Questions that deserve answers.

[Joe]

There are some fundamental questions that have been bothering me. It
seems that the basis for and mode of using calculators in math
education has been obscured by technical issues, especially on this
site. The stated purpose of this site is to share information on this
impressive new technology, so I appreciate any light you can shed on
the following questions.

1. Where is the "independent double blind statistical study" that
accurately reports on the effects of calculators on the math learning
process without giving "subjective" or "antidotal" conclusions that
are pure speculation? I have read, and perhaps you have also read,
the so called evidence for using calculators in math education where
the results are something like "It appeared that the students blah
blah blah..." It appeared that? Where is the unquestionable proof
that we are not doing irreparable harm to a generation of people by
attempting to substitute technology for math knowledge?

2. Are students being put through calculator button pushing exercises
as a substitute for a real math education and shouldn't we make
students aware of the value of math technology in such a way that they
don't become dependent on it?

3. If students are going to be taught calculator operation and how to
use PC math software, isn't in their best interests to be introduced
to a variety of such devices in order to acquire a well rounded
appreciation of the various strengths and weaknesses of all the major
brands?

4. Because there is so much math to learn and so little time to teach
it, shouldn't calculators and math software be covered in a separate
computer science course? Or math lab?

5. I get students who can not determine a least common denominator
and add 2/3 plus 3/4 plus 1/6 without a calculator. It makes me think
that calculators are not the solution, they are the problem. I find
this alarming. In the rush to use technology in the class room, are
we being pushed over a cliff in order to accommodate corporate profit
goals? Are we cheating a whole generation out of an opportunity to
get a good math education?

6. Lastly, if a student can not do basic arithmetic problems without a
calculator how is a calculator going to fix that situation?

I believe these are very important questions that need to be discussed
before spending more time on the technical details of generating more
programs using this so called "impressive new technology." Thank you
for taking the time to read this message. I am interested in your
opinion on these matters. Perhaps you can tell me why students are
shocked when I announce at the beginning of a course that they won't
need a calculator to work the problems on my tests so calculators
won't be allowed at test time?

[Nelson Sousa]

This is a one time response. I'm not the least interested in engaging in a debate. Your opinion was clearly stated in this and in previous messages, I'll state mine. I'm not interested in convincing you of anything, and I hope you respect my right to not be convinced of anything either.

First of all: This is a forum about TI-Nspire. Not about math education in general, not about the merits of the use of technology in math teaching, not about computer software in general. It's about TI-Nspire and it's use in math teaching.

The description of the group is "The TI-Nspire group is a forum for teachers who are interested in using the TI-Nspire calculator in the Mathematics or Science classroom to improve learning outcomes.   

It is a forum for sharing TI-Nspire documents, and for sharing our knowledge about this impressive technology". 

Clearly you're not that interested in this impressive technology. So... why did you sign in?

But, back to your questions...

1.  Where is the "independent double blind statistical study" that
accurately reports on the effects of calculators on the math learning
process without giving "subjective" or "antidotal" conclusions that
are pure speculation?

They're around, and shouldn't be that hard to find.

 

 I have read, and perhaps you have also read,
the so called evidence for using calculators in math education where
the results are something like "It appeared that the students blah
blah blah..."  It appeared that?  

That's opinion. Not study. Nor evidence. There are studies and there are opinions. Don't confuse them both.

 

Where is the unquestionable proof
that we are not doing irreparable harm to a generation of people by
attempting to substitute technology for math knowledge?

Answered above: it's around, you shouldn't have a hard time finding it.

 

2.  Are students being put through calculator button pushing exercises
as a substitute for a real math education and shouldn't we make
students aware of the value of math technology in such a way that they
don't become dependent on it?

Hopefully not, is the answer to the first part of the question.

Hopefully yes, is the answer to the second part.

 

3.  If students are going to be taught calculator operation and how to
use PC math software, isn't in their best interests to be introduced
to a variety of such devices in order to acquire a well rounded
appreciation of the various strengths and weaknesses of all the major
brands?

Yes. I'm sure you'll find forums on the use of Maple, Mathematica, Cabri, Sketchpad, Casio calculators, etc. This forum is about TI-Nspire.

 

4.  Because there is so much math to learn and so little time to teach
it, shouldn't calculators and math software be covered in a separate
computer science course?  Or math lab?

Computer science? No.

Math lab? Maybe.

 

5.  I get students who can not determine a least common denominator
and add 2/3 plus 3/4 plus 1/6 without a calculator.  It makes me think
that calculators are not the solution, they are the problem.  I find
this alarming.  In the rush to use technology in the class room, are
we being pushed over a cliff in order to accommodate corporate profit
goals?  Are we cheating a whole generation out of an opportunity to
get a good math education?

So what?

Students have failed to do basic arithmetic since the dawn of time. The difference is that now they reach high school and even college.

 

6. Lastly, if a student can not do basic arithmetic problems without a
calculator how is a calculator going to fix that situation?

It doesn't. Nor it's supposed to. The teacher is supposed to teach math; the student is supposed to learn math; the calculator isn't supposed to do either.

 

I believe these are very important questions that need to be discussed
before spending more time on the technical details of generating more
programs using this so called "impressive new technology." 

