Why Questioning?

Found at From-Student-to-Teacher Tumblr
From Joy of Literacy

Last week became questioning week with student teachers. It came up in two action plans and we were able to have some really interesting discussions about it.

A lot of what I'm writing about here is from work with David Coffey, inspired by Kathy Coffey, and processed from Mosaic of Thought (link includes Chap.1 as a sample) among other books. Neither Dave nor I can remember the actual origin... which is sometimes symptomatic of having done it yourself.

In my own growth as a teacher questioning is definitely one of the places where effort and reflection have helped me improve. The first level was just asking better math problems. More open-ended, that required more problem solving. When the problems are better, there's more interesting things to ask the students about later. The next was to ask more appropriate questions. Some of those excellent problems I gave to students were too much for students. This is a zone of proximal development idea. When it was too much, I needed to scaffold. Later I learned about rephrasing the question instead of narrowing it. Later still I learned about demonstrations of how I think about a problem, sometimes more appropriate than guiding students through it. Then you ask 'what did you notice?', which is - of course - one of the all time great math questions.

One of the best things I ever learned was to stop being the authority. I don't say what is right or wrong. I ask the students if they 'agree or disagree?' That might start an actual conversation. 

One of the first things I really noticed about teaching was that students would tell me that they couldn't do it (whatever it was at the time) but when I asked them questions they could get from beginning to end with no difficulty. So, obviously, I needed to teach them to ask those questions of themselves.   It was difficult. Really difficult. Shifting from asking them 'how to do (next step)?' to 'now what?' and 'how do you know?'

Literacy learning experts are good about this idea of questioning as a process, with the idea that questions are how we move ourselves forward. I like this framework to help me think about the kinds of questions that I'm asking.


Obviously, we have had a tendency to ask too many literal and application questions in math class.  I think about inference questions being predictions, reading between the lines, hypothetical questions and the like. Analysis questions are reflections, synthesis, connections, recommendations and so on.

What I shared that seemed to tie it together for the student teachers is a simple idea: ask to find out what I want to know about. I don't need to ask for answers - I know those. I don't need to ask right or wrong. I need to ask about what they are thinking. Students know when a question is genuine, and this simple idea has improved my assessment more than anything else.  I'm more persistent in getting answers when I really want to know them, also.

From A Softer World

Some good student teacher writing on questioning:

• Caitlin - Open Ended Questions
• Stephanie - Questioning Techniques

Skemp Discussed

This semester we had the opportunity to discuss Richard Skemp's great article on Instrumental and Relational Understanding in class. (“Relational Understanding and Instrumental Understanding,” Richard Skemp, Mathematics Teaching in the Middle School, September 2006; link goes to a pdf hosted at Portland State) Students read the article, with the following home workshop. When we came to class, they discussed at their table and then made one 'slide' presentations to the class on 2 ideas.  The questions are the ones I used for an online discussion before, recorded in this blog post.

Home Workshop 16 - Learning Math
Instrumental Understanding
How do I understand?
“Relational Understanding and Instrumental Understanding,” Richard Skemp, Mathematics Teaching in the Middle School, September 2006
Discuss in class Wednesday
Objective:  TLW use specific questions to better focus on and understand relational understanding.

Schema Activation: How do you multiply fractions?  How well do you understand the multiplication of fractions?

Focus:  Directed reading.
Below in the activity are a dozen discussion questions. As you read, keep notes on your thoughts about the questions.Read through the questions before reading the article.

Even though this article was written for teachers, Dr Skemp wrote mostly for researchers, and at times the language is a wee thick. Press on!

Activity: Read the article, jotting notes on the 12 questions below.  These are just notes, and you may find you have no thoughts on a couple of them. In the reflection you will expand on your thoughts for two of them.

1) What is the point of starting off with the Faux Amis story? 
(A faux amis are two words in different languages that sound similar but mean differently.  Sopa (soup) and soap (jabón) are my favorite from Spanish.  Skemp says that the ways we use "understanding" are as different as if they were faux amis.)

2) What is your favorite example of “rule without reason”? Why?

3) Does the author’s idea of looking for your own examples and his three reasons for it make sense? Why?

