Nov 062016

In my last post, Why I won’t use Direct Instruction, I was provocative and challenged some of the typical thinking about math instruction. The post generated some terrific conversation, both here and on Twitter, and although I have not changed my mind for my own classroom use, I do admit there may be times when DI has a function and purpose.

The grad class I am in has moved on, which is how classes work, and we are discussion Cooperative teaching this week. The textbook is very focused on English and Social Studies, which leaves the math and science people out a bit, but it does discuss the Jigsaw lesson plan at some length. The Jigsaw is a good strategy, and it is useful in math class for sure, but there are so many others!

To create a better list, I asked the #MTBoS for their favorites. I won’t embed all the tweets, but will give attribution to every person who submitted and idea or link in the idea. I want to feature the lesson plan ideas and the links to them. I have not used all of these. Heck, I don’t think I have used half of these! But the collection is amazing, and although some of the ideas don’t have details, you can figure out the idea from the names of some.

The really nice thing is that these are all cooperative lesson strategies from math teachers for math teachers. If you want some ideas on how to incorporate these well tested strategies, here you go:

  1. Speed dating: Me! @gwaddellnvhs, Mary-Ellen @MathSparkles; This was one of the two I suggested. I really like this method of getting learners collaborating with a purpose.
  2. Add it up or Placemats or 4Sum or Add ’em up: Me! @gwaddellnvhs; Heather Kohn @heather_kohn; S @reilly1041; Kate Nowak@k8nowak; This is another strategy I offered in my original question. I think I got it from Kate originally, forgot the name, and then called it Placemats because of a way to set it up using butcher paper. Same idea, different names.
  3. Participation Quiz or Partner Quizzes: Martin Joyce @martinsean; Rachel @Seestur ; Used these often. Very engaging way to get everyone focused. The tricky part is creating the teams for the quiz, but that is achievable.
  4. Clipboard of quotes & actions that support each other. Update whiteboard, then go over: Martin Joyce @martinsean
  5. Whiteboard Game: Lisa Bejarano @lisabej_manitou
  6. Problems around the room: Lisa Bejarano @lisabej_manitou
  7. Also a big fan of whiteboards where students keep answers secret and then they All “flash” at the same time: Mary-Ellen @MathSparkles
  8. Pass the Pen: Madelyne Bettis @Mrs_Bettis
  9. Work on the Wall: Madelyne Bettis @Mrs_Bettis
  10. Ss work prob on board while 2nd Ss “calls” it like a baseball announcer: Mary Williams @merryfwilliams, The boys get into it with the Bob Costas enthusiastic voice, “and he is STRIKING OUT LADIES AND GENTLEMAN!!” Most of the time they are really positive though – all the sports enthusiasts enjoy announcing 🙂
  11. Ghosts in the Graveyard: Mary Williams @merryfwilliams
  12. Sage and Scribe: Briana Guzman @brianalguzman
  13. Quiz Quiz Trade: Briana Guzman @brianalguzman
  14. There can be only one (marker): Nathaniel Highstein @nhighstein
  15. Having round tables in the classroom: Rachel @Seestur Rachel really enjoys having the round tables so learners have to look at each other while working. It makes total sense to me!
  16. Tarsia Puzzles: Sheri Walker @SheriWalker72; Paula Torres @Lohstorres1; In case you don’t know what Tarsia puzzles are, Tarsia is a FREE software package to make puzzles out of sets of problems. They are really cool, and when you require them to be worked in partners, can be a great way to incorporate cooperative learning in a different way.
  17. Card Sorts: Beth Ferguson @algebrasfriend; Card sorts have been around a while, and they are highly effective. I used them in AP Stats as well as algebra. Desmos recently incorporated card sorts into the Activity builder, so you can get awesome electronic card sorts now too!
  18. Row Games: Kate Nowak  @k8nowak; Beth Ferguson @algebrasfriend; I have used Row Games too. The best part is the link takes you to a folder owned by Kate that has 3 pages of mostly word docs of teacher created games. This means you can edit and change them to make them better for your class! Also, it would be awesome if you shared back your creations to help others.

Additionally, David Wees tweeted out the following people, but didn’t give more info. I suggest contacting them directly for more information.

David later did followup with this link to TEDD (Teacher Education by Design). I poked around their site. Looks promising!

