What not to do in algebra class...read if you want to laugh!

I think that I decided to write this blog post because I feel that the last 2 days I am a shining example of what NOT to do when you are teaching a problem-based curriculum. I think that everyone should have the ability to laugh at yourself so here I go...

So...I was in the middle of a discussion with my algebra class about the unit problem for IMP Fireworks which involves a celebration where a rocket is shot off of a building and the fireworks need to be set on a timer that allows the fireworks to "go off" when the rocket is at it's highest height. The problem is GREAT because some smart student (who obviously was an ace at physics) has already determined the equation for the height of the rocket with respect to time. My students have to find the answers to the following questions:

• How long will the rocket be in the air?
• When will it reach it's highest point?
• What is the height of the rocket when it is at its highest point?
• ...there are a few more but these are the ones we were mainly discussing...

So...I am supposed to be letting them determine how they might use the equation to answer these questions and I was getting this from my students:

• How are we supposed to know, Mrs. Owens?
• But...we don't know how high the rocket goes...
• So...why don't they just shoot the fireworks off the top of the building instead?
• I plugged in 3 seconds and got _____ for my answer. So, that's the highest point.
• ***I can't even remember what all this one student kept asking me...he was so bothered by the situation and the way they were doing it. He was also bothered by the fact that "quad" means 4 but for an equation to be quadratic the variable has a power of 2. I had another student to help me out and say that the power of 2 means that it is squared and a square has 4 sides.

So...my response was finally something like this:

O. My. Goodness!!!!!!  Just do the math!! You have the equation so the hard part is already done for you. JUST SUBSTITUTE TIMES IN FOR T AND MAKE A TABLE!! Quit getting so bogged down in the context that you forget how to be a math student!!!! You can use the table to estimate the highest height and the time that the rocket hits the ground!! Just be quiet and DO IT!! Use your algebra skills!!

I am laughing as I write this. I had one student to say, "No Mrs. Owens. We are learning how to apply this math in the real world!"  It is funny to reflect back on this because I was so frustrated trying to move them forward. We had worked on introducing the unit for way longer than we were supposed to and I was just trying to motivate the need to find the exact values...which we will learn how to do as we study the unit. I did have a good conversation with them about how the ACT and other standardized tests have portions (especially science reasoning on the ACT) where you are sometimes given a formula and even told what each variable stands for and all you have to do is plug in the values and simplify!! OR that they are given charts and graphs where the information is right in front of them and they have to just interpret what it means. You can sometimes get too bogged down into trying to "figure something out" when you can just read the chart/graph and find the answer!!

Math Classroom Conversations - IMP Making Friends with Standard Deviation

Math classroom conversations

#mathtalk

The things I have been hearing my students say during this activity...

"Why is the standard deviation the same?!?!"

"Why is the mean so high this time?"

"What?!?!"

"The mean for Set C is...."

"I disagree."

"I agree."

"Is this what you got?"

"Andrew shut up!" - I had to include this one just to "keep it real."

"It says explain why your pattern..."

"No pattern occurred." to which I did a loud "AHEM" and they said "Are we supposed to get a pattern?" 

So...my students had this group investigative task and I helped them to get started. BUT...in this case I made them read the directions out loud and then I asked another student to repeat the directions in their own words AND we did an example with a data set on the board. (This sentence might make more sense if you read this post entitled "Read and Follow Directions!") Then I told them that I was going to sit down and if their group had a question the ENTIRE GROUP had to come to my desk. I usually roam around the room but I believe that I sometimes have students ask me questions that they should really be asking their group members (just because I am close).  I did have a couple of groups come to me to settle an argument...isn't it awesome that they were arguing over math concepts!

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.

My Favorite Thing...my textbook (surprise!!)

I was thinking about the prompt for this week's MTBoS's Blogging Initiative during my first block class today. I was also watching them draw sketches for the unit problem in The Pit and the Pendulum unit of our Algebra text. I went down to Mrs. New's room after class and was talking to her about how much fun it is to have these days where my students get to do something that is "outside the box" of what usually happens in algebra class.

