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!

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 Alice Day 8 - Having Your Cake and Drinking Too

When I saw that the teacher's guide allowed 60 minutes for this activity I thought there was no way. I thought we would get through it quicker...haha! We didn't even finish and we had OVER an hour. This activity helps the students to explore and HOPEFULLY discover the rule for dividing powers with the same base. I love it! It is really revealing the lack of number sense that my students have. The questions are not really that difficult...that is why I thought we would breeze right through.

I have allowed myself to "sit" on this activity and not rush it because I really believe it might help to cement the concept. I am going to be absent tomorrow from my classes and I have some good exploration worksheets on exponents to leave for my students. However, it has reminded me how blessed we are to have found a book that combines the exploration with the context. Someone had a wonderful imagination!

**Update 3/7/15** Original post was made 3/16/15
This year when I taught this lesson I took the time to help the students to explore #2. I did not let anyone blurt out an answer when we first started looking at it. I have been using the random integer generator on the TI-83 (which is awesome but I just now figured out how to do it!!) to call on students. In my classes I just happened to call on students who were unsure of what to do so I just asked them to start by making a guess. I told them to tell me a number of ounces of cake and a number of ounces of beverage and then I showed them how to "test" their answer to see if this would give an answer where Alice's height was multiplied by 8. Then I randomly called on more students. The first 3 students guessed more beverage than cake (ugh!) so I asked the next student to make a "conjecture" on whether or not more beverage than cake would EVER allow Alice's height to be multiplied by 8. My 2nd class arrived at the correct number of ounces much faster than my 1st one did but I feel that modeling to the students how to "guess and check" was valuable. I am always telling them not to ever erase their guesses. I want them to learn to look back over the ideas that didn't work in order to help them to identify new theories that might work!! Anyway...the day I taught this lesson this year I felt really good about what we had accomplished:)

Show me how to teach it differently!

I remember walking into our Instructional Partner's office a few years ago because of my frustration with my algebra classes. My failure rate was climbing and I was teaching algebra just like I always had - and it had worked well in the past! I remember asking her if she knew of a different way to teach algebra. That year I taught the "repeater" Algebra IA class in the Spring and I chose to teach the majority of the class using the sample units we had received at the ACT Quality Core workshop. That was the first time that I had seen a math teacher model some strategic teaching strategies that I had seen in some ARI workshops. I was often frustrated thinking that the strategies worked for other content areas but the majority of them just didn't fit in the math classroom. That Summer I attended my first AMSTI training and decided (although I wasn't completely sold out on all the activities yet) to make the commitment to put my students in groups and keep them in groups for the entire school year. I hated it at first but once I adjusted I doubt that I ever go back!

That next school year I looked for and used several station activities and review activities. I also came across some inquiry/discovery-based activities that I loved. I was constantly scouring the Internet for resources and making copies for my classes. My student engagement improved in that school year. The following Summer I attended year 2 of AMSTI training and the light bulbs started going off. I realized that the "AMSTI activities" were the type of activities that I had been looking for on the Internet. I had always thought of them as activities to do AFTER I had taught the concepts and I didn't think I had time for that. A phrase that one of the trainers kept saying to me was , "Quit thinking like a math teacher. Your students wouldn't do that!"

Through these experiences I have come to realize that for the majority of my teaching career I have taught all my students as if they were all good math students who were going to pursue educational goals that involved upper level math classes. I do have a few students who fit that description...but the majority of them don't. However, I was teaching them all the way I preferred to be taught...but the majority of my students aren't like me. They don't love math and math does not come easy to them.

Fast forward a few months to my implementation of the IMP Meaningful Math Algebra curriculum...almost everything I teach is tied to a context. I am finding that even my students who are not great at math will interact more with the activities because the context makes the problems more accessible to them. They might not be able to just see a "naked math" problem and figure it out but when they have a storyline surrounding it they have a context that helps them to make sense of the math. So now I not only have a curriculum that is discovery/inquiry based- I have a curriculum that also presents the algebra concepts within a context. It may have taken me a few years to find the resources/ways to teach it differently, but I have definitely found it. Now...I just have to learn how to teach using them. I am working on that!