Amy Lucenta also was kind enough to let us know her ideas are found in her book from Heinemann Publishers.

I hope this helps, and if you have any other cooperative learning ideas, drop them in the comments please!

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.


Sep 072016

The struggle to understand why we teach K-12 mathematics in the order we do, and the content we do is real. I have wondered about this for a long time, and really have never found a good answer.

I threw out the idea of teaching y=mx+b as the only way to write lines (even though the district materials at the time said it was all we needed). I took a lot of heat for that decision from some people. I was told I was completely wrong; by teachers. I stuck to my guns because y=mx+b is a stupid way to teach lines. And in the end, I was told by other teachers that I influenced them to change too.

But really, K-12 mathematics education is nothing like this:

Mathematics as human pursuit

Think of Lockhart’s Lament.  You read Paul’s words, and you are hit by the poetry he sees in math. It is also 25 pages long. I read somewhere that Lockhart’s Lament is the the most powerful and often cited mathematics education document that is never acted upon. What does that say about us, as educators, who cite it?

Lockhart is passionate about math education, and he feels that the current state (in 2002) of math education is in trouble. His words may be as apt today as it was then. On page 2 he writes,

In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

How much impact has Lockhart had on mathematics education? Often cited, rarely used or implemented. And yet, my Twitter feed and Facebook still have things like this pop up regularly.

Mathmatician is like a painter G H Hardy

What beautiful words representing fantastic ideals. Are you starting to see the cognitive dissonance I am feeling today? Too bad none of these ideals are found in our textbooks or our standards (and don’t get me wrong, I am not hating on the CCSS-M here). In fact, much of school mathematics is exactly how Seymour Papert described it here.

Papert - outwitting teachers as school goal

It is mindless, repetitive, and dissociated.

So as I was thinking of the question of “Why?”, I stumbled upon this article. Why We Learn Math Lessons That Date Back 500 Years? on NPR. To find out the answer is pretty much, “Because we always have,” is sad, disappointing and frustrating. We have taught it this way for the last 500 years, so we will continue to teach it this way for the foreseeable future.

I call B.S.

Seriously. We need to rethink how we teach math in a substantive manner.

We are part of a system that is not allowing learners to find the joy of mathematics, but the drudgery of mathematics and of learning. And this is not new. Not by any means. Edward Cubberly, Dean of the Stanford University School of Education around 1900) said,

Our schools are, in a sense, factories, in which the raw products (children) are to be shaped and fashioned into products to meet the various demands of life. The specifications for manufacturing come from the demands of twentieth-century civilization, and it is the business of the school to build its pupils according to the specifications laid down.

The fact that the specifications of education haven’t changed in hundreds of years is a problem (see the NPR article). It may even be THE problem. I am not so confident to claim that for sure, but it is definitely A problem.

At what point do we, as teacher leaders, rise up and demand this change. We see the damage. We see the issues. We must start demanding the curriculum be changed to meet the needs of our learners. I am not sure that the CCSS-M is that change. It seems like it is codifying the 500 year old problems that we are currently doing.

But it doesn’t not have to.

The Modeling Standard is gold. It is also 1 single page in the entire document.

I will just end this rant with that thought. Oh, and this thought. No more broccoli flavored ice cream.

textbook math is like broccoli ice cream

Aug 232016

#BlAugust Continues with my Knowing and Learning posts


I was sitting down this morning at 7:30 to do today’s post, and I was stymied. What to write, what to write? So I opened Twitter for inspiration and Christopher Danielson had re-tweeted this:


Okay, it is on. I read the article (found here) and immediately thought of my Knowing and Learning readings (week 4) on B.F. Skinner and his “Teaching Machines.”

If you need a refresher on Skinner’s ideas, you can read the book in it’s entirety (please don’t, gag) or you can just read this one picture that sums up the entire chapter in a gut wrenching caption.

teaching machines by skinner

That’s right! There is your video that Sen. Ron Johnson referred to! You see, this isn’t a new idea to replace teachers with that “one good teacher” and have the learners then rewind and redo the material until they get it right.

On the Nature v. Nuture discussion, Skinner falls on the nurture side, but it is a nurture grounded firmly in behaviorism. While educators of the constructivist philosophy threw up a little in their mouths upon reading the words of Mr. Johnson, the behaviorists celebrated. They have been saying this since 1957, and the philosophical underpinnings of the approach are as solid as Piaget or Pappert.