4) Explain Skemp’s two kinds of mismatches (in the classroom) in your own words.

5) Of his two kinds of mismatches, which is more common? Which is more of a problem for the teacher?

6) What are Skemp’s faux amis in mathematics teaching? Is either one an issue in your math major classes here in GVSU?

7) Would you add any advantages to his list for instrumental mathematics?

8) Would you add any advantages to the list for relational mathematics?

9) Do you agree with the advantages that he lists for the two types?

10) What’s an example of relational understanding in your non-math life?

11) What’s an example of relational mathematics understanding for you? How do you know?

12) So, what about your classroom? Will you teach for one, or the other, or both? Why?

Reflection: Pick 2 questions you would like to talk about in class, and write a thoughtful response to each.

• Look over your notes/highlights/work from reading.  What did you take from it?
• In your own words describe the ideas of instrumental and relational understanding.

The other thing that we've been developing in class is the idea of questioning, both as a teacher, and the benefits of student to student questions.  This class struggles with being quiet, but by the fourth group, they've hit full class discussion mode.  I really think that conversation is the only way to work towards understanding of big ideas. I filmed the first two groups and then handed off the iPod for recording.

In their groups I asked them to share their reflection from the workshop, they discussed a bit, and then to decide on two points to present to the class. Mostly they used the questions to frame their points. We talked a bit about presentation zen, and I asked them to make a 'slide' for their two points on the board, with the idea to not have a lot of text, but to support their idea with a succinct statement or even better, a visual. They did an excellent job, and I hope you enjoy sharing in their discussion.

Group 1 focused on questions 5 and 8.

5) Of his two kinds of mismatches, which is more common? Which is more of a problem for the teacher?


8) Would you add any advantages to the list for relational mathematics?


Group 2 

2) What is your favorite example of “rule without reason”? Why?


 5) Of his two kinds of mismatches, which is more common? Which is more of a problem for the teacher?


Group 3

5) Of his two kinds of mismatches, which is more common? Which is more of a problem for the teacher?


11) What’s an example of relational mathematics understanding for you? How do you know?


Group 4

12) So, what about your classroom? Will you teach for one, or the other, or both? Why?

Group 5

1) What is the point of starting off with the Faux Amis story?

10) What’s an example of relational understanding in your non-math life?
  (Nice because it was ambiguous whether their example was relational or instrumental.)

As I listened to their discussion, I was struck by how many of the concerns of inservice teachers they already have, which is a real testament to the idea from The Teaching Gap that teaching is a cultural activity.  If we do not do something to resolve the tension between what teachers feel they are expected to do (the job) and what they want to and should do (the vocation), we're not going to make any progress.  It's almost what Skemp is talking about with the faux amis about our two ideas of learning. The same two ideas are competing and confusing us when we use the word teaching.

Glyphs to Data to Display

Me.

Story of a 2 day lesson.

In the preassessment for my 6 week math for elementary class, it turns out that the students were pretty strong on the basics of statistics measurements and displays.  So instead of spending a lot of time telling them what they know, we went right to data collection.  One of my favorite ways to collect data is a glyph.  The first teacher I saw use one was Char Beckmann, but I think there's an old Teaching Children Mathematics (er, Arithmetic Teacher) article about them.  [Found it:  Cartland, Patricia E., What's in a Glyph?, Feb 1996, 324-28] Definitely one of my main faults as a teacher is trying to get too much out of a lesson, so beware that here.

Objectives:  TLW

• collect statistical information
• formulate questions
• organize and analyze data
• display data to address a question
• consider what features of displays are effective
• consider types of questions teachers ask
• review how the next day's test will be evaluated

Day 1: (40 min)
Schema Activation:  what would you be interested in knowing about your classmates?
They brought up music, sports, food, family background, and the like.  (I think of these as cultural identifiers.)

Focus:  introduce the idea of glyphs.  The handout has this information on it:

Glyphs

The circle on the other side of this page will be your face – but not the face you see in the mirror!  A face that tells much more about you…

Hair:  Put a hair on your head for each person living in your residence.  Curly if they are 18 or younger, straight if they are 19 or older.