I appreciate all of the people who have helped me to transform my teaching. I don't want to try to name them for fear of leaving someone out.

IMP All About Alice Day 1 - Alice in Wonderland

We have had multiple delays and missed school days in the past few weeks. Therefore I have decided to skip the last portion of the Cookies unit and start Alice. I'm going to try to make up for it by using systems of equations problems as my warm-ups for the next several days.

Today we read the intro and then watched a film clip from the movie. Thank you to Lori White for providing the film clip this past Summer at AMSTI training.  After giving the students about 10 minutes to work on the 4 questions in the Alice in Wonderland activity I had them to write their answers on 2' by 2' marker boards. It has been a while since we have used them.  I like placing all of their boards at the front of the class and comparing/critiquing the answers with the class.  I rolled my 8-sided dice and called on a group to explain the answer to each question. After the explanation we compared the answers on all the other boards. It was interesting to see the different ways the students worded their answers. For the first part of #1 some students said Alice height doubled twice, some said multiplied by 4, and some said quadrupled. A common mistake made for the 2nd part of #1 was students thought they should multiply by 10 for 5 ounces. Some students did say that Alice's height was doubled 5 times. I did have one student to say her height was multiplied by 32 when she ate 5 ounces. He is such a good math thinker. It was sad to me that none of the groups created a table to answer the questions. I showed them how we could use a table to help us to recognize the patterns which helped us to write the rules.

IMP Cookies - Rock 'n' Rap, formative assessment and collaboration

Rock 'n' Rap is an activity that talks about producing rock and rap albums. The students will once again be led to find profit lines which should help them on solving the Cookies unit problem. There are 3 constraints this time. Also some of them shade below but one shades above so there is a little variety.

When graphing the inequalities Sonya New, my IMP teaching buddy, has stressed with the students that one way to graph the lines is to find values for x and y that make the equation true (they really do this by trial and error using number sense). I love that she has done that (even though I have talked mostly about using intercepts or slope-intercept form). She has taught SI form and graphing using intercepts also, but she says alot of her students still graph by finding ordered pairs that work.

When I did the problems with my class we said that there had to be more rock albums than rap albums. However, smarty pants Sonya corrected me (I hate when I'm wrong) and told me that it should have been rock is greater than or EQUAL TO rap. When you read the paragraph about this constraint it says that the company promises that it would not release more rap than rock. Then it goes on to say that the company is more closely related to rock music in the public mind. Even though I know she is right I could really make an argument about why I chose to publish more rock than rap! (But the mathematician in me knows she is right...dang it!)

Lastly, I had my students put this activity on chart paper. I have been in such a rush lately I haven't done this as much. It made me realize that having them put it on chart paper "makes it real" for the students and they invest more in the problem. Also, I get the opportunity to formatively assess at a glance by reviewing their work. The picture below is of a group of students explaining their findings from the Rock 'n' Rap activity.

IMP Cookies - Profitable Pictures...very important

This activity builds off of Picturing Pictures. Mrs. New and I decided to draw a graph for Picturing Pictures and make copies of it so the students would for sure have an accurate graph on which to do their "profit lines." It is so wonderful to "share a brain" with Sonya (Mrs. New) because she has already taught Cookies twice. We are needing to trim as much as possible because we started the curriculum late. Therefore she knows when there is an activity that you should not skip and I need to remember NOT TO SKIP PROFITABLE PICTURES.

This activity gives students the tools they need to answer the Cookies unit problem. The students should discover that the profit lines are parallel and that the higher the y-intercept the higher the profit. Therefore they need to extend their parallel lines until they find the highest line that clips a point in the feasible region. After trying to get my students to explore this activity over 2 different days I finally EXPLICITLY told them that the maximum profit is going to come from one of the corners (if you will) of the feasible region. Sonya and I  also EXPLICITLY told them that the methods we used to discover the feasible region for Profitable Pictures are the same as what they need to use to solve the Cookies problem.

Profit Lines...

