Questioning and group work

My newest focus is to improve at using quality questioning to improve discussions and student engagement in my classroom AND to learn how to better manage group work. I have just recently decided to really narrow my focus to these 2 things for the rest of the year. There are so many teachers that I have talked to about these things and I have come to realize (again) that just because something works great in someone else's classroom it may or may not work in mine.

Here's an example...I had someone (Tanya Barnes) to tell me that I should rarely be the one at the board going over problems. She said the students should do it because then they take more ownership. My argument was that I do sometimes have my students go to the board to share their thoughts or answers on a task. However, more often I stand at the board and lead the discussion and write down the answers the students say so that the class can decide if it is correct. It is so much faster!!! And I have alot of material to cover!!! So...I listened to her and made a concentrated effort to have students go to the board today to share out. I even let them do the examples  (when I had a student that understood). You see....I teach freshman. And I have several competitive boys in my classes AND a few girls who love to prove people wrong. It takes twice as long (or longer) when they go to the board because they have to turn around every time someone makes a noise or comment....then they have to be a comedian....then they have to pop someone on the back of the head on the way back to his seat. Ugh!!! I caught another teacher walking by my room (good ole Amy Walker) and said, "There are some strategies that just DON'T WORK with all classes!" I told her what I was attempting and she reminded me that no one else knows my students like I do. Even if another teacher has freshmen they aren't exactly like our freshmen. I AM THE EXPERIENCED PROFESSIONAL....I AM THE EXPERIENCED PROFESSIONAL.... (excuse me while I try to convince myself....haha!). I know how to make adjustments based on the students in my classes....right?

Ok....so then I thought about it and remembered how I have judged people for trying something one time and then giving up on it. So, my commitment is to keep on trying this "strategy" until Christmas. I am hoping my students will get more accustomed to listening to their peers and using the question stems I have hung in my room without being so immature and silly. But....I teach freshmen. I am just hoping the percentage of silliness lessens. I know it will still happen. My goal is to not be writing on the board if I have a student who can be doing the work instead. It's like a balancing act at the circus. If I lean too much in the wrong direction it's not good. (Did I really just compare my classes to the circus?) Here is hoping for a great balance of mathematical discussions, productive groupwork, and teacher-led discussions.

I appreciate the input and opinions of everyone and hope to use them all to find what works best for me and my students.

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!

IMP Fireworks Day 1 - Victory Celebration

I am excited to be "switching gears" and starting a new unit today. We did the Victory Celebration activity which introduces students to the unit problem for Fireworks. I love that the activity asks students to sketch the situation - this gives students with an artistic flair the chance to "show off" in class! There are 4 questions in the activity so I had each group split up. In my 2nd block class I had groups of 4 so I told them to let 2 people sketch the situation while the other 2 started working on the other questions. This worked out well because there was not more than 1 or 2 students in each group who were interested in drawing.

Some groups took longer than others on their sketches so I had everyone who was finished to get a graphing calculator and showed them how to enter the height equation into the calculators. It was necessary to also talk about how to adjust the window for the graph. We played with the tracing features on the calculators in order to look at approximations for the maximum height and the time the rocket was in the air.

I pulled a piece of chart paper and started talking about sketching the graph on the chart paper so we could refer to it throughout the unit. This brought up a discussion about which quadrants were needed. We also talked about labeling the axes and how we needed to be careful about drawing the graph because we didn't know how to scale the axes until we knew the maximum height and the amount of time it took for the rocket to land. (This is when we started playing with the tracing feature on the calculator but we ran out of time.)

Also, we discussed what the height of the rocket was when time was 0 seconds and what the height of the rocket was when the rocket hit the ground. These concepts are common sense really but it takes a few seconds for the answers to "hit" them.

Another cool thing that happened today was that my 4th block came in excited about getting to draw in math class. They took so long with their sketches that we didn't get as far with our discussions...but it was worth seeing them so invested in the activity.

After writing this post today I had an afterthought. I know that many people may ask, "Why are you drawing in a math class?" I told the students today that when people in the "real world" have large problems or projects to solve they often draw sketches or models in order to visualize what is happening. I think it is neat that this activity leads the students to start with a sketch!

A "case" for a problem-based curriculum with group work

As we have gone through Alice we have seen the need to just pull alot of practice problems for each of the rules. I still have students that approach these problems in a variety of ways. At this point there are some that have memorized the rules. I still have some who use expansion . I have explained to them that expansion is not always feasible but hopefully being able to expand problems correctly will help them to remember a rule.

