Friday, October 29, 2010

Connections

As a part of the Algebra 4 All State-wide project, myself and the other Algebra teachers at my school were asked to do a particular lesson with our classes and have another teacher observe the "math talk" aspects of our class. Being that we use Carnegie in our classrooms our students are used to working in groups and to helping one another. The fact that they helped each other and worked well in their groups was no surprise. However, they still managed to amaze me today!

I should start by explaining the project. My students were given a scenario about three college students who have created a budget. They all get paid on the first of the month and have to pay their rent on the last day of the month. My students were given a table showing three dates and the amount of money each student had left. They were asked to create a graph and then determine who could pay their rent. I didn't think my students would have difficulty with this part. We recently completed 1.10 Comparing US Shirts and Hot Shirts and they were familiar with graphing multiple scenarios on the same graph.

The hardest part of the problem was for students to write "a rule" to describe each student's spending. My students have not formally been introduced to slope or slope intercept form so I wasn't sure that they would be able to do it. When my first group of students were ready to try it I told them to think about the problems they had seen on the cognitive tutor. They remembered the problems with scenarios about companies that started with a set amount of money and were spending a particular amount each week. From that discussion, they decided that they needed to start their equation with the amount of money each student had and eventually they realized they needed to find out how much money each student was spending in one day. Without me telling them how to do it, several of my students were able to find the slope (although they didn't call it that)! I was so excited.

This made me realize that my students really are learning more than I realized by working on the Cognitive Tutor. I have to continue to make those connections more obvious by talking about them in class. Today's project was not from the Carnegie book or the Cognitive Tutor. However, students were able to take what they had learned (without any formal instruction on it) and apply it to a new situation. I was so elated that the teacher that was observing and I were giving each other high fives throughout the class. What an awesome way to end the week!

Friday, October 22, 2010

Co-Teaching (with a twist)

My school has made drastic changes to our schedule to try to help students achieve in both Math and English. One of the things we did last year was create a block schedule. Students at my school only take 4 classes a semester. All math and English classes still meet for an entire year for 90 minute periods everyday! All other courses meet everyday but only last for a quarter or a semester. This has really allowed me to spend time helping students truly understand the mathematics that I am teaching. A lot of teachers were nervous about teaching for 90 minute periods, but the structure of the Carnegie lessons has made it a breeze for me!

Another change we made was something we call math enrichment. Each math teacher has one period a day where they co-teach with another regular education math teacher. The two teachers can choose to use any of the co-teaching methods that they are comfortable with. The math enrichment teacher has a list of targeted students that he or she focuses on, but really ends up helping all students. Sometimes we split students into flexible groups and work in separate classrooms and other times she just walks around helping students that have questions. It is so nice to have another person in the room that can help students when they get stuck!

Unfortunately we do not have enough teachers for everyone to have a co-teacher each hour and even the hour I do have a co-teacher she does not come everyday. We have made a flexible schedule and teachers go to a specific place each day unless specifically asked to help out in another area. It's nice to know that if I need someone to help out with a particular project or activity all we have to do is adjust the math enrichment schedule.

Wednesday, October 20, 2010

My First Encounter with Cognitive Tutor

A topic close to my heart that I have yet to write about on this blog is Cognitive Tutor. I have especially felt compelled to write about Cognitive Tutor in the past two weeks. At the same time the thought of tackling such a task has been daunting and overwhelming. What subtopic(s) should I cover? What angle or perspective should I take? What do followers want to read about? How do I convey my excitement for this program without sounding like a desperate, cheesy salesman?

About three years ago I found myself dissatisfied with the current curriculum I was using in my pre-algebra classes. It’s not a bad curriculum. It is an on-going, ever-changing, multi-year collaboration of all the 8th grade math teachers in my district, thoughtful and well-planned out. Many people put in a lot of hours, sweat and tears putting this curriculum together, myself included. It simply did not meet the needs of the lowest 5% of my students. I was bothered by the fact that I did not send these students off to high school adequately prepared for Algebra I. I felt personally responsible for setting these students up for failure. (Today I blend that old curriculum with Carnegie’s, picking and choosing parts and pieces that have been successful with my students.)

To make a long story not too long, Sami was brought in to introduce Carnegie Learning and Cognitive Tutor to our high school math department. Middle school math teachers were invited, mainly because we taught Algebra I in 8th grade, but there was no initial intention of using Carnegie Learning at the middle school level. At the time, I was under the impression that my district viewed Carnegie Learning more as an intervention program than a mainstream curriculum.

Cognitive Tutor is an online software program that uses artificial intelligence-like model that customizes in real time a student’s plan based on his/her performance. In a nutshell, no two students will experience identical sequence of problems. The more competencies a student can demonstrate on a particular math concept, the fewer number of problems s/he has to solve before advancing to the next unit. I have been waiting my whole life for a program like Cognitive Tutor!

At the end of that school year, I approached Becky about the idea of me using Cognitive Tutor in my own classroom. To my pleasant surprise she thought it was a fabulous idea. Despite all the lows and highs, it has been one of the best decisions in my professional career.