When I first started the curriculum I was so diligent to read through the teacher's guide for almost every lesson. So far this semester I have not been able to do that! It is a long story... Anyway, I really value having someone (who just happens to share a planning period with me) to collaborate and discuss lessons with! It makes such a difference. Sonya is totally committed to our "new curriculum" and we have so many aha moments that we get to share with each other.

IMP Day 44 - Quiz on writing equations given 2 points

Today I gave my algebra students 30 minutes to work on POW 4 - On Your Own. This is a great POW that makes the students create do some research on the types of jobs they could get right out of high school. It also has them to find out how much living expenses would be and create a budget for living on their own. They also have to decide whether or not they will need a roommate in order to pay their bills. This is a research POW instead of a math or logic problem.

I gave the students a quiz on writing the equation given 2 points. One of the points was negative and one was positive. For this first quiz both slopes were integers. Out of 50 students who took the quiz 16 students aced it. another 3 students made between a 35 and a 39. 14 students made between a 24 and a 24 (a 24 is passing with a 60%). 17 made less than a 24. There were only 5 students who were absolutely clueless. So...67 % of my students passed the quiz. Now I have always said that having making a 60 in algebra does NOT mean that you are proficient. However, 38% of my students did extremely well on the quiz after working on this for 2 days. I wish I had this type of data for the first time I covered this topic in previous years. All I can do is tell you that my algebra grades in general were declining over the last 3 years (with the exception of last year when I started trying to find new teaching methods...even before the new IMP books). It was not unusual for my average quiz or test scores to be in the 40s or 50s. (My average score for this one was around 63.) I also feel like my students have a much better conceptual understanding of what we are doing. Several of the students who didn't perform well filled in their tables correctly and found the correct slope and had the coordinates for the y-intercept they just haven't gotten everything to connect just yet. However, I really think I can help them to get there! I intend to give them the opportunities to correct their quizzes so that they can see how close they are!

IMP Day 43 - Making "formal" connections

I have thoroughly enjoyed the Moving Along activity and decided to "sit down" here and make some formal connections to the slope formula and slope-intercept form. However, we first did the activity without using either formulas and it was AMAZING! We actually have been using slope-intercept form but they just didn't know it as y=mx+b. The IMP book uses y=ax+b and calls b the "starting point" and a the "rate of change."

Today I gave the class a "warm-up" where they were asked to find the slope of a line and write the equation of the line given 2 points. There was no context given and they did great! There were no formulas on the board but most of the students proceeded to put the 2 points in a table and then fill in the x-values from 0 to the highest x-value given. They go back to 0 for x because we have drilled the fact that x-coordinate of the starting point is always 0. We have also tried to drill that the starting point is always on the y-axis but they seem to forget that sometimes...

After the warm-up, which most of them got with a table, I had them add the slope formula and slope-intercept formula to their notes. I told them that they would receive a reference page on their end-of-course (EOC) algebra exam and that I wanted them to be familiar with the formulas. We went over how we could have used the formulas for the warm-up and then I gave them another problem.

I used this weird effect on my picture to make it a little more readable. 

He writes so light I know it is a little difficult to read. However, Raul (whose paper is above) was the first student finished finding the slope and equation of the line! Then I gave the class a problem where the slope was a fraction thinking that they would resort to using the formula (and most of them did). However, Raul and one other student STILL used the table to get the equation. Their "number sense" is very good and thinking in fractions (or decimals) did not bother those 2 a bit! We have only been writing equations of lines given 2 points for 2 days and there are many more students who do it correctly than I have seen in the past.

It is exciting to realize that there are students who really benefit from their exposure to the different methods that can be used to write equations. I guess that since I am so accustomed to using the formulas I thought they would automatically start using them. However, the majority of my students are still using tables! I don't think I have ever used a table to find the slope or y-intercept so I am getting an education too!

Math teachers are "Formula Babies" - we need to be more natural!!

My teaching buddy, Sonya New, and I are writing this post together! We have learned this week that we are FORMULA BABIES!! We ran across some problems where students need to write equations given 2 points and thought the students would just HAVE to have slope and point-slope formulas because that is how we learned to do it ourselves. BAHAHAHAHAHAHA!!

