Sonya New's Reflection after Year 1 teaching IMP Meaningful Math Algebra

Once again I thought that anyone who is reading any of my blog posts concerning the IMP curriculum might like to "hear" from someone else. We are so blessed to have 3 teachers at Etowah High who implemented this algebra curriculum at the same time. Having the opportunity to collaborate throughout the year was incredible! 

The Mom of  2 little ones (like both under age 1 year little) takes a little more time getting her thoughts together. I once again thought you might enjoy hearing from the 3rd teacher (I posted Gary Webb's reflection in a separate post and my reflections in this post) who taught the IMP Meaningful Math Algebra curriculum for the first time this year. Here are Sonya New's thoughts:

Teaching Algebra with the It's About Time curriculum is a much needed complete departure from the norm.  I was always the Algebra teacher that would look at the word problems in the textbook and think wow what a great question and would assign it just to have students not attempt it because "it was too hard" or "I didn't understand what it was asking me to do", so as the year progressed I would resign that kids just couldn't do those problems and basically stick to practice of the most basic problems.  Even after "going over" the "hard" problems my students didn't seem to get it.
When we received our new textbooks my students opened them to discover mostly words, very few numbers, and virtually no "traditional" practice problems.  Students are taught Algebra through situations.  Many students have found Algebra to be a very attainable subject that once thought it was "so hard".  As a teacher and lover of math I have also discovered that Algebra doesn't have to be so structured, formulated, and procedural.  The concepts of Algebra are often "common sense" and when approached from that direction make sense to many students.  By the end of the year my students were no longer afraid of the "hard word problems." They were not intimidated to try them anymore.  They would try to make sense of a problem and work their way around to a solution. Still not all would get the correct solution but at least we had something to work with ;-).
There were times during the year I would question the curriculum.  Are my students really getting it?  What about this formula or this method?  When is this concept covered?  I have learned to relax and trust the progression of the curriculum.  Things are not taught in a traditional progression, but the topics do get covered.  I am still working on my balance between completely trusting and supplementing more practice but I am coming around.  I anticipate each year to get easier for me to understand the beauty of the curriculum and to do a better job of facilitating.  I know this one thing for sure...it may have been my first year to use the curriculum and there were definitely flaws in my implementation but I don't want to teach Algebra using anything else!!!

End-of-Year Teacher Reflections on IMP Meaningful Math Algebra

I have been challenged by Brian Lawler to answer the same End-of-Year Reflection questions that my students answered. He reworded them a little and I am going to paste them into this blog and answer them. They are all very thought-provoking!

1. How was this experience "teaching mathematics" different from your previous work teaching mathematics?  How was the math itself different? Did you learn the mathematics differently?

This teaching experience has been different in numerous ways. First, I have never taught a curriculum that had unit problems or "themes." Having a context for almost every algebra topic that I taught this year truly did make the subject more meaningful to my students. Secondly, the tasks are written in a way that students are given the opportunity to discuss and "struggle" with the problems even if they do not initially understand the math behind it. The teacher's guides always provide you with great "leading questions" that help you to guide your students to discovering the math without you just saying, "This is how you do this problem. Write it down." Having the teacher's guides AND having seen this style of teaching at AMSTI training were huge helps for teaching this curriculum the way the authors intended (or at least close to the way it was intended to be taught). We also received training from It's About Time in which we were able to go through many of the activities as "students."

When going through the training as a student (at AMSTI and It's About Time training) I was reminded often to quit thinking like a teacher. I think that one piece of advice was one of the most helpful. At first I would only see the training from a teacher's perspective and I would be worried about what formula I should use to solve the problems. As I taught this curriculum I have realized that the students are asked to use common sense, repeated patterns, and the context in order to solve the problems. The formulas can also be used (and taught, of course!) but when a student is taught to totally rely on formulas and then they get on the ACT (or other standardized test) and forget the formulas they don't have the problem-solving experiences that will help them to persevere and be successful.