There is so much more I can say, but I should probably save them for another day. Thanks for checking in.

Saturday, October 16, 2010

Grading

One of the things I've struggled with the past few year of using Carnegie is how to grade the lab. I know that this is a very sensitive subject with a lot of teachers. Each seems to have their own way and will argue to the death to defend why it is the best.

This summer when I was working with a group of teachers at initial implementation training they wanted me to tell them the "right" way of grading the lab. Some of them had been using Carnegie before and they were convinced that since I was a trainer I must know the correct answer. I explained to them that each teacher has to find what works for them and showed them the various examples from the implementation handbook.

I've always struggled with how to grade when students are supposed to be working at their own pace. In the past I looked at how many skills students mastered in a section and how their progress compared to the other students in my class. Then I decided to start adding time on the tutor to their grade. This seemed to work better for me but did not seem to motivate my students to stay on task in the lab. My students did not seem to progress quickly enough and even my best students ended the year in section 20 - 25 (only about 1/2 through the software).

This year I decided to use a modified version of the grading rubric that Kasey Bratcher has posted in the resource center (and is also available in the initial implementation guide). The rubric takes into account student behavior, time, problems completed and progression through the software. I love that students are being held responsible for their behavior and it seems to be motivating my students to work harder in the lab. I also like that students who are not progressing as quickly can still score well as long as their behavior and time on task are appropriate. While I've still be playing with the number of problems students are required to complete and the number of sections that need to be completed this has greatly improved my ability to give a grade that reflects what the student is doing in the lab. I also like that the rubric can be shown to parents to explain how their grade is calculated and I hope that eventually I can train my students to grade themselves.

While this grading method might not work for everyone it has been working for me. Thanks Kasey for sharing your expertise!

Sunday, October 10, 2010

Kool-Aid and Skittles

Sure, kids of all ages would live on Kool-Aid and Skittles if we let them, but I am not here to argue the merits of either side. I’ll leave that to the experts – the dietitians, the General Surgeon, and the FDA. However, I did find that Kool-Aid and Skittles are an excellent way to kick-start my proportional reasoning unit. My goal was to create an activity that would allow my algebra students to experience ratios. What better way to capture their attention than with food?

Many times, students are simply taught a textbook definition of ratios, and then are given examples that really only exist in the world of mathematical word problems. I’m as guilty as the next person for keeping this math concept so distant and unfamiliar. I tried something different this year. I don’t know why I hadn’t thought of it before now!

Tapping on their prior knowledge, I had students list all that they knew or remembered about ratios. We then as a class compared ratios and fractions, mainly to dust away cobwebs and to rectify any misunderstandings. After the students gave their informal definitions of ‘ratios’ we looked at a textbook’s formal definition.

Here’s when the fun began. I had prepared two batches of Kool-Aid: one with the normal amount of sugar, and one with noticeably less.

“I’m going to place cups of Kool-Aid and a bowl of Skittles on your table,” I announced to the class, setting one cup of each Kool-Aid types in front of the student and a bowl of Skittles on each table. The response I received was one of happiness and joy.

“Here are your instructions. Take a drink from each of your two cups. Talk to your group about what you notice. As a table, write down five observations. You must use the word ratio in each of your observations.”

As I walked around and eavesdropped on conversations, I was delighted to witness all the math discourse that was going on. There were some tough negotiations about what exactly constituted as a legitimate observation, however for the most part, the chatting was light-hearted. At one point, Mrs. Scott, the science teacher across the hallway, came over to borrow something and was “upset” that she hadn’t been invited to the party!

“OK, for the second part, look at your bowl of Skittles. Your table will write down five other observations and again use the word ratio in each of your sentences.”

As the students got to work, some wanted to dump all the Skittles out onto their tables to count them so that they give precise ratios, which I didn’t allow them to do. I clarified my instructions by saying, “Make general observations without using numbers or trying to be exact.”

“Are we allowed to eat the candy once we’re done?” they all wanted to know.

“Sorry! The minimally-nutritious-food police would be after me,” I joked, wink-wink.

“Ahhhh”, my students caught on, playing along.

After everyone was done, we came back together as a class to share some of the observations. Students grappled to pick just the right words to describe their experiences. The observation we all got the most laughs out of was “Jerry’s” use of the words tangy-ness and more tangy to describe the Kool-Aid that had half the amount of sugar.

I was pleased to see that one table grouped colors together while keeping all the candies in the bowl. This made their job of making observations clearer and easier.

Keep in mind that this was only the intro to the day’s lesson. And it took less than seven minutes!

The way to a teenager’s brain is through his/her stomach. An old Chinese proverb – if it’s not, it should be.

Friday, October 8, 2010

Gallery Walk

This is my 3rd year using the Carnegie Curriculum. At my initial implementation training I completed a poster project for one of the problems and participated in a gallery walk to view others posters once they were completed.