What an education we have received! I was so concerned about how they would find the "starting point" or y-intercept without formulas! Earlier this week Sonya's honors algebra realized that once they found the rate of change (slope) they could multiply the x coordinate by the slope and find the b (or starting point) by figuring out what to add or subtract to get y. I know that makes no sense when you read it! However, it took me and Sonya 2 WHOLE DAYS to realize that what they are doing is using the slope-intercept formula to solve for b. We felt STUPID!

ALSO, I had students to use tables to find rate of change and then extend the table "back" to zero to find the starting point or y-intercept. I had one student who hated the formulas yet got EVERY SINGLE PROBLEM correct using tables. Even problems with fractional slopes!! IT WAS AMAZING AND EYE-OPENING!!

Then we laughed about the fact that we are "formula babies" and have come to the conclusion that we need to understand that the logical (or NATURAL instead of FORMULA) way to write equations makes more sense to our students.

P.S. - Sonya is a new mother and I have had 3 breast-fed babies myself...so we couldn't resist the analogy.

IMP Day 42 - Moving Along - making connections!

The teacher's guide for Moving Along says that all algebra teachers love it because it has types of  problems that we are used to seeing. The students are given two points and asked to write the equation of the line. The interesting part of this assignment is seeing the different approaches that the students will take to solving it since we have not discussed the slope formula or the point-slope form of an equation.We have explored graphing through starting points, rate of change, and in-out tables. We have used slope-intercept form (without calling it that) by discussing that when the equation is y=ax + b that b is the starting point and a is the rate of change. The majority of my students write their equations in the form y=b + ax which seems more logical when we talk about b as the starting point.

I started class by assigning each group 2 of the 4 problems (everyone did #4). I gave them 10 minutes to brainstorm on how to approach the problem. The first group who got their equation explored the problem by using a table and finding the rate of change. The two points given in this problem were (0, 36) and (6, 24) so they remembered that the starting point had to be 36 because we had discussed for several days that the x-coordinate of the starting point is always 0. They realized the values for y went down by 2 each time and wrote the equation. One of the girls actually said, "I am getting good at this!" Here are their In-Out tables:

After the first 10 minutes I had the girls share with the class how they came to find their equation for #2. I took a graph from one of the students in a group that was working on #3 where the 2 points given were (2, 300) and (10, 196). He had graphed the 2 points and drawn a line through it which touched both the x and y axes. By looking at the graph the starting point was estimated to be 325. I gave the groups another 10 minutes to work. There was another group working on #3 and they were trying to build a table that worked with a starting point of 325. One of the students at that group blurted out, "I got the rate of change. It's 13." I directed the students to try that rate of change and adjust the starting point as needed and they found an equation that worked! I was surprised that the student's rate of change was correct. I went to the boy's side and asked how he found it. He had subtracted the y values and then divided the answer by the difference of the x values!!! Shazam! He used the slope formula and didn't even know it! The slope was actually -13 instead of 13 but he figured that out when he wrote his equation because the y values were getting smaller. I had him share with the class how he found the slope and then I went to the board and wrote the slope formula there. I asked them if they knew what it was and none of them remembered it from last year. I showed them how my students from previous years found the slope using the formula. I also showed them that if they "plug into" the formula correctly they would get the correct sign for the slope of the line. I was so excited at the connections that we were making to the "traditional" algebra. The majority of the groups came up with the correct equations...on the first day that we wrote equations given 2 points!!! I was amazed!

This is Hunter sharing how he found the rate of change using 2 points. He did an incredible job of figuring it out AND explaining it!

Lastly, #4 in this activity was the first situation/problem that we have encountered where the starting point is negative. The 2 points given were (3, 12) and (7,32). I had 2 different students to use a table to find that the rate of change is positive 5. I had to give them a prompt to help them to find the starting point. The students who figured out the rate of change had created tables that started with an input value of 3 and went up to 7. All I had to do was put a 2, 1, and 0 in the input column (I put them above the 3 to help them see the pattern) and asked them if they could continue the pattern to find the starting point. It ended up being -3. 