This is my 2nd year to teach the entire year with my students sitting in groups of 4. Although I had already taught with students grouped last year, the majority of the year the only function the groups had were that my students could check to see if they had the same answer on a problem and help each other if someone was confused. This year the IMP Meaningful Math Curriculum provided my students with opportunities to utilize group work in a whole new way. The problems were presented in such a way that the students would start discussing their ideas on the best way to solve the problem. Sometimes a few of them would work quietly until they felt like they had an idea to share with the group. Other times they would sit there and talk about it before they tried to put pencil to paper. The exciting thing was that the groups this year were used for actual mathematical discussions about how to solve problems.

I think what I "learned differently" was that the students will really and truly try different approaches to solving problems if you give them the freedom. When I used to stand at the board and show them how to do a particular type of problem that is the way they did it. However, I have seen multiple times this year that if I give them a task and then give them the opportunity to figure it out on their own (with the support of their group members) they will solve it with various approaches that make better sense to them. I use to teach them the way that I thought was best. This year has taught me that struggling math students do not interpret and work through a problem in the same way that an algebra teacher does!

2. How have you changed personally as a result of your experience? Has your confidence in your own ability grown? How has your experience of working with math-teacher colleagues changed?

I had a day or two that I would kind of go back into my "old teacher" mode and stand at the board doing examples and "giving notes." I would actually stand there and think that I was boring myself to death! HAHA! I have learned a new way to teach that is much more engaging. I do not want to go back to my "old teacher" mode again.

My confidence in my ability to teach math has grown. I have always been a confident math student. I was good at math and so I wanted to be a math teacher. In the past I believed that math was something that some students were gifted at and others were not. The way this curriculum is written gives students more than random "number crunching" in math class. This is a problem-based curriculum in which they are constantly applying the math within a context that gives it a purpose. Using this curriculum literally helped me to reach students that had failed my class in previous years because of lack of interest.

I am blessed to be a part of a terrific team of math teachers at Etowah High School. Sonya New and Gary Webb were also implementing this algebra curriculum. Sonya and I were able to discuss our lessons on a daily basis because we had the same planning period. It was harder to have discussions with Gary but we did have lunch with the entire math department so we were able to talk to him some during lunch. I do not believe we would have been as successful without the opportunity to collaborate and learn from each other.

I also reached out to other IMP teachers via email and Twitter throughout this year. I have found so many helpful teachers who have shared their teaching ideas and resources.

3. What are your mathematics-teaching goals for next year? How have those goals changed over the past year and why?

My main goal is to keep improving. There are many times I felt that I was blindly going through the curriculum this year. I would sometimes hesitate to introduce a particular "math formula" because I didn't want to "steal the thunder" of a future lesson. There are so many concepts that the curriculum kind of allows the student to develop his/her own understanding instead of a teacher just telling them how to perform the problem using a formula or particular process. Another goal I have is I want to do a better job teaching my students how to present their work next year!

My goal of teaching students to present their work is different because the types of tasks that they do in this curriculum are different. For example - If a student is asked to solve a system of equations where they are already given the 2 equations there is not a lot to discuss. They can go to the board and tell the class the method they chose (substitution, elimination or graphing) and then work it out. In the IMP curriculum the students would be given a scenario in which they have to write their own equations and then solve the system. They would have the opportunity to discuss how they assigned their variables, wrote the equations, solved the problems mathematically, and verified that the solution was viable within the context. There is so much more to discuss!

Gary Webb's reflection of 1st year teaching Meaningful Math Algebra

There are 2 other math teachers who have gone through IMP Meaningful Math Algebra with for the first time this year. I have mentioned them both from time to time in my blogs. One of them is Gary Webb. We were asked to write a testimonial about our first year's experience. I thought another teacher's perspective might be interesting. Here are his thoughts:

I really enjoyed teaching from the Algebra I Meaningful Math book this past school year. It was quite different than traditional math text books. The books have few examples, fewer problems, require deeper thinking, and don't have answers in the back either.