We can see this thread of education going strong in Mr. Johnson’s remarks, but also in the gobs of money thrown at Kahn Academy. His original, poorly done, math videos were celebrated as the pinnacle of education. Well, the pinnacle of behaviorist teaching machines, at least. “Look, when the learner doesn’t understand something, the response is not correct, and they can just work around the disk again, er, I mean, they can rewind the video.”

I think it is very important for teachers to come out of college knowing that these statements by people like Mr. Johnson, and movements like Kahn’s have a history. A history of failure, but also of enough success that they just won’t die.

And there is a time and place for behaviorism in teaching math. But the extremes that Skinner, Kahn, Mr. Johnson, and others take it to is ridiculous.


[And, as an aside, yes. these are my opinions. This blog has my name in the URL, and I am unabashedly a constructivist teacher. This wasn’t always true, but I learned better.]

Aug 182016

Continuing on the #BlAugust train! Yay.


To help set the stage for the Big Questions of Knowing and Learning, I will be using the results from this survey. I asked on Twitter for teachers to take it, and it will be required for my learners to take it. (Same questions, but a different set of instructions and explanations on the prompts.)

I will take the results from this survey to juxtapose their responses so we can evaluate what it means to Know, to Learn, and to Believe.

For example, looking at the teacher responses from Twitter, we can see that the teachers mostly all agreed that “Nurture” had the largest impact on ACT, SAT, and AP Scores. Notice, however, the difference between asking about “Success in AP Calculus” and “Success in Science”.

calc  science

Notice all the “3” responses in Science? Those responses are interesting. For whatever reason, the exact same teachers who responded to this survey thought that “Nuture” is more responsible for success in AP Calc than it is for Success in Science. Or, rather, there were more teachers who weren’t sure if “Nuture” was as responsible as “Nature” so they selected a neutral response.

That is interesting. That brings up the immediate question of Why?

Juxtaposing these type of responses on the first day with college learners will give even more variety of responses (at least I hope the responses are varied.)

Also, look at the responses to these questions.


It makes sense that teachers would be almost identical in responses to these two questions, but I am hoping for a more varied response to the question from college students.

Using their own responses will be a common theme in the course. Each day they will have to enter their reading responses into a google form. This allows me to read their responses quickly, sort and categorize them, and then select items for discussion in class that afternoon.

In addition, I will be using the Annenberg Learner video called “A Private Universe”.  If you have not seen the first video on the page, do so. The video is dated (1980’s) but it is well worth the 20 minutes.

The video starts with the interviewer asking questions at a Harvard graduation about why there are seasons, and then moves into the classroom to uncover learner’s misconceptions.

This is a wonderful video to show my learners how even though teachers may think they have taught something, the learners don’t know correct things or didn’t learn correct things from the teaching.

How do we Know? How do we Learn? [which ends up at How do we Teach?]

The main projects  in the class are two Clinical Interviews, and a deeply, well thought out lesson plan.

Along the way, we dive into the different theories of knowing and learning, so the learners can select one for their own lesson plan and utilize it well.

So, the first day will involve discussion about their own ideas, discussion comparing them (novices) to experts (teachers), interviewing clinically (A Private Universe), and a closure with ….


Not sure.

I have not done closures on this type of material before.

A simple written reflection seems too … blase? standard? uninspired? Yes. Uninspired.

I need to think deeply about closures, next.


Aug 172016

Another #BlAugust post. Staying strong on building the habit of writing in the morning.


I finished my syllabus for Knowing and Learning. I have all the questions written for each reading section (a huge thanks goes out to Walter Stroup at UT Austin for his course site that has his questions on the readings).

The only thing left are the daily activities, and I don’t feel the pressure to have those 100% nailed down for the entire semester before it starts. I would like to, but I won’t.

Here is how I envision the semester.

  1. I will use the Canvas course site from the University to host all of the readings. There are 69 readings on the syllabus right now, all PDF files.
  2. I will create (as in I have not done this yet) a google form for each day, and each form will have the questions for each set of readings. The form will be linked to from the course site. This way, I can receive the comments, answers, and thoughts of the learners in the class before the class is held. I can then use some quotes and response trends to spark and drive the conversation in class.
  3. Each class period will have 5 points associated with it. Submitting the responses and participating in class is how the 5 points will be earned.
  4. Each class will have both small and whole group discussion as we build the knowledge of the different theories of knowing and learning.