Now, my teaching buddy, Mrs. New, and I have been talking about whether or not teaching the formulas is important. AND...we still think that students need to be exposed to the "old-school" formulas and even practice some problems using the formulas. However...I think I had more students to get their equations correct given 2 points (on the 1st day!!!) than I ever have. The exploration and work that we have been doing over the last several weeks gives them such a firm conceptual understanding of writing equations by finding the starting point and rate of change that I believe the "old-school" work will have more meaning!!!  Mrs. New keeps asking me to consider whether or not the majority of our students remember how to use the formulas when they see these problems on standardized tests and my answer is NO... the majority do not remember! Now our students have a "hook" (as our instructional partner, Dr. Montgomery calls it) on which to hang that concept so that they will hopefully retain the information. They have also been shown how to use various approaches to examine and solve these problems.

IMP Day 41 - Travel on the Trail and Wagon Train Sketches

Yesterday Mrs. New informed me that I skipped a couple of activities in the book! I claim that it was "turkey-induced" mental lapse! I didn't realize that All Four, One had 2 parts in the book. I was about to skip 2 great activities so I'm glad she helped me realize!

Today I started class by having them read "About James Beckwourth." Once again I am reminded how this course is truly written to be cross-curricular. This unit really crosses more with history but I know that future units will cross with physics and English also! Today I gave them time to do do #1 and #2 in class with their groups. Then I had them to put the 2 graphs on chart paper. One thing I did that I liked was take 2 people out of each of the groups of 4 and let them work on answering #3 instead of standing and watching the others write on the chart paper. I always struggle with using the chart paper because 4 people can't really be working on it at the same time. Those who are idle often get in trouble. I liked giving them the idea of answering the next question. The downfall to this idea is that all of the students in the group don't get a chance to "struggle" with the problem before they see the solution explained. I ended up explaining how to do #3 anyway so I don't know that it was much of a loss. I led a student in the class through the discussion of #3 and I think it went well.

5th period -

Sometimes getting students to have meaningful conversations about an assignment is difficult!! Today my 5th period discussed the Wagon Train Sketches and Situations activity (that they had completed a while back when I was absent one day). Sometimes getting students to engage in the math feels like roping the wind!  (venting over!) Then, on the most difficult situation that they were asked to graph one of my most talkative students blows me away by just blurting out the correct answer. He is the only one in 3 classes to get that graph correct:) We do have some break through moments!!

IMP Day 40 - All Four, One and Straight-Line Reflections

Today we were trying to "get back into the swing of things" in algebra. The All Four, One activity asks students to consider the 4 representations of a linear function (situations, graphs, tables, and rules) and create a report on how to convert between one to the other. In the instructions the text gives a "common form" for writing a linear equation as f(x) = ax + b where a is the rate of change and b is the starting point. This description fits nicely with the way graphing has been introduced and developed over the past few weeks. I "borrowed" a worksheet from another IMP teacher that already had the scenarios written out (i.e. From situations to graph, from graphs to rules, etc...). I gave my students 35 minutes to work on the task. I had to help them do a couple before they were able to work in their groups.

I am trying to improve my students' presentation skills. Therefore today I told them that I was going to "roll the dice" to randomly call on at least one person in each group. That is nothing new. However, I made each student come to the document camera and show his/her answer instead of allowing them to talk from their desks. Then I talked them through correcting the answer if it didn't fully explain how to do the conversion. I told my classes that we were going to work on giving better presentations. I tried to move toward the back of the room so that students would at least appear to be addressing the class (Jim Delawder tip!). I did have a couple of students in my 3rd Block class laugh at other students. It worked out well because their groups hadn't gone yet and the boys who were laughing had to present instead of the random "roll of the dice." I hope this helps to get them to quit teasing each other during presentations.

The main thing I liked about this assignment was that students talked over and over about the importance of finding the starting point (which was always on the y-axis) and the rate of change. Today was another day that I loved that I had all kinds of graphs on chart paper hanging around the room to refer to.