One takeaway I have is that your best students will do whatever you ask them to do. Some of the students are not going to do anything no matter what. These are the ones who complained most about the book. However, these are the same students who might do 5 traditional math problems in 30 minutes and complain about having homework.  The many students who are in the middle were the ones that I was able to reach. Students were more engaged because they were able to use their creativity in the math classroom, were in groups much more often, and were encouraged to discover mathematical concepts on their own.  I loved watching my students think and not be a robot and follow set procedures.

Gary Don Webb
Etowah High School

Results after 1 year of IMP Meaningful Math Algebra

I just wrote a post in which I shared some student reflections after their first year of IMP Meaningful Math Algebra. I have written several posts reflecting about the differences of the curriculum. I have learned so much about how to facilitate "productive struggle" in the classroom. The new curriculum along with thing I learned from blogs, Twitter posts and professional development (esp AMSTI and It's About Time training) have all combined to help me to make improvements in my instruction and test results. Many teachers ask about how the "new curriculum" is going and it went GREAT. Even though we were told not to expect growth in the first year of teaching the curriculum we analyzed the data and WE SAW GROWTH. Woohoo!

We had 3 algebra teachers at Etowah High School - Sonya New, Gary Webb, and I - who implemented the curriculum 7 weeks into the school year. There are 5 units and we only had time to complete 4 of them. We did not cover the Pit and the Pendulum. In the state of Alabama the last 3 years 8th graders took the ACT Explore. After our students complete algebra they take the ACT Quality Core Algebra End-of-Course test. We looked at this year's 2015 9th graders (who had the IMP curriculum) and compared them to last year's 2014 9th graders (who were taught with a more "traditional" curriculum). It is a little difficult to explain but I will try so that you will see that the results are valid. Instead of just looking to see if the average scores on the EOC tests improved we compared students who came in with the same score on the 8th grade Explore and then compared each group of same-scoring Explore students from the 2 years. We averaged each group's Algebra EOC test results and compared them. Then we just did a +/- on whether or not the scores improved or declined for each category (i.e. students from each year who came to us with a 12 on the Explore). When we factored in all of our students we had a +1.94. All year long we have said that we think the curriculum is beneficial for all students but that it really seems to make a bigger difference for our non-honors students. Therefore we took out the honors students from each of the 2 years and then did the +/- for growth again. We showed total growth of +9.02 which we believe to be an average of about +1.13 per student. The EOC Algebra test scores range from the 130s to the 150s so we feel that the improvement is significant.

Now...I am definitely not a statistics major so there is room for error in the analysis of this data. However, we are very excited to have seen this growth in our first year! We know that we have so much room to improve - especially since we didn't have time to cover all 5 units.

STUDENT End-of-Year Reflections on IMP Meaningful Math Algebra

Wow! What a year it has been! It has been a while since I have written a blog post due to the craziness of the end of the school year. I have so much that I would like to share.

Here are the student responses I got from the end-of-year review questions in the Fireworks portfolio. We did not have time to do the complete portfolio so I just had them answer the questions on pg. 421 in the book. I feel like what they have to say is more important than anything I could add. I only had one student to just absolutely say that he wishes he was taught out of the "old" type of textbook. Of course the responses I am sharing below are the "fun" ones for me to read as a teacher. There were some students that talked about how they didn't like that the book was so "wordy" but those same students later admitted to growing more confident and learning how to work in groups. I also had a few students to tell me that they still preferred to work alone but the overwhelming majority had positive things to say about group work. I told my students to be honest with their responses and give good explanations to support their comments. I told them I really wanted to know what they thought.

The first question set included the following:

How was this experience different from your previous work in mathematics? Did you learn the mathematics differently? How was the math itself different? 

Here are some of the responses: (I really wanted to fix all the grammatical errors...but I didn't because I didn't want to put my "spin" on what they said.)

• The books we used this year was all word problems and that will help me during high school and college. 
• Working in a group helped me understand better cause some of them understand better than I did and they helped me understand it better. 
• It was more fun with the activities and been taught different.
• ...the mathematics itself was longer and a bit harder also
• My past experiences I didn't understand anything but now everything seems a lot easier. (this is a repeat algebra student)
• This book is also different because it never (is) just straight on work it always has a fun story. Also it helps you a lot more than any other math book.
• We actually learned about real work stuff. We did a POW about having a house, paying bills, etc...

