Oct 122016

I had the opportunity to read a preprint edition of Malke Rosenfeld’s new book, Math on the Move, and here are my thoughts.

First off, let me start off with what this book is not. As educators we have probably sat through a professional development where someone told us that in math class, we can appeal to the “kinesthetic learning style” by having the learners up and moving around the classroom. We can appeal to “kinesthetic learners” by having them move their arms, or by doing gallery walks. I have sat through several of these. [yes, I put that phrase in quotes on purpose. I do not believe in ‘learning styles’. Multiple Intelligences, yes, learning styles, no.]

Rosenfeld’s book is not this. No where near this. This book is not about “kinesthetic learning” this is about making connections in mathematics through motion, body, and dance for elementary school learners. It is an amazing concept to think about. I really appreciate that on page 2, she says, “not all of dance is mathematical and not all math is danceable.” That sets the tone for the entire book. Rosenfeld looks for the strengths in using movement, and using the body as a thinking tool. This is a powerful idea, and the first chapter of the book is about what doesn’t and does count as using the body as a thinking tool. I loved the deep thinking this chapter provoked, because it made really think about dance and movement with respect to math.

And, let me be honest. My knowledge of math through motion is very limited. My idea of dancing is more aligned with this guy than anything that someone else would consider “dancing.” Honestly, I wondered for a moment if someone had recorded me actually dancing when I saw this gif.

dancing-gif via

But, despite the fact I am both musically and rhythmically challenged, I have always thought there was opportunity to connect math and movement. I have never figured out how, but I have been intrigued by the idea. After reading the table on page 17 I realized why.

table of nouns and verbs about math movement

The verbs of math are aligned with the verbs of dancing. The nouns of math are also aligned in large part. Looking at the list, and knowing, intellectually, about the ideas of dance, it is easy to understand how strong the connection is. Through examples of learner work, QR codes showing video of learners moving, multiple lesson examples, pictures, role playing examples, and well developed explanations, Rosenfeld shows me how to implement dance in a very constructive way in the elementary classroom. By the end of chapter 3, I was willing to try it with elementary kids tomorrow. That takes a lot for me to say, because I am secondary through and through. Little kids scare me. But I am so excited by the opportunity I see after the first three chapters of lessons that I am willing to try them. They are so interesting!

I think the real power comes later in the book when the 6 stages are developed further.

  1. Understand
  2. Experiment
  3. Create
  4. Combine
  5. Transform
  6. Communicate

These stages allow learners to move from the understanding of a concept and goal to the creation of a multi-step dance pattern and ending with the discussion and communication of the idea through a presentation of the dance. The last half of the book has QR Codes on almost every single page with video link examples. The depth of knowledge these can provide is stunning.

All in all, the more I read and find the joy in mathematical dancing, the more opportunity I see to push this into the upper levels. There is so much more that can be done with this idea beyond the boring and basic. It might even make me a better dancer! Well, no. It isn’t a miracle book, just a really good math book. It is authentic movement, not the usual fake stuff we see.

I think it is time to bring real motion in to math class, get learners moving in purposeful, meaningful ways, and leverage that motion into strong mathematical knowledge.

If you want to read a chapter for yourself, check it out on Heinemann’s website.


Oct 222015

As I was observing my students teaching I stood in an elementary school hallway and saw this display.

2015-09-28 12.56.29

This was on both sides of the hallway, 15 on one wall, 15 on the other. So you don’t have to blow it up to see, I will explain it. Each page says, “Who am I” and below that says, “My favorite: book, subject, pet, food, hobby, tv show, I’m Good at, When I grow up, I would like to be” on the left with blanks to fill in.

Here is the thing that really made me smile, and then get angry. Between the two boards, over half of the students  said “My Favorite Subject is Math” or “I’m good at Math.”

No joke. This is a Title 1 elementary school, and in the sample of these two classrooms, these learners said they enjoy or they were good at math.

I was so happy.

Then I thought about high school math and I got angry.

Where does this joy go?