Yesterday I spent the majority of class answering questions and going over examples from a couple of worksheets that I had left for them to work on when I had a sub. We have developed all the rules they needed throughout our Alice lessons but these problems had more "moving parts" for them to work through. After changing my teaching methods this year yesterday was such a "drag." I asked the students if they liked working through the packet instead of the Alice activities and some of them said yes. Today (while we were working through an Alice activity) I asked them whether they would prefer me just tell them the rule and give them practice problems or allow them to explore their way through a problem and help me to develop the rule. Once again I had some that preferred both ways. HOWEVER, when I asked them which way do you think might help them to remember the material 2 weeks from now not one student chose the "worksheet method." I think we will always have students that battle with you over having to think for themselves. There are many times that my students don't actually get ALL THE WAY to the rule or formula or method that they need to do the algebra. However, once they have had some time to "productively struggle" with a concept our discussion is so much more MEANINGFUL than when I just told the students the rule and had them practice problems using it.

One of my first major AHA! moments came when I attended an ACT Quality Core workshop in which Roy Dean was one of the presenters. I actually had to look back for some email communication between me and Roy in order to get his name. This was the first time that I remember sitting through a workshop (I hadn't attended AMSTI at this point) where MATH teachers modeled how to use strategic teaching strategies. He was very patient with me because I was often picking his brain about how he did things in his classroom instead of doing the actual activity assigned. When I found the emails I just wanted to share them because I learned so much from his answer. Below is the email I sent to him:

Roy, 

Thanks for the information and your willingness to share.  So...when I
came back to school and started telling other teachers about the
movement to teach using the methods we discussed I often get the same
question.  Teachers wonder if the group work translates into higher
test scores since the students take the tests (standardized - like
EOC, ACT, etc...) by themselves.  Concerns are also expressed about
having students in our classrooms to learn primarily through the
methods we discussed when most college classrooms are going to be
lecture based.  I didn't want to ask these questions at the workshop
because I feel like they seem argumentative.  However, I wondered if
you have any direction or advice on how I might answer these
questions.  I certainly share their concerns and understand the
questions. 

I have pulled out the "On Course for Success" book and am trying to
skim it to get answers...but I wondered if you could give me some
direction. 

Thanks!
Teri Owens
Etowah High School
Attalla, Alabama

And here is his reply...

Hi Teri, 

Sorry it's taken a couple days to get back to you. The severe weather yesterday had me "enjoying" the Bham airport for most of yesterday.
In answer to your question, I know the "on Course for Success" book has some data that you can use.  I would also think if you Googled reform math scores, group work and test scores, and such if you would find some data on your questions. 

As far as my personal experience, at my school our scores rose 6 points (a statistically significant rise for Colorado testing) the first year and 2 to 3 points over the next 8 when we switched out curriculum to a group/problem solving approach to mathematics. 

I also had a summer school class (not exactly your star students) that I taught with the reform/group/prob solve math for 6 weeks in the summer instead of the usual fraction ws, decimal ws, etc. The students seemed to enjoy the class more.  Of the 24 students I had that actually attended thes ummer classes, 23 improved the test scores the next spring and 8 moved from unsatisfactory to proficient (we have unsatisfactory, partially proficient,proficient, and advanced) and all but one improved their scores a substantial amount. 

As far as students to college, students that returned from college to chat mentioned that the college classes were different (having more lecture) but they weren't hard.  It seemed to me that since they knew the concepts and not algorithms, they could adjust. 

Sorry I don't have any hard data for you.  I at least hope this helps some.Thank you for your hard work during the training. Have a great rest of the year. 

Cheers,Roy

IMP Day 30 - You're the Storyteller and POW writeups

Today I had some fun with my classes. We made a "contest" out of beating Mr. Webb's class on making creative stories for the equations in You're the Storyteller: From Rules to Situations. I had one group do a rap and another do a video depicting a bank robbery. They were really entertaining and the students who were brave enough to do them had fun and were proud! The other groups just wrote the stories on chart paper. The "stories" on the chart paper below were the ones who also did the rap and the skit! It was loud and rowdy in my room today but it was alot of fun!