The second question set included the following questions:

How have you changed personally as a result of your experience? Has your confidence in your own ability grown? How has your experience of working with others changed?

Student responses:

• Working with others - I've started talking about it more than just trying to work on it.
• I'm more conficent in math now than I ever was. (this comment was repeated by several students)
• All year I've had a group to work and to collaborate with so I do believe I have gotten better working with others.
• My confidence in math has grown a lot because at first I never answered out loud, but now I know that I can do it.
• I don't hate math as much. It's not as hard as it was. My experience of working with others has grown alot and I can talk better with other people. (this student is a very quiet and shy young lady) 
• I like working with other people. You get to see what everybody thinks and their ideas. My personality has grown to like math a little bit more. I still kinda don't like it, but I like it more than I did.
• I think I have become more confident. I think I have learned to work with people that I normally don't talk to.
• It's changed (experience working with other) cause if I need help then I can ask my group members.
• It has helped me change by helping me with the word problems to look for clues through the paragraph. I myself had a hard time on word problems till this book helped me out.
• Personally I changed mathematically. My math skills have grown and so has my confidence in my own ability. My experience of working with others has changed like now I can work better with others. I can cooperate with others better. (This student stated in his answers to the first question set that he didn't like the book. I sure did like the results he got though!!)
• Yes my confidence has grown going into ninth grade. I never like working in groups but now I do.
• From a special education student: My confidence grown alot since last semester. It change because I use to just copy people because I didn't know how to do it but now I work together to figure out the answer.
• Working with others gave me more confidence and helped me understand something I didn't know and I could just tell my group and see if they know so we could help each other out.

The last question set had these questions:

What are your mathematics goals for the rest of your high school years? How have those goals changed over the past year and why?

Student responses:

• I also would want to keep learning more math cuase it can actually be fun to do.... But this year in math it has been easier for me and I'm getting higher grades.
• My goals have changed because I feel like I'm trying in my math classes and not just copying.
• I wanna keep improving my math skills for the rest of my high school years and beyond that. My goals have changed over the past year because I learned that I can keep improving my math skills. 

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 - Distributing the Area II and Square It!

Michael Reitemeyer shared with me that he uses the video above as an introduction to his class. Today, as my students were working on the Distributing the Area II activity, I was reminded of the video. The very first problem is one where the students need to guess and check in order to get the correct answer. There are several students who just stared at the problem. I gave them a hint and then gave them a few more minutes. Afterwards I had a student share HOW she got her answer. I asked her if the first numbers she tried worked and she said no. She tried some numbers and then made some adjustments until she got the result she needed. I reminded the class of the video. I told them that Jada got to an answer faster than most of the rest of them because she was willing to TRY some numbers. After she tried some numbers and saw that they didn't work she was able to make a revision and find the solution.

One of the questions in this activity actually has the students to factor a trinomial but they don't realize that is what they are doing. I stressed to the students that they are being asked to try both the vertical method and the area model to multiply polynomials but afterwards they can choose the method they like best.

Square It!  introduces the standard form of a quadratic equation and leads the students to convert quadratic equations from vertex to standard form. Number 1 has the students practice squaring a binomial. Then they are given problems in vertex form and told to put them in standard form. It amazed me that some of the students in one of my classes didn't make the connection between number 1 and number 2. I even told them to square the binomial first just like we did in number 1. (I try to help them see the connection between the order of operations and the idea of squaring before you distribute.) I kind of  "got onto" them about not trying to make connections from number 1 to number 2. They just kind of shut down on me and started whining. I noticed that there are several more places in the next few activities where the students will practice this skill again and I am glad. My other algebra class did fine with the activity - no whining or complaining. I wonder if my experience with the first class helped me to put more emphasis on the connection between numbers 1 and 2?

**While planning for the next day I realized that the students will be given a couple more chances in the next few activities to work on changing from vertex to standard form.

Squares and Expansions is an activity where the students are first introduced to the concept of completing the square. Then they practice converting from vertex to standard form.