At what point in the education trajectory of learners does the joy disappear to be replaced by frustration, anger and dislike?

And then the bigger question of Why? What changed? The learners didn’t change? They progress through the classes, learning, enjoying, and being good at math.

My conclusion was that WE, teachers, the adults, change how we approach the math. I can only speak to high school, but I know I would have many discussions about math in PLC’s, and trying to steer the conversation to the learners is tough with some teachers. Why was this hard? It should be the standard.

It is not about content, it is about learners; people, human beings with needs and desires. Are we showing them through interesting problems they need the math? Why not?

Dan Meyer has been asking frequently, if xxxx is the headache, how is yyyyyy the aspirin? This is the right question we, as upper level K-12 teachers, need to be asking. Over and over. How are we fulfilling the needs of our learners? It isn’t with “it is on the test.”

I don’t have any answers to questions in this post. I really needed to share the picture. A picture of a group of learners who truly enjoyed math, and the emotional response I had to it. It shook me to the core to realize that as a math teacher, I was and am part of the problem.

I will be part of the solution too.

Just to end on a happy note, one of my learners from last year tweeted me and made me smile. People. I teach people. Not content.

Aug 312015

I have to be honest, I started, stopped, deleted, restarted, deleted and started this post again repeatedly over the last few weeks. Why? Well one reason is my computer died in the middle of a post, and it sat for a week while I was getting it repaired. Whatever. Lame excuse.

Another reason is that I was not sure what to say, or how I felt about the change from high school teacher to college instructor. I think I am still not sure, but I am wrapping my head around it more and feeling better about myself and my thinking on that topic. This post will be a bit rambling, and more than a little stream of consciousness, but bear with it.

So, here it goes; good and bad. I am going to just get it all out and see where it leads.

do not follow leave a trail

First, the bad: I felt very guilty about leaving my school. Seriously. The process of getting this position took all summer. The interview was a 7 hour long day in the middle of July, and it was a week after that before I knew if I got the job or not. Teachers reported back to school on the 5th of August. I was not able to give my school or my department much time to hire a new math teacher to replace me. I hate that. That I left my high school without giving them a long time to search and find a replacement makes me feel like I let the people who I had a strong attachment and bond with down.

The good: This new program at the University of Nevada, Reno is amazing. Seriously. Why is not every university in the US using this model of teacher development for math and science? I mean, really. We all recognize there is difficulty in getting math and science teachers. The UTeach model out of Austin, TX is a great model to fight the shortage. It is actually doing good recruitment and instruction to bring better math and science teachers to the classroom. Let me tell you the sales pitch (and it is a sales pitch that I have given to several freshmen classes.)

The Step 1 and Step 2 classes are free through a tuition rebate (after you successfully pass the classes, you get your money back.)

In these classes, you will observe twice, and teach three times in upper elementary (Step 1) and middle school (Step 2) classrooms.

At the end of the year, you will have two free credits, AND you will KNOW if you have an interest in teaching. If you don’t, because whatever, you walk away and you have two credits, no money spent, and you have lost nothing but a little time.

BUT, if you think that teaching may be something you are interested in, you finish the major you are in (right now Chemistry, Biology, Physics and Mathematics, but that will expand) AND you take the NevadaTeach program classes and you will graduate in 4 years with two degrees. Your science / math degree AND the coursework necessary for a teaching license.

Yes, free credits. Two degrees, two career paths, and no extra time or money spent to earn either one.

This program sells itself. We were expected to have 30 students in the program this semester. My partner Master Teacher and I recruited 45. We are 150% over the goal for enrollment. That is exciting, motivating and all around wonderful.

Then, we actually met our students.


On the first day of class (heck the ONLY day of class so far) we asked them to write why they took the Step 1 class. Here are a few, representative samples of why they enrolled:

I want a second choice if I can’t get into med school  (this came up several times.)

It seems like a fun program to be in, very excited about going into classrooms to teach an be like hands on.  (again, several of this type.)

I want to have my double major through this program and I think it will offer lots of opportunity in the future.  (wow, just wow.)

