Jan 152017
 

One question that comes ups often with math majors in the program is “Why do I have to take a computer science class?”

I am not sure where the official requirement comes from, but I can say that I am extremely thankful I had a computer programming class in college. It was over 20 years ago, and it was Pascal programming, but I am very happy that I still remember the skills I learned. I don’t remember anything about Pascal, but over the last 20 years, and especially the last three weeks, I have used the heck out of those skills.

When I was in business, the programming skills allowed me do some serious Excel sheets and data crunching that got me noticed and promoted.

As a teacher, those Excel skills allowed me to strip data from the PDF reports and turn those into useful files that we could actually mine for relevant data on our learners and their learning. Those skills also allowed me to learn basic HTML and CSS coding to build websites over a Christmas break and create multiple websites.

Now, as a master teacher I have spent several weeks building a very complex database in Access to manage our check in and check out process with the hundreds (soon to be thousands) of items in our teaching supply store room. To do this, I have had to teach myself Visual Basic, Access structure, as well as some basic SQL database language.

Now don’t get me wrong.I do not have anywhere near the skills to be paid to program in any of these languages, and it is taking me 5 times longer than a real programmer would take. But, because of that Pascal programming class 26 years ago I have the ability to learn the new skills, new languages, and troubleshoot the really bad code I am writing and make it better.

Why should today’s learners learn coding? Because if this dinosaur can reap these benefits out of the class over my career, then imagine what benefits our learners today will reap over the next 25 years! It only gets more important and more essential from here.

Apr 132013
 

I have been mulling this question over for a while now, since last summer at least. It is a offshoot of the time I spent working with Exeter materials at an Exeter summer institute, and if anything the question has grown in my mind to the point where I must answer it for myself and act on it.

Here is the newest version of my question: If much of what and why we teach math the way we do is arbitrary, then why not change to make it easier to learn?

Now of course, there is a HUGE set of presuppositions / assumptions just in asking the question. First, I assume that much of what and why we learn math is arbitrary. Well, I don’t think I am that far off the mark. Let’s look at Algebra 1 as a course first. Honestly I am in good company with this thinking.

Grant Wiggins (author of Understanding by Design) and his thoughts on Algebra 1

I agree. Algebra 1 has a huge failure rate because it is very abstract, meaningless content. We don’t really ever see why we are doing it, we are just learning to manipulate variables and constants around. Grant gives a small part of Lockhart’s Lament (pdf), and it is worth linking to (and reading) completely. Again, the ‘why’ of ‘why do we teach it this way’ is completely arbitrary. Which is why we get political science professors arguing that Algebra is unnecessary because it is hard in the NYTimes. That Algebra is a gateway topic is not in question. It is. The content is essential for future jobs and future success.

If we look a the content, we see arbitrary stuff all over. Heck, just look at the old y=mx + b. Why “m”, why “b”? There is no good answer. Do a google search and get 33 Million hits, none of which can definitively tell us why. I find the answer from the Drexel University Ask Dr. Math to be the most grounded answers, which you can find here for m, and here for b. And I LOVE the answer given here by math historian Howard W. Eves in Mathematical Circles Revisited (2003), where he suggests that it doesn’t matter why “m” has come to represent slope.

“When lecturing before an analytic geometry class during the early part of the course,” he writes, “one may say: ‘We designate the slope of a line by m, because the word slope starts with the letter m; I know of no better reason.’ ” via

I totally agree. In other countries they use other variables for the same meaning (scroll down), so clearly the “agreement” that we all must use the same convention is not universal. There are so many conventions in math that are purely arbitrary. Since they are arbitrary, we must feel free to throw them away when they interfere with good learning and teaching.

So the second question, and a very important one, is: How could we teach math differently to make it more understandable?

One thing I think is important is to connect the vocabulary / language / processes of linear functions with other polynomials / transcendental functions. After all, look at the amazing similarity and simplicity of understanding the transformation processes.

image

Don’t believe me that every single function listed has exactly the same transformation rules? Try this little GeoGebra applet I whipped up. Think about that for a second. When I have shown this to math teachers I get two reactions, “Well duh” and “OMG, I never thought about these like that.”

The teachers who see this as obvious are the teachers who are much more experienced and have taught for many years and have spent the time looking at the math. The crazy thing is that very few teachers have told me they teach this. Why not? Because it isn’t how they were taught, it isn’t how the books phrase it, it violates the conventions of math teaching. So they know it, but ignore it.