**My 2nd block class didn't get as much time to "have fun" because they had to finish up the quadratic graphs for From Rules to Graphs. Only a few students completed their homework (which was to graph (Out=In^2). None of them had the "u-shape." I decided to do a graph on chart paper on the board. I only had room to go up to 25 on the y-axis so they they were limited to x-values between -5 and 5. This was an interesting activity. I asked each student (28 total) to share an ordered pair that they got on their homework. It didn't take long for us to use up all the integers. I did have one student who used a decimal even before the integers were taken up so I made the remark that he sure was thinking "outside the box." I also told them numerous times that there were an infinite number of possibilities. When the students started getting the hang of it and we got all 28 points on the chart paper the u-shape was evident. We then discussed the difference in the equation for this u-shaped graph compared to the other equations and they came to realize it was the "squared part." I thought this was a very good investigation and we were able to explore the ideas of continuity and "infinite possibilities."

The most impressive part of my day was when I read the Haybaler POW writeup written by one of my 5th period students. It was AMAZING! Talking about understanding the whole point of a write up in the first place! I was inspired and amused throughout her writing! Here is a piece of her write-up. The sentence on the previous page discussed how she must first make sure she completely understands what the problem is asking.

I have come to the point where the POW write-ups are my favorite part of the IMP book (at least for today!). When reading them it is extremely easy to realize who is comprehending the math and the problem-solving process. Some of them (unfortunately) are so far out in left field I can not figure out why they would write such stuff. However, there are many who are increasing their math and problem-solving fluency just by doing the write-ups and having to think and reflect about their work. The ones who are in left field will hopefully start getting closer as the year goes on!

IMP Training Day 2 - Confirming my AHA moment

Today we went through more of Overland Trail and part of The Pit and the Pendulum and the experience going through the units as a students were great! Having Jim Delawder there sharing his experiences with the curriculum provided invaluable knowledge. I loved being able to "pepper" him with questions about how to approach the lessons with our students. He also offered some practical advice on dealing with students working in groups. Ideas like using a folder for each group in which they put their papers that need to be turned in so that you have 7 people turning in work instead of 28. He also put the "group roles" on a piece of paper in their group folder. There would be times that he would tell the students that they could change roles as long as they wrote them down and put them in the folder. Materials, scribe, presenter, and questioner....??  Well, I may be emailing Jim and asking 1 more question. I have never been good at assigning group roles and sticking with them.

One of the things I enjoyed most today were some of the conversations we had bouncing ideas off of other math teachers. I have just recently come to the realization that for YEARS I have been teaching my students like I want to be taught. I was that student that loved math and just wanted you to show me an example so I could do my work. The problem is that the majority of students don't learn math the way I did. Sadly, the majority of students do not consider math their favorite subject. There are students that are just not going to "buy in" to learning math if they can not see how the math can be applied. Also, since math teachers have "math brains" it is very difficult for us to relate to students who do not. One of the hardest lessons I had to learn as a new teacher was that all of my students are not like me. What I mean by that is that they do not all do their homework or give their best. (They also didn't grow up in Mayberry...which is my joke for admitting that I grew up in an awesome home with no worries to speak of.) Anyway...my new realization is that I have to change the way I teach to reach the majority of my students instead of the minority. The IMP Meaningful Math program is providing me with the tools to reach ALL students. My "math brains" can soar and find deeper meanings while my struggling students will have a context in which to operate which will hopefully help them to connect with the math.

IMP PD - Day 1

I can honestly say that a "textbook company" has never given us such meaningful and useful professional development before. It's About Time does not only provide you with a textbook that meets all the algebra standards and literacy standards in the course of study; they provide you with teacher PD that would benefit any algebra teachers because best teaching practices are modeled by the trainer. Jim Delawder is such an incredible, experienced teacher. He is very patient with all of our questions and very passionate and knowledgeable of IMP math.

Takeaways from today:

• Divide the work and if there are more problems than there are groups you can have every group do the "leftover" problems
• When I did Creating Families I could have used playing cards to group students by numbers and then regrouped them using the suits. For instance, I was a 2 of clubs. Originally all the 2s were grouped together. When we did creating families we were told that the clubs were doing the nonfamily. Then we regrouped by the type of family (or suit). That way the students all got to work with someone else who was creating the same type of family.
• Ask a struggling student to just attempt to draw you a picture.
• We can trust the curriculum...we can trust the curriculum...we can trust the curriculum.
• Around the Horn POW is confusing and you will need manipulatives to model the situation!

I know that I learned so much more than what is listed above...I am just so tired right now I can't remember! It was very cool for Tom Laster to be visiting with us today also. He even took part in the PD. It is contagious to be around someone who is so passionate about STEM education. He has so many stories and examples of successful implementation of IMP. 

And...by the way. The state of Alabama (and its math and science teachers) have been taking our AMSTI program for granted. The PD we receive at AMSTI is so similar to the PD provided today by It's About Time. WOW!