What I still need to do:

  1. Build activities that will cement the understanding of the readings and make the theories more understandable.
  2. Figure out a strong way to close the lessons each day. Closure is an essential element of good teaching, and I am not confident I have thought about closure yet.
  3. Re-read each article deeply before each class so I am ready to guide the conversation. This is an ongoing issue, but it is one that must occur!

If you want to take a look at my syllabus, please feel free. The file is: NVTC 201MW Syllabus. The only thing I don’t have in the syllabus is the citations for the different readings. I have them all in PDF form, but have not gone through and cited them yet. YET. I guess that is something to add to the list above.

Any feedback? Am I missing a pivotal reading in the Theory of Ed? Do you have a favorite that is better than one I selected?

Thank you for any thoughts!

Aug 052016

Hitting number 5 for #BlAugust on the 5th of August. Excellent. So far so good!


Transitioning from teaching mathematics to teaching theory is difficult. Not because of the content, that is just reading and understanding what I read. No, it is difficult because of how I define teaching.

Telling isn’t teaching. I decided a long time ago that I was a constructivist teacher, and so to get learners to understand the meanings of mathematics and practice the skills of solving, decomposing, composing and all of the other essential practices of good algebra, all I had to do was practice questioning techniques and direct my questions towards the goals and standards I was teaching.

I read books like the Princples to Actions,  5 Practices for Orchestrating Productive Math Conversations, and Mathematical Mindsets. Moving into other deeper books on questioning like The Art of Problem Posing, or Powerful Problem Solving just extended those skills and allowed me to become a good math teacher.

There are no standards for Educational Theory (although I have other professors syllabi from other programs.)

There are no books to teach me how to teach Educational Theory (yea, I looked.)

Shoot. Now what. I feel like this.

climbing the hill

This course has no skills to practice (good writing is a skill, of course, but there are no skills to practice for the course alone). This course is a purely theoretical knowledge course. Out of the theory, the learners will be able to place themselves into a tradition, and develop skills within the traditions. But, … I am faced with a conundrum.

How to teach what could easily be a lecture course, pure and simple, without falling into the easy trap of creating ppt slides from the readings and going over them?

To keep myself from doing this, I have not allowed myself to even open PowerPoint. The only docs I have open are Word planning docs and the pdfs of the readings.

Good, step 1 complete: Define the boundaries.

Step 2: what is the goal of each day? What do I want the learners to walk out the door after 1.25 hours knowing?

Step 3: What questions am I going to ask prior to class to focus the learners on the readings?

Step 4: What questions will I ask in class to elicit deeper understandings of the readings and prompt discussion?

Step 5: What activities will we do in class that reinforce the readings and create deeper understanding of the material?


As I look at the list, I realize something. Were I doing this course as a lecture course, the list would not change at all. The exact same steps, questions, and problems would be there for doing a lecture class as a more involved, engaging, discussion course.

Doing this process has given me a much better appreciation for the amount of effort that goes into teaching a theory course. No wonder the philosophy courses I took in grad school (the first time) were taught off of copies of copies of notes. Once you go through all this effort to develop questions and activities you don’t want to change them.

Is that really an excuse? I don’t believe so, but it is an explanation.

I am through the third day with steps 2 and 3. I have some activities in mind as well. But, with respect to step 4 I am at a total loss still. I need to know my learners better, but I can’t go in cold.

This is tough, but so much fun.

But I am not sure or confident that the questioning skills I have spent the last 9 years practicing apply here.

Aug 042016

So far, doing well on the BlAugust posts. And talking through the justifications for my ed theory class is helping me.


So the second through fourth day of the class is all about Assessment. Why do I start with assessment? What am I having the learners read?

The justification is a paraphrase of this quote: Mathematics assessment is the process of making inferences about the learning or teaching of mathematics by collecting and interpreting necessarily indirect and incomplete evidence. (from Mathematics Assessment Literacy, pg 21.)

The paraphrased / modified quote for class becomes: Assessment in Math and Science is the process of making inferences about learning or teaching by collecting and interpreting necessarily indirect and incomplete evidence.