And don’t get me wrong. I am not suggesting this is where we stop teaching, we use the exact similarities as a springboard to bounce into the other types of functions. If the learner of math knew this with strong understanding, then the rest of algebra becomes a close examination of each type of function (which is all the different algebra courses are anyway.)

The Common Core Curriculum has mixed up the order of teaching these functions, but the fact that all algebra is just an examination of the skills (which are essentially the same, find ones by multiplying by the inverse, find zeros by adding the inverse) needed to solve, graph, and understand how each function is used.

The last question I have is: Why do we, as teachers put up with this, and what are we going to do about it?

I think the CCSS gives us the perfect opportunity to demand better from textbook publishers as well as our professional development opportunities. We, as teachers, need to be willing to throw the ‘conventions’ away and teach better.

Will it make a difference to the failure rates of algebra 1? I don’t know. but how can it hurt? How can it hurt to strongly connect all of algebra through trigonometry with an unbreakable thread so learners know that what works for one type of functions will work for every other type of function too. It shatters the concept that Chapter 3 doesn’t relate or have anything to do with Chapter 7. That is what learners think now.

Apr 112013
 

It is spring break, so what am I doing? I am attending AP workshops and volunteering at my local university. All in all, a great spring break.

So, Let me start with the question first. Why do we make it so hard to learn functions? I mean really. We treat each topic; linears, quadratics, cubics, transendentals, etc, as if they are a new and unique idea. And they definitely are not. I have discussed this before when I was thinking about the Exeter materials, and I have to keep coming back to it for good reason.

What brought it to me today is the fact I am presenting at UNR for the professor of Math Methods to pre-service teachers. I was asked to present on calculator technology, and I will also branch out into GeoGebra, Desmos, and the MathTwitterBlogosphere.

As I was running through what I was going to say and planning my lesson I made a short video on what I wanted to show with GeoGebra. This only scratches (heck I probably doesn’t even leave a mark) on the surface of what GeoGebra can do but it is worth discussing to present it to teachers who will be immersed in Geometer’s Sketchpad in college.

GeoGebra & Functions

 

And then I turn it into an HTML5 page so anyone can use it.

  And now I have a video as well as a usable piece of content for learners to look and and use on their own at home. I am trying to model good teaching practice that I use at school.

And yet, the question of why do we make linear functions separate from other so it is harder to learn than it should be still comes to my mind. Why? I don’t have a clear answer, and I am not sure anyone else does either. That is sad.

Aug 102012
 

I am planning several posts on this week’s time I spent with a math teacher from Phillips Exeter Academy. This first one, though, will be radically different from the others, and it is because I have to vent a little and lay out a difficulty I had today.

Today was the last day of the Exeter training, and it started with me staring at my computer at 6:45 am this morning thinking about the day ahead and looking at my notes from yesterday. Then I looked at my Google Reader and I read a post on Common Core that brought me to a realization.

As public school math teachers … we are screwed.

Let me explain how I reached this epiphany.

It is impossible to work on the Exeter math problems and not realize how carefully they are constructed and well developed the curriculum. After spending time with an Exeter math teacher and developing a deeper understanding of the Harkness Method they use (never once did this phrase come up, but the methods used by the instructor were clearly modeling the method) a person can’t help but really develop a strong affinity for their curriculum, which they GIVE away for FREE!

Okay, I really like their curriculum. It is rigorous, models real life situations constantly, allows learners to develop strong understandings without memorization, has multiple entry points for learners to develop strengths and and is completely free.  Point one to my depression today.

My state, like 44 other states (Utah backed out this week) is adopting the Common Core State Standards. This fact is point two to my depression. You see, when those two points are combined we are in a heap of trouble. Pearson and McDougal-Littel (among others) are developing many programs they are chomping at the bit to sell to our admins, and we all know they have a direct line through media and other means to our principals and curriculum directors.

And what does Exeter have? A curriculum that is fabulous, and is not aligned to any Common Core standards. They have the experience to build what is hands down the best math curriculum we could possibly use, and they give it away for free. They are not going to be lined up at our Admin Retreats pumping their product (but all the publishers had a booth at our local Admin Retreat this week, I looked.)