Eyes: I purposely leave left and right ambiguous (like a mirror or a mask) because I want there to be issues in data collection, but

• left eye - favorite pet :   circle-dog, oval-cat, triangle-bird, spiral-fish, X-exotic or other, crescent    don’t like pets       
• right eye - favorite TV show:  rectangle-reality/game show, square-police/mystery, trapezoid-doctor/medical, rhombus-historical/documentary, kite-sports, Y-other (should be a chevron), crescent-don’t watch TV

Nose:  Make a shape with as many sides as books you read for fun last month.

Mouth  :If from outside the state, add a tooth for each year you’ve lived in Michigan.

• Smooth line: from Grand Rapids area
• Crooked line: from Michigan but not GR
• Rectangle: from another state in US
• Circle: from another country

1)    What other characteristics of a face could we use to ‘store’ information?

2)    What are some other categories of information that would be good or interesting to represent on a glyph?

Activity:

As a whole class they added categories for music (country, hip hop, chill, rock, classical, show tunes) as the left ear, food (italian/pizza, asian (incl. sushi), mexican, chocolate) as the right ear, and hobbies (sports, outdoors, shopping, games, etc.) as the eyebrows and came up with symbols -usually very pictographically, for each.  (It's okay for me that my starting questions are a bit boring,  as they ask about what they care about.  I don't have to do it for them.)  They completed their glyphs.

Reflection:  look over the glyphs of the whole class and share their reactions.
They remarked on how much they enjoyed making them, their interest in each others, and how cool it was to see them together.

Day 2: (2 hours)
Schema Activation: polish up your glyph (or make one if you were absent), move it to the back table, see what you notice about them as a group.  (Most people from Michigan, lots of pizza, music types remarked on, questions about living situation...)

Focus:
First we reviewed the types of elementary displays and covered any questions.  They asked about pictographs and boxplots.

Teaching note:  I like talking about questioning with statistics anyway, but they were really interested in what Jo Boaler brought up about teachers' questions at the last book club, so the timing was perfect.

Activity:
Pick a column.  Pick questions in that column so their numbers add up to four or more.  Answer the questions. (Display) means that a display is required.  Make a poster of your answer that includes your justification.

They collected data and dealt with interpretation issues, what to do with people who gave more than one answer, left/right, figured out pretty efficient ways to record their data, and started discussing display type.

After the posters were mostly complete they were passed around, and each poster was evaluated by each other group using our communication rubric: 0, 1/2, or 1 each for clear, coherent, complete, consolidated and content.  (Created with Coffey so the consonants all alliterate appropriately.)  This is how their exams will be graded the next day, also.

We came together as a group and discussed what makes for effective displays.  This is what they thought.

We also discussed the question types and made connections with reading.

• Literal.    Literal questions have answers that are found directly in the text or are answered by factual recall.  Examples:  How many people come from Michigan?  What was the main character's brother's name?
• Application. Application questions require computation or processing to determine the answer from the information at hand.  This usually is considered more mechanical than involving conceptual reasoning.  Example:  What's the average number of books read this month?  How long was Bilbo's journey?  
• Inferential.    Inferential questions require the answerer to create something unique, something that is implied by the information at hand.  Sometimes this is by combining prior knowledge and experience with literal information.  Inference may require students to imply, guess with support, or deduce.  Can be forward-looking.  Example:  How far would the average drive be from where people are from to Grand Rapids?  Why did the character do that?
• Analysis.    Analytical questions may require synthesis of literal information with information from other sources.  They typically require justification.  Sometimes analysis is referred to as synthesis.  It revolves around examining the information in and from the problem and solution.  Reflective in nature.  Example: Is there a correlation between favortie food and favorite music?  Why did the character do that?

Reflection:  Pick two of the following to address as a group.  Turn in your group response.

• What issues came up in data collection?
• How did you go from glyph to data?
• What was a useful form for recording data?
• How did you decide what graph to use?
• Any decisions you would make differently if doing it again?
• What do you see that was effective in other groups work?

Typically people thought about the teaching implications of what we did, but also thought a bit about the effective display idea.

Bonus:  better classroom decorations.