For a few months now, the NYT Opinionator Blog has been hosting a series of pieces that do a phenomenally good job of explaining mathematics in layman’s terms.

The latest article is about Calculus (with a promise of more to come): Change We Can Believe In is written by Steven Strogatz, an Applied Mathematician at Cornell University.

There are several other articles in this series, and if you haven’t been reading them, you really should go check them out.  Assign them.  Discuss them in your classes.

• From Fish to Infinity (Jan. 31, 2010)
• Rock Groups (Feb. 7, 2010)
• The Enemy of My Enemy (Feb. 14, 2010)
• Division and Its Discontents (Feb. 21, 2010)
• The Joy of X (Feb. 28, 2010)
• Finding Your Roots (March 7, 2010)
• Square Dancing (March 14, 2010)
• Think Globally (March 21, 2010)
• Power Tools (March 28, 2010)
• Take It to the Limit (April 4, 2010)

Given the discussions we’ve been having about teaching Series and Series approximations lately on Facebook, Twitter, and LinkedIn, I wonder if he’d consider writing an article explaining “Why Series?” to students.

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• Calculus Tweetwars: The End
• Calculus Tweetwars: 1676-1698
• The Calculus Tweetwars (1661-1675)
• The Calculus Tweetwars

For those of you who are curious what we were actually doing in class in yesterday’s post (Record with a Document Camera and a Flip), we were “fingerprinting” the factors of composite numbers with their prime compositions. The wooden “prime number tiles” are created using the backs of Scrabble tiles and the white tiles you see on the board are the student version of the prime number tiles (each of them cut out a sheet of their own prime number tile manipulatives at the beginning of class).  Just for the record, I would like to confess to destroying more than 5 Scrabble games in the last 6 months.

I tell students that the prime numbers are like the building blocks of the whole numbers, in the same way that the nucleotide bases (adenine, guanine, cytosine, and thymine) are the building blocks of DNA. It was ironic, then, that at the end of our prime factorization fingerprinting, the board looked (to me) the way an agarose gel electrophoresis looks.

You can also use the prime number tiles to line up the prime factorizations of two numbers (leaving spaces when the prime is not in both numbers) and read the GCF as the intersection of the two lines of tiles and the LCM as the union of the two lines of tiles.

I’ve tried explaining these concepts in writing before (circling common factors and using colors or highlighting to show the steps), but the ability to easily rearrange the prime numbers after they’ve been found makes all the difference.  Students find the prime factorization using a factor tree or short division, then place out all the tiles for each number.  At this point, they can rearrange each row into least-to-greatest order.  Then line up the primes, bumping the whole row when there is no overlap in primes between the composite numbers.

We also were able to look at more interesting problems now that students could “see” the inner workings of the factorizations better.  For example, find a pair of numbers with a GCF of 42 and an LCM of 4620 (you may not use the “trivial” answer of 42 and 4620).  By constructing a “board” of prime number tiles, starting with the factorization of the GCF and the LCM, students begin to see which primes have to be in the two numbers and which can only be in one of the two numbers.  Note that there will be more than one answer here … which is another interesting discussion to have!

I’ve never seen “prime number tiles” in any math manipulative kit … they were just something I created last semester.  I think this method of using Prime number tiles would also be helpful with explaining how to find the GCF in the factoring unit of algebra, and with explaining how to find the LCD in fractions.

Feel free to print the prime number tiles and use them in your own classes if you’d like.

Possibly Related Posts:

• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Algebra is Weightlifting for the Brain
• Playing to learn math?
• How to Grade a Student Blog

Last semester I began using learning blogs as one of the assignments for Math for Elementary Teachers.  It was the first time I have ever used blogs as a graded student learning assessment, and I didn’t really know what to expect out of the students.  Would they all have created blogs before? [no]  Would they understand intuitively how to make hyperlinks, load in images, and embed videos? [no, no, and no] Would they write naturally in a conversational tone (in the style of most blogs)? [yes]  Would they make their blog posts two or three times a week (as directed) or would they cram them all in during the last couple days? [some of both]

Overall, I was thrilled with the results.  The students reflected on their learning, both in class and out of class.  They found and shared games, videos, articles, and vocabulary sites that they found on the web.  Some of them acted as a class reporter, summarizing what was covered in class each day (with their own personalities coming through).  Before you read the rest of this post, you might want to browse a few of their blogs to get an idea of the variety or writing and styles.