The next time textbooks are adopted who is going to be at the table? Pearson? Yes. McDougal? Yes. Exeter? No. Who has the better curriculum that will BEST meet the requirements of CCSS? Hands down, Exeter.  Are our admins going to even consider a curriculum that isn’t handed to them pre-aligned and packaged for the CCSS? No.

Who are our admins going to listen to; the missing voice of Exeter, or the loud and well funded voices of the textbook companies? Right.

And the worst thing is that this is NOT Exeter’s problem. They just write the problems. They write them for their own use and then make them available. They can not and SHOULD NOT be expected to advocate for their curriculum in public schools.

But, Exeter, WE have a problem.*

—————–

*I think I have a solution that I will write about after I detail some great stuff from this week. I am not sure my solution is achievable, but I don’t think we have a choice.

Aug 022012
 

I am rather late to the gate with these thoughts, in large part because I drove (well, rode my motorcycle) to St. Louis from Reno, which took 4 days to get home. More on that in a different post when I do the math from the trip video.

If you ask one of the teachers from my department about me, one thing almost all of them will say or agree with is that I hate paper. I hate paper note, paper suggestions, paper anything. I ask my department to submit everything to me through email, because I lose paper notes, throw away binders, and just downright hate keeping track of paper.

With that said, I admit I took 11 pages of notes, kept track of them through 4 days of a conference, and 2000 miles of motorcycle riding. This event meant that much to me, and that is saying a lot.

I am going to start on day 1 and work through all my notes. I am composing this more for myself than anyone else. Like all of my reflective posts, it really doesn’t matter if anyone else ever reads them. This is the place where I reflect and compose my thoughts for my future self (because if I do it on paper, it gets thrown away!)

Wednesday – A personal exploration:

To say I was nervous on Wednesday would be an understatement. I had just ridden 1900 miles over three days to meet with a group of people I had never met and only talked to through twitter, emails and blogs. Yea, I was nervous. You see, I am an incredible introvert. I attended a NCTM conference my first year as a teacher with 2 other teachers from my school. At the end of the conference, I had spoken with exactly 3 people in a meaningful way, 2 of which came with me. I attended sessions and sat in the back. I wandered the floor and just kind of nodded and said the minimum I had to.

At that point I realized that if I was going to become a half way decent teacher, I had to overcome this fear of putting myself out there. Even riding my motorcycle to the event is a sign of my hesitance to talk to people. I was riding alone, where the only conversation going on was inside my helmet. If I flew I might have to actually talk to someone (although I usually don’t when I fly, either.) This has been my most difficult challenge as a teacher, because it is so incredibly easy to just stay in my room and never reach out. I used to actually have it on my to do list every week, “Make contact with other teachers.” I don’t any more, but the tendencies remain.

So I walked into the hotel dirty and sweaty from riding in the heat and the first thing that happens is Lisa H. tries to give me a hug! Okay, ice broken, I can deal and grow.

After a shower so I was feeling like a human being again, a group of us walked up to the nearby mall and had a nice dinner at a southwestern restaurant and chatted. It was nice, and it gave me a chance to get to know people in a very casual way. It definitely was the right thing to do. I did think about staying in the hotel and sleeping, but decided otherwise. I am glad I did.

The actual events of the week after the break (warning it is long & detailed):

Continue reading »

Jul 292012
 

Many people ask me why I ride my motorcycle long distances in the summer. This summer I traveled from Reno, NV to St. Louis, MO. It was around 4000 miles, round trip, and brutally hot for a couple of states worth of riding.

But, that traveling allows me one single thing I rarely get. Time away from all distractions. It worked. I thought long and hard about the problem I talked about last post; A visual representation to imaginary solutions of quadratics. Somewhere in Wyoming I had the idea on how to prove it. By the time I hit Utah, I had the solution worked out in my head, and I needed to jot some notes. It honestly took me several hours to type up the solution, and without further ado, here it is.

graph5

The Goal:

To prove that in a general case, the circle that is created by reflecting a parabola with imaginary roots (the orange one) about its vertex (the black one) will have as its radius the value of the imaginary roots of the original.

We will begin with clip_image002[12] as our initial equation, with one requirement that the discriminant is negative;  clip_image004[10]. This will ensure that our initial quadratic equation has imaginary roots and the parabola exists above the x axis as shown.

