MTBoS Blogging Initiative - Better Questions

Boy...when I look at the prompt for this blog post my mind goes in so many different directions. I wrote this post in which I discussed trying to use "quality questioning" in my classroom. I was not really talking about questions to put on an assignment, quiz, or test. I was thinking about questions used to do the following:

• guide students to think deeper during discussions
• guide a struggling student toward understanding a concept 
• scaffold and access prior knowledge
• defend and/or explain answers or reasoning

The prompt seemed to be more along the lines of writing questions for assignments or quizzes. I happened to attend a PD today on Webb's Depth of Knowledge (DOK) in which we discussed asking more level 2 and 3 questions when we assess our students. Of the 4 levels of questioning we were told that the ACT and the ASPIRE assessments have very few questions that are level 1 (basic recall or computation) and the majority of questions are levels 2-3 (harder stuff...HAHA!). Anyway, the majority of textbooks are filled with level 1 questions but not many that are levels 2 and 3. 

For those of you who want to know here is a VERY brief description of Webb's DOK:

Level 1 - Recall and Reproduction - "Right there" questions where you can look it up in a book or follow steps from an example
Level 2 - Skills and Concepts - "think and search" questions where you have to put information together or categorize - these may be open to using different approaches and explanations are often required
Level 3 - Strategic Thinking and Reasoning - More than one way to approach and more than one possible answer - non-routine problems are often used here - often asked to state and support with evidence
Level 4 - Extended Thinking - Extended thinking that takes more time - possible products would be films, plays, research reports (with multiple sources), video games, documentaries, newspaper articles, etc...

(source: A Guide for Using Webb's Depth of Knowledge with Common Core Standards by Karin Hess, E.D - copyright 2013 Common Core Institute)

We were given some strategies on things to do in order to use our textbooks and resources that we have and take the questioning up a notch. One example of moving into the Level 2 questioning is to ask for "non-examples." We often ask our students to give an example of a _________ but they can demonstrate an even greater understanding of concepts if they can also give a non-example.

I had the pleasure of using two non-routine tasks with my algebra classes this week. Both of the tasks seemed impossible at first but when we continued to work toward the solutions we found that there were ways to arrive at a solution.

The first task was the Shuttling Around Problem of the Week #13 in my IMP Meaningful Math Algebra book. It is actually a puzzle where you really have to get out manipulatives to work through it. On the day we introduced the problem only one student found a solution. It took him a while but he finally videoed it so that he could email it to me as part of his POW write-up. The funny thing is that even though I stood there and watched in order to verify that he had a valid solution...I could not do it myself. So, today I allowed another class some time to work on the task and I was going to sit down and figure it out myself so they would see that it was possible...but I couldn't. I called down to the classroom where the guy who found the solution was and he came to my class and showed us the solution again. After watching him do it I had several students go back and work to figure it out themselves...he and I went around the room trying to help and I FINALLY got to where I could do it. The task asks them to investigate other problems too so we weren't taking away all of their fun. It was a great way to end the week! The coolest part of this is that the student who really excelled is not an A/B student. He is rarely ever one who aces a quiz or test. He has an incredible work ethic and tries to do every thing that I ask of him. It was so rewarding for him to have an opportunity to shine!!

The other task was A Mini-POW About Mini-Camel again from our text. One of the great things about our text is the "key questions" in the teacher resources which helps you have ways to guide the students. In this one all I had to say was, "Who says you have to go straight there?" and I had students to begin to find possible solutions. I even had multiple students to go to the board to try to prove to everyone else that their answer was correct. (Here is a link to my Instagram where I posted a video of them.)

I had one student ask me why we had to do these types of problems and I told him that it is important for him to realize that just because something seems impossible at first glance it does not mean that a solution can not be found. I even told them that I may be helping to save their future marriages (haha!) because they may think one day that the only solution is to give up but remember that one time in algebra class they kept on trying and working at a task that seemed impossible only to find that there was a solution!! I know that is goofy but I got some giggles and I do hope that these problem solving skills stick with them after they leave my class.

I love that I have these tasks included in our textbooks! I wrote my last MTBoS blog about how my textbooks are my favorite tool that I use in my classroom here.