• Leichia’s Blog
• Ohio State Princess
• April’s Blog
• Ashley’s Blog
• Cosine Larry

So let’s just say that this first time using blogs was a learning experience for both my students and for me.  I drafted a rubric for grading the blogs, and stuck to it all semester.  However, I realized that both the clarity of the assignment and the specificity of the rubric needed to be improved for “Round Two” (starting next week).

During the last round of blog grading, I revised my old rubric to try and tighten up the quality of the results.  Here are the specifics of the assignment now.

Set up a blog using Blogger or WordPress.  You should make at least six blog posts of at least two paragraphs each, using appropriate spelling and grammar.  The mathematics in your posts should be correct.  Blog posts should focus on what you have learned, what you’ve struggled with, or what you’ve found to help you learn.  Posts can discuss learning in class or out of class, but must relate to the current topics we are covering in the unit.  You should not refer to specific chapter or section numbers in your blog posts, and if you mention an activity from class, please use enough detail that a 3rd party reader would understand it.  Here are some specific details:

• Blog posts should be spaced apart (not all at the last minute).
• Your blog should include an appropriate  title (not just Maria’s Blog)
• Your blog should include a profile (picture and brief bio). This can be fictional if need be.
• Your blog should contain a “blogroll” with five of your favorite educational blogs.
• Your blog should contain a list of tagged topics or categories.
• Your blog should contain four images (or embedded videos) and should contain at least six links to web resources that you’ve found yourself.
• Links to web resources should be properly “clickable” within the text of the post (not just a pasted URL).
• Each post should be tagged with appropriate keywords.
• You should make at least six comments on the blog posts of other students.

I think that the nature of the blog (what to write about) needs to stay as open as possible, but the fine detail of the assignments is difficult to assess if the quality of blogs varies wildly.   If you choose to try an assignment like this, I highly recommend a table-style rubric (like the one below) to keep track of where you are assigning points.

I also found it helpful to use a screen-capture program (I used Jing and SnagIt) to make grading comments about specific blog posts (because, of course, you should not comment those in on a public blog site).

One last tip:  About halfway to the deadline, I give every student feedback on how they are doing so far.  I gently remind them about details that they might have forgotten so that they have time to correct or regroup.  I’ve found this results in immediate improvement in the blogs and is well worth the effort.  I use quick 1-3 minute Jing videos to give the feedback most of the time.

Note: You can see the rest of the learning projects and a “big picture” idea of how I fit all this in (timewise) by reading Transforming Math for Elementary Ed.

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• Levers of Change in Higher Education
• NYT Opinionator Series about Math
• How do WE learn?
• Prime Number Manipulatives

A few weeks ago, I gave a test where the grades were less than stellar. Whenever this happens, I try to sit down and reflect on whether the poor test grades were a result of something I did differently in class, a poorly written test, or a result of poor studying habits. After careful reflection and analysis of my own, I was pretty sure that this was the result of lack of studying (a theory which was verified … later in this blog post).

I was dreading the task of passing back these tests and prepared myself for an onslaught of questions aimed at trying to discredit the test (or the teaching).  Then I got one of those great last-minute ideas that come to you right before you walk in to face the students.  Maybe I should let them “pick apart” the test BEFORE they see their own tests.  The class in question is Math for Elementary Teachers (MathET) and I figured that a detailed test analysis would not be an inappropriate topic for us to spend class time on.

First, I made some blank copies of the test (enough for each group to have one).  I also created a handout with every single learning objective and assignment that I had given the students for each of the sections on the test (these are all available in their Blackboard shell, but  I compiled these in a paper-based handout that was 3 pages single-spaced). Here is what one section looked like:

5.1 Integers
• Describe operations on signed numbers using number line models.
• Demonstrate operations on signed numbers using colored counter models.
• Explain why a negative times a negative is a positive.
• Add, subtract, multiply, and divide signed numbers (integers).
• Know the mathematical properties of integers (closure, identity, inverse, etc.)
• Complete #1, 3, 7, 9, 15, 17, 19, 21, 23, 25, 37
• Be able to model addition, subtraction, and multiplication of signed numbers using a number-line model
• Be able to model addition, multiplication, and division of signed numbers using a colored counter model (why not subtraction? because subtraction is really the addition of a negative – treat it so)
• Read the blog posts about why a negative times a negative is a positive and be able to paraphrase at least two arguments in your own words.
• Study for your Gateway on Signed Numbers (be able to add, subtract, multiply, or divide signed numbers)
• Play with Manipulative: NLVM Color Chips Addition
• Play with Manipulative: NLVM Circle Game

When we met in class, I counted the class into groups of 3 students each. Each group received a copy of the learning objectives & assignments (by section) and a blank copy of the test. All of these were un-stapled so that the group could share and divide up the pages as they wanted.