I want to explore teaching as an option.  (no fewer than 5 people said this.)

I’m taking step 1 because I want to have the best choice that allows me to have the best option to succeed in my future career.  (yes, this is the same as the last one, options, but notice the addition of choice. )

These are our students’ words. No editing. Just my comments in parenthesis. We have a motivated group of students who think teaching may be an interesting career. It is up to Megan and I to show them that it can be.

How do we do that?

One major element of our classroom and the program is that it centers around the 5E model of instruction. As we teach science or math lessons to our learners to teach to the ES or MS students, they are all 5E, inquiry based lessons. The math teachers who graduate from this program are going to have a strong basis for creating inquiry  based lessons for their classrooms. This is truly exciting. I am fully committing to dispatching an illusion of learning.


What else is exciting is that this program did not exist last semester. I am part of the first year of creating the program from the ground up. If it fails, I will be a large part of why it fails. If it succeeds then I will be a part of why it succeeds (well not really, it can’t help but succeed.) But it is a risk to leave the safety of teaching, being department chair, teaching the courses I love, interacting with amazing learners and stop all of that for the complete uncertainty of a program that does not exist, in a completely different environment, and a radically different culture.

great achievements involve great risk

So, do I step up and leave everything I was comfortable with behind and bet it all on a new, untested, untried program to create and build new, more and better math and science teachers? Clearly the answer I chose was yes, but it was a tough decision. I miss the teachers I interacted with daily, but I know that I am doing something that will benefit more students in the future than I could just as a high school teacher.

As far as the massive culture shock, I have overcome it. Mostly. I have had a couple of “Am I on candid camera” moments. Being told “good job” for submitting $20,000 technology requests that were detailed and approved. Being told “ask for it, we don’t short change instruction, if you need it to teach, ask” by directors of the program. Coming from K-12 where we were starved for resources and now have the resources is odd.

Having to navigate the minefield of tenured professors walled gardens has been a shock. As a high school teacher, I just did things. I always could justify it because it was in the best interest of my learners, so there was never any blowback, just an “okay, that works, thank you.” Now, however, that is not always the case. And, what is in the best interest of my students is NOT the best interest of the departments students, the colleges’ students, or the University’s students. That is absolutely true. So having to think bigger picture and take a step back is new for me. Not hard. Just new.

The last thing that really is different for me is that I always sought out teachers to inspire me, to motivate me. As a high school teacher I lived by this quote daily.

Teachers inspire other teachers

My list was easy. Go on Twitter. Search for #MTBoS. Follow them. All of them. I have found so many teachers who pushed me to be better through their ideas, motivation, and inspiration that I never felt alone the last 4 years.

I am feeling alone now. I have a beautiful office. (seriously, it is the best office on campus, look at the view from my office window).

2015-07-27 17.56.52


I have a fellow Master Teacher, Megan, who is amazing. I have directors in my program who are supportive, helpful and all around great people. The faculty and staff here are supportive and helpful.

And yet, I feel alone. The college culture is different than K-12. There are no faculty plays. No “Friday happy hours.” No fabulous twitter chats of supportive higher ed professors. At this level it is about what you produce, not how you feel. K12 is different. I am working over that, around that, and through that, but it is true. I think this is the largest culture shock to deal with now. I can still drop into the Friday happy hour, but I am not part of that group. Will they still have me? And what am I producing now for my new position?


Yes, I just smiled. I realized what I have to make sure I produce.

Teachers inspire other teachers I need to be that teacher who uplifts, inspires, and drives others.

More so now than ever.

Aug 262013

At TMC13  I attended Ilana Horn‘s (@tchmathculture on Twitter) presentation on Culture in the Classroom. I didn’t write much down during the talk because I ended up thinking so much about the things she was saying and it is hard to describe the video we watched in words.

But, there are some pretty serious take-aways from the presentation that I have acted on and implemented. First, the serious topic of how much culture is created by you (the teacher), how much culture is brought to you by the learners (from prior teachers) and how much culture is created by the learners independently is very eye opening.