Hey...I still love math:)

I know this is a strange comment for a math teacher to make. For years I have just taught math. I chose to become a math teacher because I love math but to be honest all the years of teaching math to people who do not really want to learn it had just "sucked the life" right out of my math enjoyment! I was covering the standards but rarely ever used any activities that peaked the curiosity of my students.

Thanks to our "Meaningful Math adventure" (see this blog post for an explanation) I am having fun teaching math again. I see my students having more fun learning math. Last week I had a student to tell me that she had fun in class that day. I also had some students tell me that we do the most work of any of their classes but my class is also the most fun. I read Teach Like a Pirate this Summer and I have come to realize that it is okay to have a goal of having fun with your students...as a matter of fact we need to throw in some activities that the students will consider a "fun break" from "regular math."

Today I also found myself sitting at my desk working on the High-Low Differences activity in Overland Trail's supplemental activities. I was "noticing and wondering" myself! I was thinking that I really need to find some extra time to investigate why this works like it does. Then I was so ambitious that I answered one of the questions (in a survey I had to take) to indicate that I considered myself to be a mathematician! (HAHA!) I have found value in addressing problems from a student's perspective. Our new textbooks from It's About Time give me many opportunities to have fun working on math and then turn it around to my students as an opportunity to problem solve and enjoy themselves while they do it. I asked them a few times last week if they wanted me to "introduce" them to the activities or let them just try to figure it out on their own. I was amazed at the number of students who wanted to try it without any assistance.

Now, don't get me wrong. I still have students who sit there like "knots on logs" and wait for the problems to be presented to the class so that they can write down the answers - they just hope that when I roll the dice to call on someone that their number is not called. And when I do call on them they tell me they didn't do that problem...and then I talk them through it until I pull the answers out of them...in some cases it would be easier to pull their teeth without anesthesia. I also still have students who gripe and whine and ask for help before I even get the page number out of my mouth. However, it is so cool to catch that student who says he hates our textbooks truly engaged and enjoying himself during an activity (because he figured it out by himself!). This certain student that I have in mind was "called on the carpet" when I told him that I noticed he had fun working on the activity for the day - which just so happened to be "Getting the Gold" that I blogged about here.

I would like to end this blog with a funny picture of what some of my students did last year after I had gotten onto them for sitting there like "knots on logs" instead of doing their work.

Comedians!! 

The Four 4s - an activity from Jo Boaler's book

Today I spent most of my day in the computer lab where my Algebra IB students took a "mock" end-of-course exam. Those days are so draining for some reason! I am happy that it gave me the opportunity to finish reading Jo Boaler's What's Math Got To Do With It? which I believe every math teacher should read! Thankfully one of the last chapters discusses some puzzles and number talk activities that are good for students. I was so tired I could not imagine having a "normal" class with my 5th period today. Instead I gave them The Four 4s to do as an activity. The task asks them to try to make every number between 0 and 20 using only four 4s and any mathematical operation. The directions for the task gives one example and then asks them how many of the numbers between 0 and 20 they can find.

At first my students wanted me to give them more examples but I refused by telling them I didn't want to rob them of the opportunity to get them on their own (haha!). I finally got a few of them moving by telling them to just write four 4s on their papers and then put some operation signs in between them. Once they did this I told them to evaluate the expression making sure they used the order of operations correctly. This really got them rolling. A cool thing about this task was that everyone worked on it. At the beginning I had to seperate a few that were totally off task but once they saw that they could get some of the numbers they worked on their own.

I think that you need to have variety in your classes. I have many students who do not enjoy an activity when they view it as purely mathematical but when you give them a puzzle to solve they engage. I intend to use activities like this more often. One of the discussions on Boaler's website (youcubed.org) talked about how they just listed the numbers 0 thru 20 on a board in the back of the room and allowed students to write their expressions and put their name beside it. That way all of the classes throughout the day could contribute until all of the numbers are found. This task will engage some students that are bored with the normal daily routine!

Just in case you read this blog because you are using the IMP Meaningful Math textbooks, Jo Boaler has a list of 3 curricula that she recommends for use in 9-12 and the Interactive Mathematics Program from It's About Time is on that list. After I started reading her book I realized that she was one of the keynote speakers at NCTM this year. I learned so much about what the research says about the best ways to teach math for student success!