Task #1: Look at all the objectives and assigned tasks/problems. Determine where these objectives, tasks, and problems showed up on the exam. (20-30 min)

Objective: Make the connection between what I tell them they need to learn/do and what shows up on the test.

Task #2: What didn’t show up on the exam? We discussed why these objectives might have been left off (for example, maybe it was not something that I emphasized in class) (5 min)

Objective: Make the connection between what is likely to show up on an exam and what is not likely to show up (with the caveat that any of the learning objectives are really fair game).

Task #3: Make a chart that shows how the points for each test question were distributed between the sections that were covered on the exam. We then compared the results from each group and compared these results to my analysis of the point-distribution for the test. (5-10 min)

Objective: Clearly see that it is necessary to study ALL sections, not just a couple of them.

Task #4: I passed back the individual tests. Each student was given three questions to answer as they looked through their tests. 1. Where were the gaps in your knowledge? 2. What mistakes should you have caught before turning in your test? (read directions more carefully, do all the problems, etc.) 3. What can you do to better prepare for the NEXT test?  I collected these, made copies, and passed them back to the students the next class. (10 minutes)

Objective: Take responsibility for your own studying.

It was here that students surprised me by being honest on Question #3. Most of them confessed that they had not studied at all, but now realized that they needed to start studying. I cannot help but wonder whether I would have gotten the same result if I had simply passed back the tests with no analysis.

Task #5: At the same time the students were looking over their own exam, I passed around one more blank copy of the test and asked students to write their score  for each problem (no names) on that problem so that we could see what the score distributions looked like.  When this was done, I placed the pages on the document camera one-by-one so that they could see the scores problem by problem.

Task #6: We had already covered the first section of the next unit, so I had the students begin a set of “How to start the problem” flashcards. On the front of the flash card, they wrote a “test question” for the new unit. On the back of the card, they wrote some tips for starting the problem and details they might otherwise forget.

Objective: To begin to see tests from the perspective of a test-writer instead of a test-taker.

Take-home assignment: I told each student that they must come to the next test with at least 5 flash cards per section (35+ flash cards). I suggested that a great way to study would be to swap cards with each other and practice with someone else’s questions. I checked to see if they carried through (although I assigned no consequences if they didn’t). All but two carried through. Anyone want to guess how those two fared?

Results: I just finished grading the latest test (signed numbers, fractions, and decimals – not easy topics), and the test results were almost all A’s and B’s (instead of C’s and D’s on the previous test). Most students left the test with a smile on their face, and several finally got the “A” they had been trying for all semester.

Three questions for you, my busy and wise readers:
1. Will the students persist in better study habits now? For example, will they study like this for the next exam?
2. Would this detailed test analysis have had the same effect if the class hadn’t just crashed & burned on a test?  (i.e. is it necessary to “fail” first)
3. Was this a good use of class time? Would it be good use of class time in a different math course, like Calculus?

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Math ELITEs (Classrooms for Active Mathematics)
• Prime Number Manipulatives

The second unit in Math for Elementary Teachers (MathET) is on numeration systems and operations on whole numbers.  Again, the students had to complete a “learning project” for the unit.  Some blogged, some mapped concepts and resources, come made presentations to the class, and some built digital lessons.

The students are getting “braver” with what they try with each unit we cover.

Here are the best projects from Round 2:

• Two great Prezi’s, one on Addition & Subtraction and one on Exponent Rules
• A mindmap that attempts to find games or videos for every topic from the unit (in addition to providing notes on each topic)

• Another mindmap that used some great color-coding to explain the material

• A  cartoon (made with Pixton) that is funny AND provides details about the history of the number zero
• Two great blogs: Ashley’s, Alyssa’s Ohio State Princess, and Leichia’s BusyMomLa

Round 3 ends tomorrow, but AMATYC starts tomorrow too, so it will be a few days before I post round 3.  If you’d like to learn more about the Learning Projects for this class, you can read Transforming Math for Elementary Ed.

Possibly Related Posts:

• NYT Opinionator Series about Math
• Prime Number Manipulatives
• How to Grade a Student Blog
• Can we Teach Students to Understand Math Tests?
• What we’re doing with Wolfram|Alpha

Originally, I started this post with the title “What I’m doing with Wolfram|Alpha” and then I revised it, because it’s not just me using Wolfram|Alpha.  My students are using it too.  Here are some of the things we’re doing:

Discussion Boards: Wolfram|Alpha + Jing = Awesome

Before Wolfram|Alpha, it could take several steps to get a graph or the solution to solving an equation to the discussion board in an online class.  You had to use some program to generate the graph or the equations, then make a screenshot of the work, then get that hyperlink, image, or embed code to the discussion board.

With Wolfram|Alpha, sometimes a simple link suffices.  Suppose, for example, I needed to explain the last step in a calculus problem where the students have to find where there is a horizontal tangent line.  After finding the derivative, they have to set it equal to zero and solve the equation (and calculus students notoriously struggle with their algebra skills).  Rather than writing out all the steps to help a student on the discussion board, I could just provide the link to the solution and tell them to click on “Show Steps.”

Sometimes, a bit more explanation may be required, and in these circumstances, Jing + Wolfram|Alpha really comes in handy.  For instance, I needed to show how to reflect a function over the line y=1.

Here’s what the reflection over y=1 looks like.  If you graph y=sqrt(x) and y=-sqrt(x)+1 you will see that they are not reflected over y=1.

Here’s another example of Wolfram|Alpha + Jing:

Classroom Demonstrations

We’re also finding that Wolfram|Alpha can be a good program to use for exploratory learning.  One of the subjects we cover in Math for Elementary Teachers (MathET) is ancient numeration systems.  Rather than just tell students how the Babylonian number system worked, students can use Wolfram|Alpha to explore the number systems until they’ve worked out the pattern.

1. Start by exploring numbers under 50 (42, 37, 15, 29).
2. Now ask students to figure out where the pattern changes (hint: it’s between 50 and 100).
3. Explore numbers in the next tier and see if they can figure out at what number the next place digit gets added.
4. Discuss how a zero is written (and why this is problematic).

Supplement to Online Course Shell

Another topic in Math for Elementary Teachers is learning to perform operations in alternate-base systems (like Base 5 and Base 12).  You can easily supplement your online course shell by providing additional practice problems and then linking to the answers with Wolfram|Alpha.

1. Find the sum of 234 and 313 in base 5.  (answer)
2. Subtract 234 from 412 in base 5. (answer)
3. Multiply 234 by 3 in base 5. (answer)

Student Projects

Wolfram|Alpha has also started making its way into student projects because of the ease of just linking to the mathematics instead of writing out or drawing the math.  Here are a few examples.

For one of the calculus learning projects, the group built a mindmap that demonstrates the graphs and translations of exponential and logarithmic functions.

Another group recorded some help tutorials on using Wolfram|Alpha for evaluating limits.  Here are two of their videos (one with sound and one without).

Several of the MathET students have used Wolfram|Alpha and Wolfram Demonstration links as they mapped out the concepts in our units.

Checking Solutions and Writing Tests

Personally, I’m finding that I use Wolfram|Alpha from a simple calculator to a CAS for checking answers as I write a test.  I’ve also been snagging images of graphs from Wolfram|Alpha to use on tests (use Jing for simple screenshots). Here’s a short 1-minute tutorial on how to change the plot windows to get the image you desire.

Homework Day

Oh, I almost forgot to tell you.  I’ll be down in Champaign, IL for the rest of the week at Wolfram Research.  Tomorrow I’ll be one of the “experts” participating in Wolfram|Alpha Homework Day (a live, interactive web event).  The events begin at noon (CST) and end around 2am.  I’ll be interviewed somewhere around 3 pm and participate in a panel discussion about technology and math education at 8pm.

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• TED Talk on Wolfram Alpha
• Calculus Tweetwars: The End
• Calculus Tweetwars: 1676-1698
• The Calculus Tweetwars (1661-1675)

After several months alone to think about why education has become so transactional, I decided that I’d have to “walk the walk” and not just “talk the talk” and so I set about revamping my own classes.  For several weeks, my brain processors whirled while I tried to figure out how to make courses that have a highly structured and full curricula into courses that are transformational and revolve around learning.  Eventually, I hit upon the solution: Learning Projects.  Each student in Math for Elementary Teachers (MathET, as I like to call it) has to do five learning projects during the semester:

1. Writing a Learning Blog
2. Building a Mindmap
3. Giving an Inquiry-Based Learning Presentation in class
4. Creating a Video for the Internet
5. Creating a Digital Portfolio to house their projects (this will be done by everyone last)

We cover four “units” in MathET, and each student completes the first four learning projects in a random pre-assigned order (I made a chart of all project assignments at the beginning of the semester).  This means that at any time, 25% of the students are blogging, 25% are building mindmaps, 25% are working on a 10-minute presentation for class, and 25% are building a video on a specific topic.  Projects are due two days before the unit exam so that everyone can learn from reading and clicking through each others’ projects.