I did not spend much time on Straight-Line Reflections. However, I did use Desmos on my Ipad and project the graph for #3. It is really cool how you can just pinch or expand the graph in Desmos so that it is easier to identify the y-intercept and the rate of change. As of right now we find rate of change by discussing the change in the graph over 1 x value. I am going to assign #4 from Straight-Line Reflections as a warm-up tomorrow.

My 5th period completed the If I Could See This Thing activity. It is interesting to see how many students could figure out the correct population (after the 90% decrease) but their explanations on paper were "train wrecks." Writing mathematical expressions correctly is a topic that is difficult for that class. I was excited because some students found the 90% and then subtracted from the original population and some found 10% of the original. It is cool when students come up with the different ways to complete the same task.

Reflections after 8 weeks of IMP

Areas for improvement:

• Getting students to present their work
• Getting through the lessons on time
• Managing vocabulary - stopping and explicitly teaching vocab after we have "had our hands" on a concept or idea
• Getting students to do their homework
• Ensuring all group members are working when given time to work individually or with their group
• Telling them too early whether or not they are correct
• Letting the students correct/critique each other

Areas I am making improvements:

• I'm taking students' pencils out of their hands much less
• I am recognizing that it is okay to let them put incorrect work on chart paper (this is hard for me) -  however, when I do this and I allow the students to discuss their "findings" the STUDENTS can critique and learn to analyze and discuss their ideas
• I am beginning to allow myself to divide assignments up where I assign a few problems to each group instead of having everyone do every problem. Picking and choosing the assignments is hard though. There are some that I want each student to have at least read and "struggled with"  before anyone starts sharing their solutions.
• Celebrating different approaches
• Giving a quiz that has depth but using a rubric so that success on the quiz is easier to achieve. I used to be scared to put too many "hard ones" on a quiz or test for fear that I would set the students up for failure. However, with our new curriculum every activity we do is based off a word problem within the context of the unit. I have found that my students are much more willing to attempt word problems now. The quiz I gave Friday had 2 multi-step word problems on it. That was it. These are types of problems that the students would skip if it were a 20 problem test and the other 18 were just computational. I made a rubric for the 2 problems and gave 5 points for each item (labeling axes, scaling axes, plotting points correctly, drawing the line of best fit correctly, generating the rule for the line, etc...).
• Trusting the curriculum...I must admit that this is more of a "forced" thing right now due to time. There are times I think about stopping and pulling out old tests or other standardized-test-like questions to see how the students will do on them. However, I don't have time since we started using the Meaningful Math books 7 weeks into the year. I do believe in the curriculum - more and more every day. I do think that my students have really engaged with the content and will have a much better shot at retaining the information because of the way it has been presented within the context and revisited several times. 
• I remember our Instructional Partner, Dr. Montgomery, telling me a few times in the past to create a project that covers several standards at once (when I was stressing about covering everything in the COS). Well, most of the activities in this book do that. Therefore, even though the activities are in depth and at first difficult to the students, they will have the opportunity to become "fluent" in them because they get opportunities to do the same type of activity multiple times. There may be a few tweaks to the activity but the topics are usually revisited. Especially the big ones. 
• I have often said that the 2 most important concepts I want my algebra students to be able to understand (and retain) is graphing and solving all types of equations. Well, as far as I can tell in our new standards these 2 topics should technically be mastered prior to entering algebra. My interpretation of the standards is that once in 9th grade they must learn to APPLY their knowledge of graphing and equations. WOW is that covered in these books! The majority of my students are not proficient at solving equations and graphing when they come to me but hopefully they will be stronger every year.

IMP Day...the math teacher in me makes me do this...39 - Quiz day

If any of you are reading this blog because you are teaching using the IMP books let me tell you about an awesome website that has great resources...The Greater Philadelphia Secondary Mathematics Project. Our trainer from It's About Time shared this website with us and it has some invaluable resources. I found some questions on there that I used for my quiz today on graphing. I only used two graphs but set up a rubric where they had a very good chance to pass (is that bad?) whether or not they could come up with the rule for the graph. I gave points for labeling the axes, scaling them correctly, plotting the points correctly, graphing the line of best fit, answering the question, and getting the rule. The 2nd problem gave the students a situation and they had to graph it, answer a question about it and give the rule.

