Aug 052016
 

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

MTBOSBlaugust2016

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?

Whew.

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.

MTBOSBlaugust2016

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.

majors

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.

scale

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

calc

science

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

theory

seasons

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!)