No lies.  This required a large amount of time to get a new syllabus in place, verbage about privacy and appropriate computer use, tutorials on the LMS, and grading rubrics (and I already knew how to use all the technology).  I had to move one hour of class (4 hours each week) into a computer lab (and lab time is as precious as gold on our campus).   I set up an RSS feed (via a class netvibes page) to put news about math and teaching at the fingertips of the students.   I have to create a page to hold all the RSS feeds from student blogs, videos, and mindmaps (see the Unit 1 Tab of the class netvibes page).  This project also required a pep talk on the first day of class to explain why I was requiring that students use technology as they learned (because it will help them find jobs and provide them with valuable ways to teach and learn).  It was a bit of a shock, especially to those students who had barely touched a computer before.

However, the work was 100% worth it (maybe even 200% worth it).  We have never (and I mean never) had so much fun with a class before.  Every day of class I automatically get fresh learning assessments from the students who are blogging or mapping out the concepts we’ve learned.  The students really enjoy participating in each others’ active presentations and gain lots of fresh ideas about how to incorporate different teaching strategies into their own classes.  It’s also fun to watch the students get more brave (technology-wise) as the semester progresses – I really can’t wait to see what these projects look like by the end of the semester!  As I walk through the lab or peek at laptop screens before class,  I see students getting sucked in to reading blog posts and news articles that they might not otherwise even see (e.g. Math in the News).  I see them playing with interactive manipulatives from NLVM, and getting hooked on logic puzzles.

Because every single project is organized around learning, they all enhance the students’ understanding of the material.   How do I know?   There were no failing grades on the first test.  Students write and talk about how learning Venn Diagrams is “awesome” and how learning base-5 arithmetic is “tricky but cool” … it’s like math has gotten turned upside-down. What was once scary and difficult is now fun and interesting (maybe still difficult, but more tolerable now).  I think it may even be possible that students are now more likely to study for the exams because they actually enjoy learning the material (this is just conjecture on my part).

There are lots more details to share about how, exactly, I’ve pulled this off (release forms, privacy issues, etc), but for now I’d like to share a few of the best projects from Round 1 of the Student Learning Projects.  I hope that by the end of the semester, every one of my students will have found a project where they had a chance to shine the best and brightest!

Best Student Web-based Projects: Round 1

• Blog: Hez B’s Math Adventures
• Blog: RoseMath
• Mindmap: Ashley’s Map
• Video: Deductive Reasoning

Honestly, I wish I had recorded more of the student IBL presentations, because many of them have been clever and well-designed.

In addition to the projects, we’ve found ourselves doing some other fun things:

• Venn Diagram Contest (Indexed-style)
• A short clip from Scott’s IBL Battleship Presentation (on coordinate systems)
• Video recordings of hands-on demonstrations during class (here is one on Base-5 Subtraction and another on the Closure Property)
• Using Wolfram|Alpha to look up numbers written in Egyptian and Babylonian or to complete number patterns

One more thing I’ve changed in all my classes this semester, I try to begin every class by asking students what they’ve learned in their other classes (an acknowledgment that these things are important too).  The only way to refocus education on learning is to make sure it actually is the focus.

Learning Projects Round 2 are already well underway!  Students can see each others’ blogs and mindmaps in progress from day one of the unit.  This (hopefully) encourages them to explore and read more about each topic as they follow links to resources and read about how math has been applied.  Stay tuned for more in our little learning experiment.

Possibly Related Posts:

• Math Technology to Engage, Delight, and Excite
• NYT Opinionator Series about Math
• Community Site for Algebra Activities
• Math ELITEs (Classrooms for Active Mathematics)
• Prime Number Manipulatives

There are lots of “games” out there about solving equations, but I haven’t found a single one that is more than algebra homework dressed up with pretty packaging.  The “games” are all of the same format.  We’ll give you problems, you give us answers and we’ll reward you (or your character) if you get them right.  These are not teaching games, these are just more of the same kind of practice that you would find in an algebra text.