I was really very pleased with the quizzes. Every student in the class can not get the rule for the graph yet, but they do SO much more with this word problem than I believe my previous students would ever have done. I hope to one day soon have the opportunity to find some multiple choice questions where students are given a graph and asked to find the equation that matches it and see how they do. We still have not "formally" learned slope-intercept form.

My 5th period did a Thanksgiving coordinate plane graphing activity today. It was the end of the day on Friday before Thanksgiving and I noticed as they worked on it that they NEEDED to review plotting points so I am glad we did it!

IMP Math Day 38 - Finishing Fort Hall Businesses and POW Write-up

Today my 2nd and 3rd blocks finished up Fort Hall Businesses. The neat thing about these questions was that the starting points were not given. The students are given a couple of data points in the situation itself and one of the problems gives the rate of change but the second one doesn't. It is so rewarding to see the students work through these problems and figure them out. The odd thing is that my 2nd block class solved the problems using graphs and my 3rd block class mainly used In-Out tables or just reasoned through them.

#2 had to do with a movie theater selling tickets and it gave the amount in the cash register after 20 tickets were sold and then after 60 tickets were sold. This one gave my 2nd block alot of trouble (they didn't have as much time to work on it either) so I asked them how many points does it take to draw a line. I then had a coordinate plane that one of the groups had labeled but hadn't put a scale to it yet or graphed any points...they were frozen. I had talked with all of the groups doing #2 and we pulled out 2 ordered pairs from the information that was given so during the class discussion I showed them that one method of solving the problem would be to simply graph the ordered pairs and draw the line containing them. From this info we could answer the question of how much money was in the cash register to begin with. Then I guided them to find the amount of each ticket (slope) and we were able to write the rule for the graph. They are taking a quiz tomorrow on graphing and I can't wait to see how they do. I am anxious yet optimistic!

My 5th block took a quiz yesterday and I gave them feedback on their papers without assigning grades. Today I went over a similar assignment from the book (again) and then gave them their quizzes (with the feedback) back and told them to make corrections based on the feedback. Understanding variables is a difficult concept for 9th graders for some reason. I expect to have to offer a quiz retake but maybe I won't!

I read another encouraging POW Write-up today. An excerpt is below:

IMP Day 37 - Following Families and Fort Hall Businesses

Today we finished Following Families by answering questions 3 and 4 and finding the rules. We defined slope (informally) and parallel lines. It was fun to see them realize that #3 had a point where the families were the same distance from the river because the lines intersected. Also, in #4 some of the students' explanations included comments about the starting points for the amount of coffee being different and then they consumed the coffee at the same rate. This opened us up to talking about rate of change being the slope. Today we also got to discuss that the "starting point" on the graph is where it crosses the y-axis and that value needs to be written down first when writing the rule. I hope they became better rule writers today!

My 5th period was supposed to go over Ox Expressions at Home and then take a quiz today. They were not quiet while we were going over Ox Expressions so I decided to cut the discussion short and make them start the quiz. However, I am going to give them written feedback on the quiz and give them the opportunity to address the feedback. I will not assign them grades until they turn them in the 2nd time. I actually used pg. 110 as the quiz. I read the intro on pg. 109 and discussed subscripts with them before they started the quiz so that wouldn't throw them off.

I'm Calling Bullcrap! - Adventures in teaching IMP

Sonya New is my hero! I'm just saying... If it were not for Sonya I would not be the teacher I am today. She makes me want to be a better teacher. She makes me think! UGH! AND...she cracks me up sometimes.