 

Now, we need to reflect this equation around the vertex, but just adding a negative sign in front of the “a” will not do it. If we add that sign in and make it “-a” it will reflect around the x-axis, not the vertex. Therefore, we are going to need to complete the square, get the original equation in vertex form and then add the minus sign to reflect.

 

Given equation                                                                       clip_image002[13]

 

First, divide all terms by “a” and set the y = 0                              clip_image006 

This gives us a first coefficient of 1, which makes

Completing the square possible. Next, we will complete

the square by using clip_image008 and its square.                        clip_image010

 

now that the perfect square trinomial has been constructed       clip_image012

we can factor the trinomial into vertex form.

 

The center of the circle above can be clearly seen in this form, and is: clip_image014 We will need this later.

 

Now we need to solve the reflected parabola for x.               clip_image016

 

Add & Subtract the constant terms from both sides to get:          clip_image018

 

Move the negative sign from the right to the left side:                 clip_image020

 

Take the square root of both sides:                                       clip_image022

 

Finally subtract the constant term from both sides:                  clip_image024


Notice that we have essentially derived a version of the quadratic formula. It doesn’t look exactly like the standard version we all memorize, but it is the same, with one important difference. There is a sign change to the terms inside the radical sign! That will be very important.

 

This formula gives us where the reflected parabola crosses the x-axis, so we now have 2 points on the circle, the plus and minus, and the center of the circle.

 

The final step of the proof is to show that the radius of the circle, or to put it in another way, the distance from the center of the circle to one of the roots of the reflected parabola, is identical to the imaginary part of the solution / roots of the non-inverted parabola. So, onward to the distance formula.

 

We need to find the distance from clip_image014[1] to clip_image026.

 

Distance formula:                                            clip_image028

Insert the point values for x and y       clip_image030


Using just 1 of the 2 values for the + or -.

 

Simplify the subtractions:                                               clip_image032

 

Finally, square the inside term leaving the following:             clip_image034

 

This leaves us with a pseudo-determinant of:                     clip_image036

 

 

However, in setting up the problem initially, we stipulated that the determinant clip_image038 would be negative. If that is true, then the value of inside the radical sign in our last step must be positive!

 

[And yes, I am cheating. I am leaving it to the reader to show that the way it is written above in the last step as the “pseudo-determinant” and the regular determinant are essentially equivalent.]

 

Not only that, but the value of clip_image040 which is from our inverted quadratic, is the same value but opposite sign of the more familiar clip_image042 from the quadratic equation.  If clip_image038[1] is negative, our inverted quadratic will be positive with the same value (oh, and it works in reverse too!)

 

There, I now proved that the reflecting a parabola with imaginary roots around its vertex will allow you to calculate the imaginary part of the complex answer as the radius of a circle created by the reflection.

 

QED.

Jul 272012
 

For today’s #myfavfriday I am presenting an idea that has been percolating in my head for a while. If you want to know what a #myfavfriday is, then see Druinok’s blog here.

MyFavFri-t

Learners have a devil of a time with quadratics. Afterall, there can be 2 solutions, 1 solution, or no solutions in Algebra 1, and then in Algebra 2, we come at them with the fact that those equations with no solution really do have 2 solutions after all, they are just “imaginary” (could there be a worse name for them, really? Thanks a lot Descarte.”)

But I came across a picture on some site one day, and it has stuck with me. I never bookmarked it, or wrote down the site, so it is lost to me (and I have searched hard for it) but the work blew my mind, and as I have shown it to learners, they have at least gotten a sense that the “imaginary” really does have meaning.

Let’s begin with 2 equations and graphs that are simple, straight-forward and make sense. [all images are clickable to see full size]

graph1and graph2

The equations are y = x^2 – 4x + 3 and y = x^2 – 4x + 4.

A simple change of one number changes the number of solutions from 2 distinct to 2 repeating solutions, and learners don’t have a problem with that idea, generally. Then comes this bad boy.

graph3 y = x^2 –4x + 6

Now they have to do the whole Quadratic formula on it to get the solution, and the solution has those i thingies in it, which makes them all confused and irritated until they wrap their heads around it. And why does it still have 2 solutions? It doesn’t touch at all!

But wait! We can play a game with this quadratic function. What if we reflect the parabola around the vertex in the downward direction? Then we end up with something that looks like this:

graph4a To do this reflection, we first had to complete the square on the original equation to get y = (x-2)^2 + 2. Now, with this equation, we can put the – sign into the equation and get the reflection, y = -(x-2)^2 + 2.