I am great at research and can find some cool activities by Googling or asking the "all-knowing" #MTBoS on Twitter but that takes a lot of time and although I enjoy it there are moments during the school year that I just can't dedicate time to finding the "perfect" activity. This is why I LOVE our IMP Meaningful Math Algebra books. The units are so creative. The students have opportunities to draw sketches, write, perform experiments, and apply the majority of algebra to a context that helps them to wrap their mind around the topics. We still solve algebra problems in class, of course, but if you teach from this text you will already have creative lessons and ways to make connections to history, English, and science within the units.

I know that there is a movement out there to "ditch the textbook" and I get it. However, I am blessed to be in my 2nd year of teaching from a textbook that I can feel good about teaching from cover to cover. I love days like today where my "non-mathy" students come in and realize they will have the opportunity to show off their art skills. I am a math/English certified teacher so I love that 2 of our units use literature contexts to make them more interesting (the other is Alice in Wonderland).

I heard NCTM's president, Diane Briars, speak this past Fall. I remember her talking about how some teachers are trying to piece together resources from here or there in order to teach. I am paraphrasing here and I hope that I don't misrepresent what she was saying that day - but I feel like her intention was to remind us that a teacher's job is not to write curriculum. This made me realize that it is okay that I do not come up with original ideas and activities to use in my classroom! Sometimes I feel guilty about not having that "gift." However, she talked about how we should be careful during the textbook adoption process to find texts that are well written. I had never been shown how to analyze topics in a textbook. That seems silly I guess but until I started teaching from the IMP books I never cared what textbooks we used because I was of the opinion that they were all the same. Definitions, examples, and problems sets... I had never heard of research-based curriculum that had been developed with the "approval" of the NSF (National Science Foundation). After teaching from these books I understand the difference!

So...one of my favorite things that I use in my classroom is our "new-to-me" textbooks!

Intro to Systems of Equations with Gallery Walk

This year I ran across a document in my Google Drive that Sonya New and I made in order to introduce solving systems of equations. I decided to do this on the first day back after Christmas break in order to get us "back on track." We have solved systems algebraically and had begun discussing the substitution and elimination methods the week before school let out.

I loved doing the assignment. I only had 6 groups but I still wanted to have them graph all 8 systems so a few groups had 2 systems to graph. I did not call them systems. I just told them to graph both lines on the same coordinate grid. I first allowed them to graph the lines on graph paper and then I had them put them on chart paper. Afterwards I assigned each group a different color marker to write with and had them do a gallery walk and put feedback on the graphs. If they agreed with the graph they put a check mark. If they thought there was an error they had to place an x and then tell what they thought was wrong. The last direction I gave them was to write down the solution to the system of equations. (We have been talking about solutions for systems of equations ALOT in class. I have even OPENED and CLOSED class MULTIPLE TIMES by randomly calling on a student and asking them, "What is the solution to a system of equations?" AND offered candy when they get it correct!! Many of them still don't know. I accept various answers: an x and a y that make both equations true, the point of intersection, an order pair that works for both.... It hurts my feelings but I still haven't gotten it to "sink in.") I had one student in the room that asked me if I meant for them to write the ordered pair down so eventually everyone caught on. Almost every group asked me what I meant by the solution but I would not tell them. I told them to discuss it within their groups because we had talked about it in depth before Christmas. Anyway...after they completed their gallery walk we "debriefed" as a class and settled any differences of opinion. It was a wonderful way to review graphing and reintroduce them to solving systems of equations - we had one no solution and one infinitely many solutions so we also discussed what those would look like algebraically. I did have them solve a couple of the solutions algebraically (using substitution) at the end of class.

Here is the document if you would like it.