Yesterday we were looking over some of the Meaningful Math Algebra lessons that we were going to be teaching the next few days. She had her honors algebra students complete the Who Will Make It activity for homework and she told me that they had asked if they could use a "squiggly line" between zero and the first output value so they didn't have to label all of the values in between. She told them no. However, when we were discussing it she said she wished she had let some of them go ahead and do it so that they would be able to talk about the inaccurate conclusions that would be drawn. She decided to do a graph with the "squiggly" and talk to them about it. Her graph is below:

The context of the story is to see who will make it to Green River before the flood that is predicted (by the almanac) to happen in 30 days. The y-axis is distance to the river and as you can see all 3 of her families make it to the river (the x-axis) way before 30 days. After discussing the class's answers she put her answer under the document camera and told the class that she had all of her families to make it before the flood. She said at first they were starting to erase their answers...they assumed she was right and they were wrong. However, she had one girl yell out, "I'm calling bullcrap!" and run up to the board to point at her "squiggly line" to say that Sonya's answer was wrong. I loved this story. I have told Sonya over and over again I wish she would blog about her personal "imp adventure" so that I could read all about it. We talk almost every day but we don't always have alot of time to go into detail. I told her I just had to tell this story. I loved that a student ran from the back of the room to prove that Sonya was wrong and she was right.

P.S. - I hope nobody is offended by the title...it is a renaming of a popular card game that has to do with calling someone's bluff when you think they are not telling the truth about their cards.

IMP Day 36 - Following Families on the Trail

With today's activity we venture from using discrete (nonlinear) data and finding the line of best fit to being given a starting point and a constant rate (average miles traveled per day or amount of coffee drank per day). The students were asked to graph the information and then answer some questions about the graphs. Lastly they were asked to write the rule for the graph.

These pictures are in reverse order to what they needed to be. We started the activity with "noticing and wondering" about the problem. I am trying to teach the students to "notice and wonder" about the parts of the problem that help them perform the mathematical task...we sometimes get sidetracked!

I was so excited to hear one of my students say, "I'm going to make me an In-Out table!" so I had to take a picture of her paper! The teaching guide for this lesson tells you to go ahead and tell the students to let July 12th as Day 0. I still have students that use the x-axis as a "data point" instead of letting it be zero. Many of them counted by 25s or 50s today and wrote 25 or 50 at the origin. Also I still had some students that didn't use consistent spacing. I sometimes wonder how many times we have to practice something for it to sink in! I am giving a quiz on Friday so I hope my students remember by then!

My 5th period students finished Ox Expressions and started Ox Expressions at Home. All of my classes were given an assignment to complete for homework and I am assigning a grade for it tomorrow. Lately I have only had 1 or 2 per class (of 20-28) attempt to complete any homework tasks. And I am not asking for them to do something that should take more than 15-20 minutes! I hope the grade motivates them to actually attempt the work. We shall see.

IMP Day 35 - The Basic Student Budget

Today was a neat lesson because the students were asked to "break away" from the Overland Trail theme and consider using lines of best fit to analyze data considering the budgets of 3 college students who share an apartment.

Common mistakes today:
1. "connecting the dots" instead of drawing a line of best fit
2. not extending the lines of best fit to touch the x and y axes...even though one of their data points was (0, $ that each student had at the beginning of the month)!!
3. Scaling their axes incorrectly - by this I mean one "box" was 100 and then later on they spread 100 over 2 boxes
4. When answering #3 several of the students looked at how much money the guys were projected to have on April 21st instead of how much extra they had on April 30th.
5. One student started all of her lines at some random starting point on the y-axis because her group had Who Will Make It last week and all of the families started 330 miles away from the Green River...

I got frustrated today because I expected a higher percentage of the students to "get it" since we have been working on similar types of problems for 2 or 3 days now. I was disappointed to see students connecting the dots and not extending their lines to the axes. I felt like I had done such a better job covering this because of the experiences they have already had with "lines of best fit." I also need help on reacting better when my students are way off the mark. I am so good sometimes...and then other times I know they can see it all over my face and hear it in my voice that I am frustrated... This is my confession day I guess!

On a positive note...I had some students that flew through the activity and had a very good conceptual understanding of what was going on! The rules were difficult for everyone but we went over them today and I know that we will continue to work on writing rules and equations as we go.

**It is good to use chart paper and leave some of the graphs hanging up in the room. I still had several graphs from Previous Travelers hanging up in the room so we used them to compare the graphs that start from the origin with those that don't (like in The Basic Student Budget).

My 5th period today did Vermillion Crossing in class and I introduced Ox Expressions and assigned it as a bonus for the student with the most meaningful algebraic expressions.