But hold on, see those 2 points where it crosses the X-axis? And see the Axis of Symmetry that goes through both equations? If we use those three points as definitions for a circle, we get the following graph and equation.

graph5 (x-2)^2 + y^2 = 2

Guess what the solution to the quadratic equation y = x^2 –4x + 6 is. If you guessed 2 + root(2)i and 2 – root(2)i  then you are absolutely correct.

The real number part of the complex solution of a quadratic with two imaginary roots is the X value of the Axis of Symmetry, and the imaginary part of the solution is the radius of the circle created by the center and endpoints created when the inverted parabola crosses the X-Axis!

Okay, mind blown. Why? How could I prove this?

Aha! now come into play the hours I spend on a motorcycle every summer. How could I PROVE that this will always work? I have the proof. I am working it up, but it is a pain to type. That, I think, will be the focus of a future, #myfavfriday!

[And I really need to look in to a LaTex module for my blog if I am going to do math. The equations look horrible.]

Edit: 29 July 2012: I proved this assertion, at least to my satisfaction in a followup post: http://blog.mrwaddell.net/archives/348

Edit: 4 August 2012: I found, stuffed in the bottom of my backpack, a rumpled piece of paper with this link on it. I think I did this page justice with my treatment. I wish I had found the page before I spent hours thinking about how to prove it, it gives the suggestion right there at the bottom!

Edit: 18 Dec 2012: @Mythagon posted this picture on Twitter. It is a great visual of what is discussed above, and clearly shows why the rotation is so important.

From: Teaching Mathematics, 2nd edition by m. Sobel and E. Maletsky

Edit: 27 Sep 2015: Wow, a long time since the original post, however I still come back to this every year. Love it. Now, Luke Walsh, aka @LukeSelfwalker added this to the mix. Love it. Click it for the live Desmos file.

Jul 172011
 

It was the best of conversations, it was the worst of conversations, but in the end, it was an educational conversation for my cousins and I.

Okay, enough with the Dickens reference. During the summer I take a little motorcycle trip. Okay, not so little. I do around 2500 miles from Nevada to Montana and back to see family and some beautiful country. During the trip this summer, I attended a family reunion north of Missoula, MT, and a family picnic in Helena, MT. During each family event, I met with a very bright and talented young girl who was going into the 5th grade. I will call the first one C1 (for Cousin 1, they are actually my cousin’s daughter, but cousin is close enough) and the second one C2. These two bright young girls have some amazing similarities.

Both C1 and C2 come from very supportive families with several siblings. They both have college graduates either as parents and / or grandparents. Both C1 and C2 are entering the 5th grade next school year, and they both are encouraged to do well and school and are given any resource or opportunity they need to succeed in school.

And then the similarities end. There are some irrelevant differences. They each live in a different state (Utah and Montana), but the school districts are similar sized (I looked them up.) Because of this, and because I don’t know any different, I will assume that both C1 and C2 are given similar opportunities in the school for success. [Okay, this might be a deal killer of an assumption, but I have to make it in order to not be angry at what is to come.]

There are also some amazingly important differences. I asked C1 what she likes best about school. Her answer was “Lunch” and then “Recess” and then “Friends”. Even after all that, I couldn’t get her to name an academic subject. When I asked her about math, her reply made my die a little inside. She said, “Math is icky. Math is where you do this.”  The ‘this’ was put her head on her left hand, a thoroughly bored expression on her face, she looked up at the imaginary board, and then with her right hand she mimicked taking notes and writing numbers.

I died. Seriously. I wanted to cry right in front of her. C1 thinks that math is the time when you are bored stiff, quietly taking notes on something on the board. Later, just to make sure I was not imagining that she was as bright as I thought, we walked down to the railroad tracks about a 1/2 mile away. I challenged her to give me an estimate on how many steps it would take. She said 200 the first time. We started walking, and she counted to 100 before she looked up and said she was too far off. I asked her to revise her estimate. She squared the number to 4000 (in her head, as a 4th grader!). Then she said that 4000 was too big, and she cut the number in half to 2000. Then she said that she guessed, based on the 100 steps she counted already, that the number of steps it would take would be between 1500 and 2000.

Yea, she is bored in math class. Go figure.