OBSERVATIONS:
1. Even my best students needed the graphing review. I had one of the top students in my class put his y-intercepts on the x axis!! I want to do a better job of spiraling my algebra class. I love that our Meaningful Math Algebra books include graphing in every single unit! I hope to incorporate more spiraling review as my warmups this semester.

2. It scares me how much my students forget AND it bothers me that I have to move on when I have so many who have clearly not retained what we have learned.

3. Many of them wrote that the solution was 5 and 2 when they really meant (5,2). They think I am being picky when I make them write the answer as an ordered pair.

4. Students like the opportunity to get out of their seats! I did have some really good student dialogue and I feel that it was a productive first day back after Christmas:)

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!! 

IMP Overland Trail - Getting the Gold

I skipped Getting the Gold when I taught Overland Trail last year. I am so sad that I did! This is such a cool activity because it has such real-world applications. In this activity the students are asked to compare the profits of 2 different ways to gather gold. While discussing this activity it is fun to bring up discussions about making business decisions.

The discussion points that are a part of this activity include:

1. Business start up costs
2. Profit
3. Breaking even
4. BONUS...This is the first activity where the starting point is negative so it is fun to watch the students say..."the starting point is negative this time!" 

**I still catch myself wanting to give the student too many hints. I am sometimes excited about how the activities bring in different aspects and I just want to point them out! HAHA!

This activity and Water Conservation are fun "wrap-up" activities that have the students once more create graphs and answer questions. I love to ask questions like:

How do you know how much profit they had on Day 7 according to the graph?

Now, how can you answer that same question using the rule we created?

Could you use a table to answer that same question? 

 

Courageous math teachers

I had the opportunity to spend 2 days last week with some incredible math educators in Alabama. The pilot that was started at Etowah High School last year has expanded through a partnership between AMSTI and It's About Time. There are math teachers throughout the state that are now piloting the full IMP Meaningful Math curriculum. While sitting there listening and learning with these teachers I was in awe. These math teachers are committed to trying something new in order to improve student achievement.

Susan Jeffers says to "feel the fear and do it anyway" and many of these teachers are doing just that. I heard many teachers grappling with the unfamiliar territory of things like assessment and assigning homework within such a different teaching format. It is exciting to be associated with teachers who are willing to get out of their comfort zone in order to try a curriculum that is time tested and has brought results over and over again.

A few years back I came to the realization that I wasn't reaching as many students as I used to and I started seeking a different way to teach math. God directed me down a path that involved coworkers, workshops, Tweets (the MTBoS especially!), and a "chance" meeting of the president of It's About Time in an elevator! Remember that the sky is purple in my world (haha!) but I really believe all these things have lined up to improve math education in the state of Alabama. I am amazed that the small pilot at one school has grown into a state-wide pilot involving many. I am thankful that AMSTI and It's About Time are providing this opportunity for the schools in our state!

AMSTI/IAT training Day 1

Lately I have not been a "person of many words." HAHA! I guess sometimes we hit a busy season and there are some things that have to be "cut" from our daily routine. So far this school year the part that has been cut out of mine has been taking time to blog and reflect. I really enjoy doing it and intend to continue...at some point.

The pilot that was started at Etowah High School last year has expanded through a partnership between AMSTI and It's About Time. This past week we had 2 days of professional development. Again, I have never seen a textbook company invest in the teachers who used their books in this way. They are truly committed to teaching teachers the best way to teach with their curriculum. Thank you to AMSTI and It's About Time for this opportunity.

One of my favorite conversations on day 1 was about "prizing the doubt." Michael Reitemeyer was the presenter for our algebra training and he had a course with a professor named Mandy Jansen who had told them that one "scholarly disposition" is to prize the doubt (Here is Michael's blog about this topic). Below I am going to paste the notes I took during that discussion.

