numerical or symbolic. There are, and always will be, mathematical problems that can’t be solved by a calculator or computer, regardless of its size and speed. A calculator or computer does stretch the human capacity for handling numbers and symbols, but there is still considerable scope and necessity for “thinking before doing.”

For project #3, choose one of the following exercises. (Comment on this post to indicate which exercise you have selected—do not choose an exercise that has already been selected by someone else.) Prepare a short lesson introducing the topic and explaining the issue the calculator encounters in this case. Your presentation must include the use of the virtual TI calculator (available on our classrooms’ desktop). You may also include hand-drawn graphs and/or Desmos graphs if they are relevant for your topic. In addition to your presentation, include a post on your ePortfolio outlining your presentation. Include screenshots or photographs of the graphing calculator.

  1. Imagine you are trying to help your students understand \lim_{n \to \infty} (1+ \frac{1}{n})^n. Try substituting larger and larger numbers for n in your calculator. What do you expect to see? What do you notice?
  2. Graph the function f(x)=\sqrt{4-\ln(x)} on your calculator. What behavior do you expect near the y-axis? Do you see it on the calculator’s graph? Compare the graph your calculator gives you with the graph Desmos gives you.
  3. Graph the functions f(x) = \sin(10x), g(x)=\sin(100x), h(x)=\sin(1000x) on your calculator. Do you see what you expect to see? Do you notice anything weird? What happens if you graph the same functions on Desmos?
  4. Graph the function f(x) = \sin(\ln(x)) on your calculator in the window [0,1] for x and [-1,1] for y. How many roots does it look like there are in [0,1]? Change the window to [0,0.1] for x and then to [0,0.01] for x with the same y-values. What has happened to the roots? Try graphing the same function in Desmos.
  5. In the standard window on your calculator, graph the piecewise defined function f(x)= 3x - 2 if x < 1.5 and x^2 if x \geq 1.5. Ask the calculator to tell you the derivative at x=1.5. Is this what you were expecting? Try graphing the function on Desmos.
  6. Use the equation solver on your calculator to solve \frac{\sin(x)}{x} = \frac{1}{x}. How many solutions do you expect?

Due date: Tuesday, November 28

Homework – graphing calculators

November 14, 2017 / / 0 Comments

Here is a 20-year-old report from Texas Instruments about the role of the calculator in math education. The report was put out by the same company that has had a near monopoly on calculators in classrooms for years…so it’s not exactly unbiased. However, the report discusses some themes we’ve been discussing this semester.

Read the report, with special attention to the sections:

  • Dispelling the myths
  • Calculators: Elementary School Teachers’ Concerns
  • Graphing Calculators: Issues Affecting Secondary School Teachers and University Professors

Here is an article about some perils of using calculators in the classroom. Read the article with the report in mind.

Write a 5-7 paragraph OpenLab post with the category Graphing Calculator Homework reflecting on the following questions:

  1. Summarize the main points in the report. Summarize the main points in the article.
  2. Do you agree more with the report or with the article? Are you more skeptical of one or the other? Select a few points from each that you agree with or disagree with to support your answer.
  3. Select one of the five myths discussed in the report. Does the article address this myth? How do? If the article does not address this myth, guess how the author of the article would address this myth.
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