There is one applet that is worthy of mention, though.  The Algebra Balance Scales from the National Library of Virtual Manipulatives is quite good.  It isn’t billed as a game, but when you’re using it, you feel like you are playing a game because you’re interacting with the algebra on the screen.

I recorded an example to show my students how it works.

An interesting assignment for an online or hybrid class would be to have THEM record an example explaining the process (you could, for example, use Jing like I did) and turn in the link.

Possibly Related Posts:

• Random But Organized Thoughts (9-5-2010)
• Random But Organized Thoughts (8-29-2010)
• Random But Organized Thoughts (8-22-2010)
• Math Technology to Engage, Delight, and Excite
• Mindmap: Play and Learn

I’ve been using a web-app called Mindomo for about two years now. With it I am able to map out ideas and create interactive sets of resources in a non-linear fashion. You may have seen some of my resources or been in a presentation where I used one of these maps:

• Web 2.0 for You
• Online Calculus
• Organize Your Digital Self
• Using the Internet to Spice Up Your Math Class
• There’s More to the Web than Facebook (for students)

I think that using these interactive maps gives three main advantages:

1. If you present with a map, you are no longer forced into a linear presentation and can easily respond and adapt to audience questions.
2. The audience can play along during the presentation, wandering off to explore the areas of the map that interest them most.  This is the same idea behind Edward Tufte’s “supergraphic” – a data-rich resource that the audience becomes engaged with, each person in their own context.
3. The process of creating a mindmap helps to organize resources and ideas, think of applications to ideas, fosters thinking about comparisons and contrasts, and helps you to see the holes where information or resources are missing, all in a very visual manner.

It is this third item that has me particularly intrigued.  When I begin building a new presentation, I now find it helpful to organize a mindmap as one of the first activities I do.  The process of building the map teaches me more than I would ever learn on my own.

This year I’m planning to put this idea to the student test and have each student in my MET class (Math for Elementary Teachers) create a Mindomo mindmap for one of the units as one of their four Learning Projects.  The Mindomo accounts are free (for up to 6 maps) as long as you are willing to live with a 1-inch wide strip of advertising on the right-hand side.

I had been stressing over the need to create a tutorial video, but one of our workshop participants (Rose Jenkins of Teching Up) has created a fabulous video on getting started with Mindomo (click here for her tutorial).  I’m planning on just sending my students right to Rose’s video for their introductory tutorial on using Mindomo.

Rose has also got an interesting idea for pushing out a partially-created mindmap to her statistics students, and then asking them to add the appropriate resources and annotations to the map (Read her post, Mapping Out Math).  It was a little tricky to figure out HOW to create a map and then share it to students in a way that makes each copy their own, but Rose made a tutorial about THAT too! (click here for the tutorial about sharing maps)

Kudos to Rose for taking charge of a set of tutorials that really needed to be made!

Possibly Related Posts:

• The Calculus Tweetwars
• NYT Opinionator Series about Math
• Prime Number Manipulatives
• Record with a Document Camera and a Flip
• How to Grade a Student Blog

Somewhere around hour #28 of dissertation research, I began looking for the answer to this question:

Anyone know a resource where someone has documented a timeline of math technologies for teaching or math innovations (pedagogical) that have been introduced?

Today (at hour #53) I stumbled across a possible answer to this question. Yes, there is a book (with a 2008 copyright) that outlines tools of American Mathematics Teaching.  I’ve got it ordered, so I can’t review it yet, but for those of you intrigued about technologies (computer-based and other) I thought I would at least pass along the resource!

In Tools of American Mathematics Teaching, 1800–2000, Peggy Aldrich Kidwell, Amy Ackerberg—Hastings, and David Lindsay Roberts present the first systematic historical study of the objects used in the American mathematics classroom. They discuss broad tools of presentation and pedagogy (not only blackboards and textbooks, but early twentieth—century standardized tests, teaching machines, and the overhead projector), tools for calculation, and tools for representation and measurement. Engaging and accessible, this volume tells the stories of how specific objects such as protractors, geometric models, slide rules, electronic calculators, and computers came to be used in classrooms, and how some disappeared.

Possibly Related Posts:

• NYT Opinionator Series about Math
• Prime Number Manipulatives
• How to Grade a Student Blog
• Can we Teach Students to Understand Math Tests?
• The Projects Get BETTER