Prize the doubt - to be comfortable with uncertainty, embrace and welcome times of uncertainty, not having everything figured out all the time, people go through "early foreclosure" just to feel certain again 

*assume that I think you are all smart 

*an alternative way to engage is to wonder...or posing thoughtful questions 

*get excited about having things in progress

I am proud to say that I spent the entire year last year dealing with the doubt and uncertainty of teaching a new curriculum (IMP Meaningful Math) that was very different than anything I had ever done before. I truly believed the research and the testimonies of other teachers but it really felt so strange and different. I can relate to the "early foreclosure" part because I remember the first few times I tried teaching my students in groups I thought it wasn't for me. I kind of thought that teachers at other schools with different types of students might be able to teach that way but it just wouldn't work in my classroom. Thankfully...in the 2013-2014 school year I had already spent the year determined to make groups work in my classroom so the transition into teaching using the IMP curriculum (2014-2015) was not quite as hard. Since I trusted the curriculum I was willing to just have the attitude that I was going to do the best I could because I believed it was best for my students. As time went on I was less nervous and really enjoyed teaching with the curriculum. After spending the day with veteran IMP teachers/trainers and other incredible math teachers throughout the state of Alabama I feel like I have so much more growing to do. I just have to take a deep breath and remember I can not completely change my teaching practices in a year. But I will "prize the doubt," remember that I am smart, and get excited about the things I have in progress!!

Other things that stood out to me during our Day 1 training are listed below:

• Wonderment wall/board - when students have good questions write them down and display them in class...then as you have ways throughout your lessons/units that you can address the question you have a visual reminder
• I need a document camera!
• Sometimes when you have a student to "share out" it would be good to sit in the desk that they vacated to have a visual cue that they are leading the learning at that moment
• Give students space to ask questions and have "divergent thinking" - the questions may not be mathematical all the time but they own the math more when they have invested
• According to Michael the #1 quality of a good teacher - listening....compassion would listen, flexibility comes from listening, connecting comes from listening 

Lastly, I was honored to be included on the panel for a brief question and answer session at the end of the day. Brian Lawler facilitated the discussion and afterwards we talked a few minutes. One of the questions during the discussion had to do with pacing and how much time to spend on the units. He said that Sherry Fraser (one of the authors of the curriculum) told them in a training one time that if the pacing guide says to spend 20 days that you should stop that unit after 20 days even if you are not done - which is mind-boggling but I intend to follow her advice! I told Brian that I took forever teaching Overland Trail last year. He said, "I know. I was following your blog and felt sorry for you students. I thought that they would never get to California!" HAHA! 

IMP Pit and the Pendulum Days 1-2 - The Question and Initial Experiments

On the first day of Pit I was actually issuing books. Therefore I used the WONDERFUL advice of Jim Roebuck and we listened to a Youtube video in which the entire story was read. If it were not for the fact that I needed the time to issue books anyway I probably would have gotten too impatient and skipped to the portion that read the excerpt from our algebra books.

After the story I assigned The Question where they draw a sketch of the situation and look for information in the story to answer the big question...does the story's hero really have time to carry out his escape plan? On the first day we didn't completely finish the sketches and didn't even start the discussion so we continued it on the 2nd day. We made a list of what we know from the story (especially the items that are mathematicaly relevant). They include the following:

• The ceiling is 30-40 feet high
• The pendulum swings perpendicular with his body
• The pendulum was 3 inches from his body
• He thinks he has 10-12 sweeps or vibrations (back and forth) before it will touch him
• It will take the rats one minute to eat through the rope (yuck!!)

Then we arrived at a "revised question" - How long does it take the pendulum to make 10 swings? We are also going to use the assumption that the ceiling is 30 ft high. 

Initial Experiments pg. 201

Okay...the fun part was then asking the students what we needed to know to answer this unit question. I had one boy who instantly said that we needed to know how long it took the pendulum to make one sweep. We had a class discussion about all the things that might effect this time and we narrowed it down to 3 things that we could actually test in class: weight of the bob (end of pendulum), length of pendulum (which is the height of the ceiling in the problem), and the angle of release (amplitude??) of the pendulum. I am not used to using the word amplitude for this type of problem. I keep picturing the perpencicular distance between opposite sides of a parallelogram!