Then I visit with C2 in another city. C2 and I have met once a year for the last 2 years. Last year, we talked about mathematical patterns in oven hot pads she was making, then had a discussion of 9’s, adding, multiplying, and dividing, and the neat patterns that are present when doing math with 9’s. That was when she was just finished with the 3rd grade, and entering the 4th grade.

This year, that was old hat. She wanted to know some addition “fun math tricks”. (her words) I asked her if she remembered the things we discussed last year, figuring that she would have forgotten some things and I could re-cover them. No. She had expanded on them. She went on to explain to me the difference between prime numbers and composite numbers, and factoring and dividing.

Long story short, we ended up doing modular arithmetic, in mod 5, 7, and 9. She, on her own, continued to do tables for the multiplicative inverses in mod 11 and 12. Why 11 and 12? 11 is prime, so they all work, while 12 is composite, so there are numbers that don’t have inverses. AS A 5TH GRADER!

I found out that C2 will be taken to the middle school and doing 7th grade math while in 5th grade. C1 will be doing 5th grade math in 5th grade, but could be doing so much more. The best of conversations, the worst of conversations, all rolled up in one week.

What did I learn? I learned that some learners are being driven away from math. Whipped, beaten, and driven away, even though they are smart and very capable. I learned that WE are teaching some learners that math is a subject to be feared and avoided, not because they can’t do it, but because WE have not given them a REASON to do it.

Why are we doing this?

Feb 192011
 

The other day, this article popped up in my reader (really! I think they were recycling their content). It is from August 2009, and it is a list of 100 iPhone apps for education. It got me thinking, because I don’t use an iPhone. I really have nothing for or against iPhones. I use Verizon and when I bought the Android phone I have, it was the only smartphone for Verizon.

In the end, I love my Android (a moto-droid currently) and have no desire to purchase an iPhone now that it is available. But I still want some educational apps. In fact, a year and a half later,I wonder how good the list will be for Android apps? Without further ado, here is my attempt to create a list for the Droid. Why 53 do you ask? Because 53 is a prime number, and I like prime numbers. Here are my criteria for selection.

1. Must be free. Yes, I know that will immediately kick out a ton of VERY good apps. But I want a list I can give my learners, and I will never ask them to pay for something.

2. If I don’t use it myself, it must be highly rated (3.5 stars at least) by over 500 people. This will shove out the new apps that have 35 pp who rated it a 5 star, I know. But it is the only way to ensure a representative sample of ratings. [I break this twice with good reasons below]

The list is after the break.

Continue reading »

Feb 062011
 

This week I downloaded a free piece of software from Microsoft. Actually, 2 new free pieces of software. The first piece was the new Microsoft Mathematics “calculator”. I put calculator in quotes because it is so much more than just a calculator.

For instance, it is a calculator and a grapher.

image

If you click on the “Worksheet” tab, you get a calculator with a ton of functions.

image Notice all the different statistics options available! As an AP Stats teacher, I am kind of liking that. It has a backspace key obviously placed, so correcting errors is easy, and to the right of the screen is a large white space where all the math shows up. Very nice.

The Grapher does 2D or 3D, and will pop up a box to enter the equation into with a little bit of help at the bottom. For instance, here I am typing in an interesting polar graph.

image The second I hit the spacebar, the theta I am typing turns into the symbol. The only downside I see to this graphing module is it takes two more clicks to see the graph. You hit “Enter” on the pop-up, and then hit the “Graph” button below.

image Ah, a pretty butterfly. The Graph controls has a nice animated trace function.

This is nice and all. It is a terrific way to get a free graphing calculator into the hands of learners at home, but the really neat part is the solver.

image Hit the Worksheet tab, and solver, and it will solve just about any equation step by step. That’s right, STEP by STEP. A learner can now see HOW to do a problem, instead of just and answer. Will that help the unmotivated learner? No. Will it help the learner who is trying to figure out how to do the problem and will take what the machine says and apply it to the next problem? Yes.

There is a lot more to the program, but this is enough for me to dedicate space on my website to it. Very worthwhile.

Oh, and the second piece of software? That is the Microsoft Mathematics module for Word and OneNote. It lets me insert graphs directly into my word document, so I don’t have to mess with copying and pasting graphs any more. I like it.

Links here:

Microsoft Mathematics 4.0  advertising page. Direct download page here.

Microsoft Mathematics Add-in for Word & OneNote

MrWaddell.net