Think about that for a second. There really are three independent sources of the current classroom culture in our classrooms. I have certain expectations; the learners have learned how to “play school” in other classrooms; and finally the way they interact with each other independently of what my expectations and other teacher’s expectations are all mash together into creating the current “Classroom Culture” of what happens in my room.

I had never really looked at it in this three part way, and definitely not considered that my expectations are only 1/3 (maybe!) of what is going to occur in my room.

Eyes opened. Jaw dropped. Now what do I do?


Enter some serious thinking and changes to how I opened the year. I wanted to open the year in a totally different way, so that that culture could be more of my own expectations and less of what other teachers wanted them to do in prior years.

Some other things I am aware of and have done.

Seating charts – I used a totally random way to construct them. I handed out cards at the beginning of the year with A – 8 on them. Each number was a table number, and that is where they sat. Seating was completely random, they recognized it, and they commented on it.

Next, no syllabus until middle of week 2. I didn’t talk at them. They worked. They worked bell to bell on interesting and engaging lessons. They noticed and commented on that too!

So far, in all of my classes the homework turn in rate is around 95%. That is exceedingly high for my school (very high FRL rate). I think it is because the homework makes sense to them. I have been asking them to create their OWN problems and solve, not do mine out of a book.

Finally, and most importantly, I have been overly encouraging of questions, noticing, wondering, and thinking. Everyone has gotten involved. Each table must come up with a solution or a question or a noticing, so they need to discuss at the table level and class level.

I am hoping this encourages all learners to take more possession of their own learning. Only time will tell at this point. I will say thinking about this has made me add a tag to my writing. Culture. I think it does need to stand on its own.

May 022013

I have had this long term struggle going on in my head this year that we really don’t do a good job making connections between material in our classes, and that lack of connection is one reason why “transfer” (ala. Grant Wiggins and Understanding by Design) doesn’t occur as  frequently as I would like.

Well, I am not going to talk about it any more. I have the beginnings of a plan to enact. There will be many steps to this plan, but I think the starting point needs to be simple to enact and creates some opportunity for connections to be made.

Every test in my department from Algebra 1 through Trig/Precalc must have a couple of different kinds of problems on it. This is step 1 I am implementing next year.

The first type is a literal equation. Of course, as a stats teacher my first thought was M=z*root(pq/n). Perhaps at the algebra 1 level we won’t start there, but we can select most of the formulas needed in geometry and use them as literal equations and every quiz and test solve for a different  variable of one of the formulas. And, here is the kicker, EVERY time, the learner must explain why they are doing the operation. Justification is mandatory. If we look at the Margin of Error formula above, there are 4 different questions to be asked. That is 4 quizzes or tests that one question can be used.

The goal is get learners to think of literal equations a part of algebra and the justifications as the same thing as every other problem. By the time they reach AP stats, they will have seen this equation repeatedly and know how to manipulate it as a literal, not just with numbers in it. We need to connect AP Stats to Algebra 1.

Next, every test at algebra 1 level must have some form of the following question:

Evaluate (x – (x+h))/x with x = 2 and h = 3. Yes, I know it reduces to h/x, but as we move forward with notation, it becomes:

Evaluate [f(x) – f(x+h)]/f(x)  with f(x) = 2x+5, x = 2 and h = 3.  As the years progress the function can be moved from linear to quadratics to absolute value to cubics or rationals.

Finally, truly stress and monitor that verbage “rate of change of” every time the word “slope” is used.  The learners need to hear and write over and over the “rate of change of” the line in algebra 1, geometry, and algebra 2.

The goal is to create a common language / strands through all math courses and chapters that lead to AP calculus and AP statistics. All learners need to be exposed to the language of statistics and calculus repeatedly throughout their education so it is not different at the upper levels.

So those are the three things I can and will implement next year, without fail.

What am I missing?

Any other language to implement? Any other formulas / concepts that can be used at the lower levels of math that lead directly to the upper levels?



Dec 282012

This month, Grant Wiggins wrote an article on the correlation between SES and academic achievement.  There is a strong correlation between SAT scores and the families income and there is not a single data point out of place in the table. Here is the full 2012 report.


Look at the scores climb as the family income climbs. Every educator will tell you this occurs, but as Grant points out, we have no real explanation for why. The number of lurking variables and confounding variables in this discussion is tremendous, and we don’t know how or why or what they are. We do know the correlation is strong, however. [I strongly encourage everyone to read Grant’s article. He has so many supporting links that are all very worthwhile and constructive.]

Which is why I am really annoyed at my local newspaper, the Reno Gazette Journal. They are running a series of articles on the “Smartest Seniors”. Guess what they are using to determine this. Yup, you guessed it, SAT scores.

So where do these seniors come from? 2 private (and very expensive) schools and 3 public schools that are all in the highest of income brackets in the county are the home schools of the 5 featured seniors. And don’t get me wrong, they all are very awesome kids who deserve the write up in the newspaper.

I am just frustrated because I don’t know how to push my learners to this level. What am I doing wrong that I don’t have any of my learners on the local lists? I don’t teach at a high SES school, in fact approximately 40% of my school is on free and reduced lunch. But correlation does not mean causation, and I should be able to get some of my learners in the top.

How? I just feel like I have way more questions than answers right now, and it is frustrating the heck out of me.

Dec 162012

I have been thinking and struggling with these ideas for a week now. I read Dave’s post summarizing the study about repeating Algebra 1 and the lack of success in CA, and I really felt I needed to dive deeper in this topic.

So I read many link and downloaded almost every article that was linked in the following pages.

EdSource: Many math students are failing, repeating courses without success

Which leads to the Center for Teaching & Learning’s report: College Bound in Middle & High School.

As well as WestEd’s complete list of Reports (didn’t read all of these for this article) which features the above report. November 2012 is the date on it, so it doesn’t get more recent that that.

There is also this brief from EdSource on Math Readiness in CA.

Dave said something that caught my eye in my Google Reader, and started me down this road of thinking and stressing.

From my limited time in the classroom, too many students seem to have given up on their chance to go to college well before they even get to algebra I, much less algebra II, at least in terms of their effort towards improving their performance or achievement in mathematics.  Yet, if you ask these students, they nearly unanimously say they want to go to college.

It was as if he taught in my department at my school!

Let me backup and tell a story of my department and school.

For the last six years we have had essentially one red cell at my school, SPED Math. Sometimes we have had ELL Math in addition, and one time we had Math as a red cell across the board. We have an extended learning period that meets 4 days per week, and the Math Department has been on the Remediation Roller Coaster teaching proficiency classes 3 of the 4 days for the last 6 years.

No other department at my school teaches during this time, but the math department has stepped up and has voluntarily rode the coaster.

Finally, we said enough this year, and we jumped off that coaster (and have caught some huge flack for it from some in our admin) and focused on freshmen. Now we each have a freshman class of Alg 1 learners who are struggling, and we work with them 45 min per day on math support and skills.

And some of them are choosing to continue to fail, and some are failing because they don’t know how to do middle school math.

Some of them can’t add –11 to 5 to get –6.

The “negative times a negative” is confused with the “negative plus a negative” so some are saying –4 + –5 is + 9.

Yes, these learners are struggling in Alg 1. These learners are the “Can’ts” I mentioned above. They are trying, they are struggling, working, and learning and they will turn into “Cans” by the end of the school year because of this one on one support.

But will they earn credit? I don’t know. They have 2 weeks left in the semester and that time is ticking away quickly for them.

How do we take these learners and get them Algebra 1 Semester 1 credit? According to the report by WestEd it looks bleak. But I have confidence from working with my classes that if we continue to give these Cant’s the constant support they will be able to earn both semester of credits.

Then there is the other group in my support class, the Wont’s. I have 5 learners that just won’t try at all. I am there one on one, I have mentors who are sophomores working with them, and nothing works. They are completely shut down.

These learners have hopes, dreams; they all say they want to go to college and do something with their lives, but they won’t do anything to make those dreams come to pass. How do we remediate this group?

According to WestED, making them retake Algebra 1 will not work. My anecdotal evidence supports the research as well. The Wont’s have made a decision, whether consciously or not, that they will not try. And they will not go to college, let alone graduate from high school without the Alg 1 credit.

According to the WestED report, the reason why is they were pushed into mathematics at a higher level then they were probably ready for. Since they were working far higher then their cognitive skills allowed, they just gave up.

How do we get a learner who has given up to re-engage? This is a struggle I face daily in my support class and as a department chair. I need to come up with a plan to help them, but no research I have seen gives me any confidence in how to approach this.

All I know is I can’t just say “retake the class.” That is a path towards failure on top of failure. It is also what our district considers “Accepted Practice.” (see number 16).

If anyone has any ideas, research, articles, or any other thoughts, please send them along. I need them. Badly.

Nov 042012

A little background before I explain what was said to me.

I was part of an IREX grant program that brings teachers from other countries to the US to learn about education, etc. My part of this was to host a teacher from Jordan for 6 weeks in my classroom 2 times per week, and mentor him on mathematics education, technology, etc.

It was a great program, and I learned a lot from interacting with Mr. S. and I think we will built a relationship that will continue in the future for the benefit of us both.

With that said, on his last day in my classroom he told me something that really changed how I viewed myself and my classroom behavior.

He said (and I am paraphrasing here) that in 2008 he wrote an essay for a teaching award in Jordan and in the essay he said he wanted to be the kind of teacher that leads learners to the result, but doesn’t tell them how to get there. He wanted to be the kind of teacher that creates problems for the learners to solve, and lets them work through the problems together, and the learn along the way how to solve other problems because of that. And then he said he wanted to be the kind of teacher that has a mutual respect in the classroom that allows for a good exchange of ideas between learners and teacher.

I said, of course, I think we all want to be that teacher. To which he dropped the largest complement I think I could ever get.

Mr. S. then said, “I wrote that 4 years ago, and I have never seen that kind of classroom until I had the opportunity to sit in yours. You are that teacher I said I wanted to be several years ago.”

You know, it took me several hours of thinking of that to really realize just what he said and what it means to me. I don’t think I have ever had someone say anything so nice, so supportive and so mentally Earth shattering to me.

I have never considered myself to be the teacher he described, but clearly this veteran teacher from Jordan, with many years of experience, and national awards in his own country thinks I am. And he thinks it because he spent 2 days a week, for 6 weeks in my classroom.

How do I live up to that? It still shocks me, and it was 4 days ago he said it. I guess I have never thought of myself that way, but maybe I should start. So I can grow, develop and continue to improve.

Or does that improvement come because I DON’T think it is true? I am not sure, but I am still blown away.

Thank you Mr. S. for making me think of myself in a very new way. I hope I can return the favor someday, because you have impacted me tremendously.

Oct 272012

I will preface this by saying I am tired. Yes, tired. The faculty play is kicking my butt major hard core (1 more week to go before we go live, thank goodness), I have been at school for 12 hour days more than I can count in the last 3 weeks, and I just spent all day writing a grant proposal for more calculators because the 12 year old ones we have are dying. Yes, that was my Saturday.

But I love my coworkers and learners. We had homecoming last week, and one of the days was Star Wars Day, which our leadership turned into “Nerd Day”.

Of course, I made sure to tell all my learners that it was Star Wars Day, not nerd day, and they needed to get their Jedi on. I made a big deal of it. I dressed in Star Wars. I wore a lightsaber all day (even to a parent meeting!) Dedication I tell you.

And Monday morning, this is what I saw when I walked into my room:

2012-10-22 06.52.17

2012-10-22 06.51.49

2012-10-22 06.52.28

Yes. Our lovely Leadership kids and teachers put all the Star Wars hallway decorations in my room. That was on Monday, the 22 October. They are still there. I think I will see if I can leave them all year long.

I love them (the coworkers and learners, that is). They make me happy!

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?