I can't the the cause-effect relationship between the discussing the use of technology in math teaching in general and discussing a particular technology, but whatever.

Nelson

[Marc Garneau]

Well said, Nelson.  

I, for one, get very tired of hearing calculators get the blame.  Have calculators been misused to ill affect the learning of mathematics of some students?  Absolutely, but that happens when the calculators are not used effectively.  We as teachers bear an important responsibility to ensure the effective use of technology, as well as any other tools.  I have seen the ill-effects on student understanding when students' learning of mathematics is focused on algorithmic procedures.  So do we ban algorithms?  No, but we strive to provide students with learning opportunities that help them make sense of the mathematics they are doing.  The same can be said for manipulatives.  Used effectively, they are a powerful tool of learning.  Used ineffectively, they are no more useful than just telling kids what to do.

 

Technology, when used effectively, has been a huge benefit to students' understanding.  I don't need a double-blind study, even though there is lots of research out there.  What matters to me is what I have seen.  What matters to me is witnessing the mathematical thinking that students can do when solving problems, with or without technology.

 

What excites me most about the TI-Nspire is that it is a tool which is pedagogically focused.   Using this technology with well constructed documents, students can engage in investigations that develop strong mathematical understanding.  Rather than hinder their progress, this technology can take it to new heights.

 

Provided it's used effectively.

 

Marc Garneau 

[Joe]

Thank you Nelson for the reply. I hope others will also offer their
reasoning on these important issues. I appreciate your declaration
that this forum is "about TI-Nspire and it's use in math teaching."
Re-read my post and you will find that I have questions "about TI-
Nspire and it's use in math teaching." Just one more thing. If this
your personal site to control and not a public forum, then you need to
post a warning at the top that says: "This site is the property of and
controled by Nelson Sousa and anyone who has an opinion that is
contrary to his is not welcome here."

For the record, I have four calculators some of which are made by TI
and I access three PC math programs. I use all of these tools and I
value them highly. When I question an answer, the first thing I reach
for is the Voyage200 but in the class room I stick to teaching math,
not calclulator operation. There isn't time for both and I sincerely
believe that the former is more important than the latter.

[Joe]

Mark, for the record, I have 4 calculators and I access 3 PC math
programs on a somewhat regular basis. When I question an answer, the
first thing I do is reach for one of my calculators. I value all
these tools very highly but in the classroom, I teach math. That is
what I do, that is what I am good at, that is my passion, and I can
tell by the look on a students face the instant that they get it.

I cover a lot of material in my classes and I don't see how calculator
operation can be added to the same class without the math coverage
suffering. How do you do it? Do you get extra class time for
covering calculator operation? Or is it done in a separate class? I
get students that have trouble doing basic arithematic and I don't
blame the calculator, I blame situation where a teacher has to cover
both math and calculator operation in the same time that was
previously used to cover math only. Your comments?

[Marc Garneau]

I have a couple of comments.

 

First of all, I'm fortunate that our curriculum up here in BC, Canada, is such that the content is manageable.

Secondly, I don't see the technology as a net time coster.  Yes, it takes a bit of time to build up student fluency with a tool, but that's typically done in little chunks.  And, lessons where technology is used a tool for building understanding gives a lot more 'bang for the buck'.  In other words, I find that students can develop concepts more efficiently (and deeply too) with a lesson inquiry that uses technology.   This is not to say that technology is part of every lesson, but where it can be used effectively, that's when I choose to use it.

 

It is about the math, not about the technology. 

 

Marc

[Nelson Sousa]

Really? Well, I re-read it. On your original post you asked 6 questions; some of which composed of several sentences. Plus and introductory paragraph and a conclusion. And you talked about TI-Nspire a total of ZERO times. In fact your post doesn't even have the word Nspire on it! Not once. 

Now, just for fun, in what way is your post on topic? You ask about the relevance of calculators, in general, computer software, in general, and technology, in general. In what way, specifically, did you enquire about TI-Nspire's merits or lack thereof for teaching mathematics?

Nelson

[Rex Boggs]

When I first started this group, over a year ago, I wasn't sure if I wanted to use YahooGroups or
GoogleGroups, so I created a tinspire list in each. In the YahooGroups list (now deleted), my blurb
about the group included a statement that this is not a group for debating the merits or otherwise
of using calculators in the classroom. There are already a number of groups for that, with hundreds
of posts on the topic, notably math-teach and math-learn.

I wasn't able to add such a statement to the googlegroups blurb because of the 300 character limit.
But the blurb I did write implies it:

The TI-Nspire group is a forum for teachers who are interested in using the TI-Nspire calculator in
the Mathematics or Science classroom to improve learning outcomes. It is a forum for sharing
TI-Nspire documents, and for sharing our knowledge about this impressive technology.

So, if anyone want to discuss the merits or otherwise of using calculators in the classroom, whether
it be calculators in general, graphics calculators in general, or the tinspire specifically, this is
not the forum for doing so. You have other choices.

Is such a debate valuable? - YES. Is this the place to do it? - NO.

If anyone wishes to comment on this post, please send an email to me privately and not to the list.

Cheers

Rex Boggs
list moderator
rexb...@optusnet.com.au