Anyway...the students enjoyed building pendulums. I assigned each group one variable to test but I didn't give them any guidelines other than to test each weight (or length or angle of release) 10 times. Therefore they did 30 total trials. Also they only timed one sweep. After the experiments they decided that the angle of release didn't matter but that the other 2 variables did. Then we discussed issues that may have effected our data like not using the same angle or pendulum length when you were trying to test different weights. Or not using the same pendulum length and weight when testing angle of release. Also, some student held the pendulums in their hands and kind of helped the swing by moving their hand up and down. I look forward to doing more investigations and tying in the statistics as we go!

Students working on their sketches

P.S. - Thank you Jim Roebuck for giving us helpful hints on how to best teach this unit!

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 I and Views of the Distributive Property

I love that Mrs. New has already been through this unit a couple of times. She give me great tips! For "Distributing the Area I" she advised that we make a handout with the 6 area model rectangles so the students could just write inside them. This helped the activity to move along faster than if they had drawn the area models. Some of my students are perfectionists so they would take forever to draw a perfect rectangle and then have little time to work on the actual task in the lesson. My students seemed to really enjoy this activity. After I showed them #1 as an example they pretty much took off with it. I even had one boy who I have to get on to often for sitting and doing nothing to be the first one to get the answers for #6. I was proud of him!

"Views of the Distributive Property" was an activity that made them think about the way that they multiply 2 digit numbers. They are shown through the activity that they have really been using the distributive property and partial products all along. My students whined a little bit about having to do the problem involving the long form but I tried to explain to them that this was just a foundation on which we were going to build as we started multiplying algebraic expressions.

I have taught multiplying and factoring polynomials using the area model for a couple of years. I have called it "the box method" but it is the same thing. Even though I feel like it gave the students a more visual way to work through the problem and it also helped them to organize their work I still had some students who would take forever to get the idea that the product inside the box comes from multiplying the 2 values on the outside of the boxes. I am excited about the way Fireworks has built the idea of using the area model. My students will have the idea of the "lots" changing size from the "A Lot of Changing Sides" activity so hopefully they will feel like the answer is just like adding up all the smaller areas even when we are multiplying polynomials.

Another thing that excited me today is that I got through these activities in the time that the teacher's guide recommends. That is an accomplishment for me!

IMP Fireworks - A Lot of Changing Sides

I really enjoyed doing this activity with my students. It starts with a background story of a housing developer wanting to change the lot sizes for a new housing development. Instead of all the lots being square the city planner wants some of other types of rectangles. The questions tell the students exactly how to change the dimensions of the lots. The first 4 are situations where they increase the size of the lots and the last 2 involve a decrease in the length of at least one side.

Mrs. New had already taught this lesson and showed me the way the teacher's guide recommended the sketch of the lots be drawn. These diagrams will look like "the box method" that they will use to multiply and factor polynomials. The activity asks the students to express the area as the product of the length and the width (which will be binomials) or as a sum of smaller areas. Since the 2 areas are equivalent the students are led to realize that the 2 expressions are equal. I aksed them to look for connections between the sum and the product and a few of them saw it.  I love that the authors have once again provided a context for the formal math to make sense to them!

I led the students through #1 so I could model how to sketch the diagram with the original side length of X. In #5 and #6 I let them come up with their own diagrams to represent the situation. Also, just for the sake of organizing, I labeled the bullets as A, B, and C so that it would be a little easier to organize and discuss.

IMP Fireworks - Using Vertex Form, Crossing the Axis, and Is It a Homer?

In Using Vertex Form, the students have another picture to create with their graphing calculators. Then they are given equations in vertex form and asked to give the vertex. Most of the students could do this without using the graphing calculators but a few still depended on them. I advised them to use the "Trace" feature of the calculator to find the coordinates of the highest point and then compare the coordinates to the equation. This improved their confidence in finding the vertex.