Assessment is about making INFERENCES.

Assessment makes those inferences from NECESSARILY indirect and incomplete evidence.

I start with Standarized Assessments (ACT and SAT) and move on from there to Formative Assessments over the course of 3 days.

The reading list over the 4 days is:

  • Lemann, N. (1999). Behind the SAT. Newsweek, 134(10), 52.
  • Atkinson, R. & Geiser, S. (2009). Reflections on a century of college admissions tests. Educational Researcher, 38(9), 665-676.
  • Sacks, P. (1999). Standardized minds: The high price of America’s testing culture and what we can do to change it. Cambridge, Mass. Perseus Books. (chapters 1 & 2, origins of testing and cost (not financial) of testing).
  • Popham, W. J. (1999). Why standardized tests don’t measure educational quality. Educational Leadership, 56(6), 8-15.
  • Feynman, R., Leighton, R. (1985) Surely you’re joking, Mr. Feynman! (Adventures of a curious character). New York: Norton & Company. (only the chapter on Brazilian Science teaching)
  • Popham, W. J. (2003). The seductive allure of data. Educational Leadership, 60(5), 48-51.
  • Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. Phi Delta Kappan, 80(2), 139-144, 146-148.
  • Gardner, H., Kornhaber, M. L., & Wake, W. K. (1996). Intelligence: Multiple perspectives. Fort Worth, TX: Harcourt Brace. (chapters 2, 3 and 5)

The goal is to move from the history of national assessments, to the idea of formative assessments and how to do formative and summative assessments well in the classroom.

In addition, the focus on biological (Nature) forces and assumptions that went into the creation of the testing movement will be discussed.

Hopefully, at the end of this progression, learners will have an understanding of the history of the national movement of testing, why these tests are given, what is learned from these tests, as well as having the stronger grounding in the theory of formative assessment and how and why to focus on formative assessments in the day to day teaching.

The Black and Wiliam article is required reading for every teacher, as far as I am concerned. It is an article that I will be referring back to repeatedly.

The Popham articles are interesting and very anti-testing. I am okay with that (clearly, because I am assigning them). The rest of the articles are not all that favorable either.

Teaching is a political act.

I will not just teach educational theory to reinforce the status quo.

I mean, after all, this was in my Twitter feed THIS MORNING.


The quotes are from a Pennsylvania Department of Education representative.

Assessment is the issue with which I will start the Educational Theory class. I believe it is important that future teachers understand the assumptions and implications such statements have for the learners in the classroom.

Aug 032016

Day one of my Knowing and Learning class will be about the syllabus, the 4 major assignments, and starting the conversation regarding what it means to Know something or Learn something.

There are going to be 4 major assignments. Two interviews, a midterm, and a lesson plan for the final. The first interview is a “expert v novice” interview. An expert is someone who has a PhD in the topic at hand, while a novice is a freshman / sophomore in the topic. My learner will come up with a short, open ended question set of interest, and compare the difference between how experts and how novices view the material. In math, it could be about factoring quadratics, or polynomial long division.

Next up is an interview of an expert regarding questioning techniques and going deeper on the issue presented before. How does the expert question others on this topic. Then a midterm on the theories presented so far, and finally a lesson plan, written according to one of the theories in the class, taking into account the information gained in the two interviews. This will pull the entire course together.

But back to the first day. How DO we get learners to understand that not everyone Learns the same things from the same lesson, and how do we get learners to understand that Knowing is different from Learning? That is a new concept for many learners. I am going to use an instrument that I asked people on Twitter to answer.

First off, because they are in my circle of friends on Twitter, I can assume these individuals are mostly teachers of math. That is a pretty good guess. There may be some higher ed people in the sample, perhaps some science teachers, but … mostly math.


Um, no. That is a totally incorrect assumption. Or is it? Just because someone majored in something other than math, that doesn’t mean they don’t teach math (after all, I majored in Physics and Philosophy.) Still, assumptions can kill.


Okay, I have to put this here. I like Google Forms, but COME ON GOOGLE! Why don’t you have the words on the graph? This is the scale used for the following responses.

act sat



I think it is interesting to note that the teachers are falling mostly on the “nurture” side of things, but not all, and not always. And notice that on testing, regardless of the test, there is almost complete agreement, but there is a difference when it comes between math and science.