In my haste to move through the curriculum I never took the time to actually have my students do the gallery walk. They created posters which I always displayed in class, but I'm not sure how much the other students ever really looked at them. There really was a lack of closure to the entire project.

As I mentioned before I'm part of a state wide project called Algebra for All. The project reminded me that students should be evaluating each others ideas. Inspired by attending the workshop I had my students create posters for 1.8 and 1.9 from the Algebra 1 text. It took a few days, but they really turned out great (I plan to post photos soon but forgot my camera at home today :( ). Today each group placed their posters on their tables. I had the groups move around the room getting 1.5 minutes to look at each poster. Not only did students have to look at the posters but they also had to write 1 thing they liked about the poster and 1 way that the poster was different than their own on a sticky note. Each group left a different colored note on each poster and once they finished the groups had a chance to look at the comments their peers left for them.

This lead to a great discussion of the two problem scenarios. We talked about how the problems from 1.8 and 1.9 were different and how they were the same. Students commented about differences in the equations, tables, and graphs. This discussion led us right into the 1.10 lesson where the two scenarios are compared. I now realized that although it did take some time, the gallery walk was a great way to spark conversation and a great way for students to take pride in their own work.

The posters are now displayed in my classroom for all to see. I plan on trying out different variations of this activity through out the year hopefully it wil continue to lead to great class discussions.

Thursday, October 7, 2010

Picture Algebra

One of my absolutely favorite lessons in Carnegie’s Bridge to Algebra is Picture Algebra. This has not always been the case. It is the opening lesson to the solving equations unit. I have to admit that last year Melissa and I were totally baffled to why Carnegie would start a unit with a lesson like Picture Algebra, so “foreign and complicated.” The sequence of lessons did not seem logical. Why weren’t we starting the students with learning the skill of solving one-step equations, leading up to two-step equations, and finally ending with word problems? There were many nights of teeth gnashing and hair pulling from teachers, students, and parents!

I remember thinking and telling Melissa, “Carnegie must have a good reason. We must have faith and trust them. I am sure they know what they’re doing, I hope.”

Now it all makes sense! Thank goodness.

Apparently if you give students a hypothetical situation (aka word problems) to begin a unit, students can use prior knowledge and experiences to help themselves work through the problem. The new math skills and concepts make more sense if worked concurrently with a real-life application. Duh!

In Picture Algebra, students draw diagrams to represent the situation. They then use these diagrams to solve the problem and answer the question(s) as well as come up with an equation. In other words, application leads to algorithm, instead of the reverse practice that most of us experienced in a math classroom.

Give Picture Algebra a chance. Like anything new, different, or requires some thinking, Picture Algebra will receive resistance from many students. Repeated exposure will help the students feel more comfortable. I had half a dozen or so students show up this afternoon for tutorials to get help on Picture Algebra. It warmed my heart that these students cared enough to take the initiative to seek the extra help. In addition, they seemed to enjoy each other’s company as they worked through the problems together. “Frank,” who came in lost and clueless, caught on the quickest this afternoon and was given the charge of guiding the other students. He took on the responsibility with great pride. I couldn’t have asked for a better tutorials session.

Tuesday, October 5, 2010

Out of the Mouths of Babes

I had to share this story! It's a humorous anecdote that happened in my classroom yesterday.

I was starting a unit on solving equations and was reviewing inverse operations.

Teacher, "What is the inverse, or opposite, operation of add?"

Students in unison, "Subtract."

Teacher, "Subtract?"

Students in unison, "Add."

Teacher, "Multiply?"

Students in unison, "Divide."

Teacher, "Divide?"

Students in unison, "Multiply."

Teacher, "How about to square a number?"

Dead silence. I saw a lot of clueless stares across the room. "Danny" then looked towards me, as though he had something to contribute.

I prompted, "Danny?'

In all seriousness, he hesitantly offered, "Circles?"

Needless to say, we all, including Danny, had a good laugh!


Saturday, October 2, 2010

Seeing Stars

How do you motivate your students to keep progressing through the Carnegie Cognitive Tutor? My class is structured so that we go into the lab for one ninety minute periods and one 45 minute period a week. Ninety minutes can be a long time especially if students are not motivated to work.

One thing I do is keep a poster that tracks students’ progress in the lab. The poster lists each student in my class by student number (to keep confidentiality) along the side and lists the unit numbers across the top. Each time a student finishes a unit (and sees stars on their screen) they can go up to the poster and put a star sticker by their number. This helps students to visually see where they are in relation to their classmates and helps motivate them to keep going. It also encourages students to work on the tutor at home to catch up to their peers. At the beginning of each lab I ask students who have completed a unit at home to come up and get their stars. This little piece of recognition is exciting for them.

Now I know what you're thinking.... this would never work with my students. But I think it will. I teach 9th grade and my students love the stars. When I run out or forget to bring them to the lab they get really upset. I won't lie and say that this works for all students. Some of them could honestly care less about the stars and I end up putting their stickers up for them. But this simple poster (which can be purchased at any teacher supply store) and some dollar store stickers has helped me to motivate a lot of my students.