I gave my students a quiz where they had 6 questions in which they matched quadratic equations to their graphs. Then they had a couple where they had the equation and had to list 3 things they know about the equation. The last 2 questions had them describe how to flip a graph so that it was concave down and then sketch a graph with 3 different parabolas and give their equations. I was so excited about the quiz results. I wish I could say that all my students aced it but that is so not true! However, the large majority of my students passed the quiz and many made As and Bs. I have never expected my students to be able to do so much with graphing quadratic equations. The way the activities led the students through the process was so thorough it made the quiz seem easy.

The Crossing the Axis lesson gets students to start thinking about how many x-intercepts the graph of each quadratic equation will have based on the phase shifts. The activity also has students to write the equation given the vertex and another point on the parabola. They have to use the information to solve for the value of a. Numbers 5 and 6 are very important to complete because they give the students the tools they will need to complete the Is It a Homer activity.

Is It a Homer is an awesome activity to me as a former softball player and coach. It was also fun to the students. Mr. Webb shared a link with me of a Youtube video of a "dramatic reading" of a poem about the "Mighty Casey." We watched it before we read the activity. They are challenged to figure out if the ball clears the fence and they must prove it mathematically. I had the students sketch the graph with height on the y-axis and distance from home plate on the x-axis (which was advised in the teacher's guide). I gave the students the hint that they will be using the same process they did on 5 and 6 of the previous activity. After giving the students some time to think I went to the board and sketched the graph and labeled the vertex. I asked the students if there was another time when we knew what the height of the ball was. My 2nd block students chose to use (0,0) and but my 4th block students pointed out that the ball was not hit off the ground so they used (0,3). They struggled some with the computation of this problem but a few students in each class got the answer correct based on the height of the ball at contact. I had one student who told me that he estimated that the ball would fly 400 feet because the maximum height was after the ball flew 200 feet. Even though we have not yet talked about the symmetry of the graphs he had recognized it and used it for his reasoning. Unfortunately he didn't tell me his thoughts until AFTER class. I will be sharing it with my classes tomorrow.

IMP Fireworks - Parabolas and Equations I, II, and III and The Vertex Form of a Parabola

I am absolutely loving the way Meaningful Math develops the Fireworks unit. These graphing activities go through each of the ways that parabolas are transformed using phase shifts. The students explore each of the phase shifts using graphing calculators. They start with different equations to enter and analyze and then they are given a picture of multiple graphs on the same coordinate plane. They areasked to create the picture by typing equations into the calculator.

The first few activities I gave each student a TI-83 and each group also had an Ipad. Once they figured out the correct combination of equations the group displayed their graphs on Desmos which I projected on the board using Airplay. This was a neat way to have the students to "show off" their work. However, as we were going through the activities I noticed that many of the students were just waiting for the person with the Ipad to type in the equations. They were not using their calculators like I had intended. I wanted them to use the calculators first and then display their findings using Desmos. Therefore, today I had the students to let me know when they got each of the pictures correct. I initialed their papers where they had written down the equations that gave the picture. We did not use the Ipads today. I liked the change - especially since we were working on the activity that pulls all the shifts together. By requiring initials for each of the problems I was able to formatively assess each individual instead of each group. Since each graph took a good bit of  time to create it was feasible for me to initial.

Today's activity introduced the students to the vertex form of a parabola. It combined all the pieces that we have been working on in the last few days. I feel that after working on getting the equations that generate the pictures the students were beginning to demonstrate a firm understanding of the phase shifts. 

On a side note...Thursday Tom Laster and Laura Murphy from It's About Time came to our school to observe our classes and discuss plans for next year. Observe is really the wrong word...they actually came into my class and sat with my students and participated in the graphing activity. My students really enjoyed this and I was honored that they came to visit!