Here is the scale for the next graphs.

scale 2

Compare these next graphs. Good teachers are born, not made. Most of the responses were disagree, but 7 people said no comment or agree. But, 9 people said disagree or no comment to the Theory is important to becoming a good teacher. (BTW, I was very happy to see this group had the same outcome for being a physicist as a teacher, that made me smile.)

What does it mean that more people think teachers are made, but at the same time, not all of those view theory as important? Hmm.

born not made



math facts

Interesting. Strong agreement between Math Facts and Seasons, but almost total agreement that calculus does not need to be a graduation requirement. Interesting dichotomy between the graphs. Why? Why do we place some knowledge at a higher level than other knowledge? Why isn’t all knowledge equally important?

If all knowledge is not equal, is all learning also not equal?

Honestly, I expected this type of response from the educators who use Twitter (totally a convenience and voluntary response sample.) There is nothing unexpected here. But look at the variety still. There is not complete agreement on anything.

I am excited to see what my learners say. I believe they will have much more varied responses to everything, which makes the entire exercise more interesting. Now, however, I can also show them what a group of “Experts” in education think as compared to their responses.

Which lets me set up the “Expert v. Novice” interview event better.

Thank you Tweeps. You just made my first day even better!

(btw; any other conversation or comments you want to make? These are really interesting questions!)

Jul 272016

Brian Lawler posted this today:

This statement hit me in the feels, as it is intended.*** Then my brain took over. I realized I should question first whether or not it is really a dichotomy. Does it have to be one or the other? Can a teacher, no, stop. Let me be clear. I am not calling out anyone. I am not directing this question at anyone but myself.

Starting over. Can I teach with one foot in both camps? Is there a continuous line between “teaching conformity” and “teaching to change the world?” What would that look like?


Put another way, if this is our scale of -10 to +10,  is it possible to be at a neutral 0?

I know teachers like to tell themselves that they are at the +10 all the time. I did for the first few years of teaching. I was doing great things, I was teaching math dog-gone-it!

But was I really? Was my practice and my vision aligned? I don’t think so. I think I told myself I was at +10, but was really down around -10. What changed? When did it change? When did I realize that the vision and the reality were not aligned? And back to the original question, is it a dichotomy, or is it a continuum?

No feels here. No emotional response. My heart says “go positive, all the way.” But this is a brain question. What would a zero look like in the classroom?

I would be punishing non-compliance sometimes? So on some days I expected compliance, but other days not? Or is it on some subjects compliance, and other subjects not? That just seems to me to be a recipe for disaster in the classroom. Learners have no idea what to expect every day when they walk in.

The idea of memory and memorization is interesting. Do I reinforce memorization of some topics, but not others? So you have to understand and be able to explain how to transform quadratics into all 3 forms (standard, intercept, and vertex form) but you have to memorize the translation rules and just spit the rules back to me with no conceptual understanding.


I think a lot of topics are presented as dichotomous when there are gradiations between the two sides. Politically this is very true. Very few people are actually Democrat or Republican, but in truth some version of purple in between. We stereotype the “other” into the two camps, and yet sit down and have conversations with friends and family (well usually we do.)

But is there a middle ground here?

I don’t think so.

I think we have to choose one or the other. As math educators we especially must chose. Mathematics is too often a gatekeeper that reinforces social stereotypes and serves as the barrier to higher education. Read the works of Danny Martin or other educators, or follow the #Educolor hashtag if you need evidence for this statement.

I don’t see any cogent arguments from the “recreating what is” side. The status quo is broken, and it is breaking a large segment of our population. I am part of the status quo, or I am part of the agency that transforms the status quo into something new.

So to answer my question, “Is it really a dichotomy?” I have to answer with a yes. It is one, or the other. I don’t understand how there can be a continuum on this issue.

I am fully open to discussing it. Maybe I am wrong. Maybe I haven’t been reading the right articles. If there is evidence to the contrary, please let me know. In the mean time, as a teacher educator, a teacher of teachers, this quote will be front and center in my thoughts.

[As an aside, I am building the reading list and teaching the ed theory class in my program this semester. Yes, this will be an issue brought up in the theory of education for math and science teachers. It is too important not to discuss.]


*** Brian sent me the link he was paraphrasing from. The original article is: