The Practice Predicament (Part 2)

I followed through with my goal of differentiating for more in-class practice for students.  It was nothing too extreme.  One day the warm-up problems were based off of the previous day's lesson (for example factoring x^2 +bx+c).  Students who were able to show proficiency from the warm-up problems were given a worksheet immediately.  They could ignore the rest of my teaching and begin working or they could listen and work once the rest of the students got to work.  It was up to them.  Either way I would not be able to provide assistance as I was still working with the rest of the class.  (I let them listen to music while they worked, and they always get excited for that.)

With the students who had not shown proficiency from the warm-up problems went through them with me.  Different students had been able to factor different ones, so together we made it through all four and restated some hints along the way.  At this point I gave them a few more to do independently and put a star on their paper if they could now show proficiency.  Those students received an intermediate assignment (from the textbook in this case) and began working.  I moved students who still had not shown proficiency to the back of the room and worked on a beginning assignment with them.  This was a guided reteaching worksheet from the textbook.  Most of my energy for the remainder of the class period needed to be focused on these students.

Oh I forgot to say how I introduced this idea...I shared a "new plan" with students the day before that would include "less homework" which excited them (even though I rarely assigned more that 5 problems/night and none the whole month leading up to this...).  I clarified that this was an important part of our learning and students who were not willing to work in-class would be sent to the office and would work with me after school in the form of a detention.  I also clarified that my goal was to reach all students where they were.  Sometimes it might be embarrassing if you are beginning, but the goal is to get you to proficient, and then it wouldn't be embarrassing anymore.  I also reminded students that the same people are not always going to be advanced; I'm basing it off of what I see.

Random Thoughts:

• I am not capable of creating 3 assignments from scratch at 3 levels for each concept that students need to practice.  I wish I was, but I do not have enough time.  So you can see that I relied heavily on the textbook and its resources.  In this case it was a smooth alignment because it was a "traditional" Algebra 1 concept.  However, my textbook is not fully aligned to the Common Core, so there will likely be times when I will have to create 3 assignments (but maybe not from scratch) at 3 levels.
• I did not like making the lowest students get up and move to the back, because I think it was still a little bit embarrassing for them.  I still think it's better than making them come to the front of the room. Perhaps if we had been doing this all year it would be less embarrassing.  Perhaps there is something else I could try that would be less embarrassing...still thinking.
• I need to consider students with an IEP and how they would best fit into this.  They are able to leave the classroom to work with an associate, however I want them to have some understanding before that happens.  Is this fair to them?
• There were almost equal students in each group in some classes.  Others had more beginning than intermediate.  What are good amounts to have in each?  I would think that intermediate should be the largest group, what are ways that I can quickly help students who did not demonstrate proficiency at the beginning of class be able to demonstrate proficiency?  Maybe working through examples is not best?  
• Perhaps if I had been doing this throughout the year not as many students would be beginning.  Some students who really don't struggle with learning the Algebra, but struggle with the motivation to do the Algebra, were in the beginning group.  Maybe they thought they could get out of doing work???  But I think if they would see that the beginning group is sometimes more work they would show proficiency earlier.
• I posted all answer keys on my bulletin board and made students check their own work during this time.  I did not spend any class time going through answers the next day.  I'm trying to teach them to be responsible for their own learning in that way.
• It was a little bit frustrating that so much of my attention was focusing on the beginning students.  There were other students who had questions, and I felt like I wasn't able to do them justice because of needing to push those beginning students. Once again, perhaps if I had been doing this throughout the year not as many students would be beginning.  And then I could meet all students needs better.
• During this time I had almost no behavior issues.  There was one (out of 85 all day) student who showed intermediate level of proficiency and then didn't get much of the practice problems done.  I didn't notice soon enough because I was so focused on the beginning students.  That was about it.
• I also had one student who "showed" advance proficiency by copying (I think) and really thought he was ready for the advanced assignment.  He got almost none of it done and score extremely low on that target on assessments.  I likely should have "manned" up and just told him no.
• It ended up that usually students who were absent the day before were in the beginning group.  Not sure if this is OK or if I should address them in another way.

I did have a student directly thank me for doing this.  Other students offhandedly mentioned that it was better, but this student directly approached me after class and thanked me for doing this.  He said that it really meant a lot to him because he knew it took more work for me.  I count that as a win, at least for now.

Day 4: Cancelled

Our Day 4 was cancelled due to snow :(  I was extremely disappointed.
Also they didn't notify us in time for me to make it to school on time (I lived closer to the training than school).

The Practice Predicament

So as promised, I am going to share my new teacher predicament between practice and understanding.

Last year I taught with curriculum that was based off of the idea that practice could lead to understanding.  The philosophy was that following an algorithm for how to solve a problem repeatedly would somehow reveal to a student why the algorithm worked.  One thing I know is that this does not work!  It is not fair for us to expect students to gain understanding when all we show them is a process.

However, not all practice is bad.  Students who have developed understanding often need practice in order to develop the skills to use the mathematics independently.  This should occur alongside opportunities to strengthen understanding.

My struggle is finding the appropriate balance of practice for students.  I find that often I actually stray on the side of too little (just basing this off of what I see on assessments after I feel like I have helped students develop a strong understanding).  Here are some problems I have had with getting students the right amount of practice:

• If it is an out-of-class assignment, many students do not complete/start it
• If it is in-class, not all students need the same amount of practice, so major differentiating needs to occur.  I struggle with differentiating appropriately as at different times different students are at different levels.
• If it is in-class, independent practice leads to more push back from some students, causing me to have to address many behavior issues all day long.  Perhaps this is because I do not differentiate enough or because I have not stated my expectations clearly enough.  Many reasons for this, but whatever the cause, it is a challenge for me.
• It is valuable to practice recall of the mathematics, so all learning cannot occur at one time.  Students who are on top of the learning one day in class may come back the next day and feel totally clueless.  The idea of working through recalling learning is super important for students.  I feel it is harder to address this when all practice is done in class.

Thinking through all of this, I have decided that a good next step is to work on differentiating for in-class time to practice independently.  I will have to state my plan clearly to students ahead of time, so that they understand I am not doing this to select favorites, but to help all students learn.  Hopefully this can be helpful in finding an appropriate balance.  I will let you know how it goes.

Multiplying Polynomials

As part of our homework for the challenge, we were supposed to try to increase the rigor of an upcoming lesson using the practice standard we had selected as a district to work on implementing more effectively.  We had chosen practice standard #1:  "Make sense of problems and persevere in solving them."

When they gave us that assignment I said to the people at my table, "I'm multiplying polynomials next week, how am I going to do this?"  So I brainstormed the whole way home, and I had a pretty good idea, but I decided to create the UbD template for the standard.  (Any feedback on what I have come up with would be welcomed as I am very much still struggling with knowledge vs. understanding and other things necessary for breaking down the standards.)  The standard is:  Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.  Unfortunately, with they way that the common core has ramped up our curriculum, it is unlikely I will be able to dive into the "analogous system" part of the standard as much as I would like :( But maybe next year...

After working on what the standard says, I did an internet search (using websites I know of that have CC aligned assessment) for ideas for this standard, but I came up short, so I decided to run with my idea and see how it went.  I used this chart to guide students through a repeated process of individual, small group, class discussions on a variety of multiplication scenarios that slowly increased in difficulty.  After going through each pair as a class, I assigned each small group another similar problem.  They were to process as a group and present to the class.   It took the good part of a week to make it through the chart, and it is still a steep stair between a monomial multiplied by a binomial and a binomial multiplied by a binomial.  I had the students complete a survey of several internet sites in order to see three methods of representing the multiplication of polynomials (vertical, distributive, and grid).  

Overall, I believe the process was productive for them.  I was able to quickly address misconceptions that arose with the entire class (a common one was that (x)(x) = x rather than x^2 which lead to the phrase "ninja one" which was much more successful than I would have ever thought) and give them more opportunities to practice.  (I still gave practice problems for students to work on individually, but I post an answer key also so they can check as they go.  I have struggled a lot with finding an appropriate balance in beginning mathematics (Algebra) between practicing too little and too much, but I will save all those thoughts for another time.)  I also thought that it lead to some of the best mathematical conversations that the students had ever had in my classroom.  I heard them discussing exponents, coefficients, and terms! Oh my!

Day 3

We had Day 3 of this project and we got to present right at the beginning of the day (Well after a Kid President video--he's hard to follow!).  We shared the key points of our action plan...almost like what I posted previously, but not the "why?" part.  I figured that part would be better to share verbally if the conversation went that way.

But I have to admit I was totally wrong in my assumption that people wanted to know why.  Most teachers are totally on board with the plan.  They want to see it happen, they just need help figuring out the logistics.  What was best about presenting was all the questions that came from this.  Everyone is trying to figure out how to make it work and so not all of the questions were addressed to us, some of them were addressed to others, too.  And that helped us realize some of the things we still have to figure out.  What great collaboration!

For the rest of the morning we split into groups:  Math teachers, Special Education teachers, and AEA staff. As Math teachers we continued our work to unpack standards in Unit 1 and find appropriate assessments.  We were working with 1-2 other teachers on a standard of our choice.  I worked with a teacher I had never talked to before, and we picked a standard she had worked on previously.  I felt as though it was much more productive this time.  She and I communicated well together, and I was able to be a little bit more flexible about the whole process.  I tried to avoid the things that had stressed me out too much previously.  We made some progress and we will continue to work on Unit 1 and maybe Unit 0 next time.  I hope that we can get the first part of the year planned prior to the beginning of the school year!

In the afternoon we discussed standards based grading in a little bit more detail.  This is one area that I feel like I have a good start to because of our school's PD, but there are lots of flaws that we need to work through.  I felt like the conversation we had around this were good, but I feel pressure to iron out the flaws prior to next school year.  I have to put my grading plan in my syllabus, and I want to have something fair figured out the communicate to students and parents.  This is a big challenge that I discussed with some of the AEA people.  They understand and also want to work to find a solution for us, however not all participants are going to fully jump into this shift next year, so it is going to be challenging to meet the needs of all the schools/teachers represented.

To conclude our day we got to be students in the lesson DVR Dilemma from Yummy Math.  The purpose was to get us to think through the practice standard that we are working on improving.  We have been challenged to work to improve our teaching strategies to better address this for our lesson plans in the upcoming week.  I will be working on teaching students to multiply polynomials...it's really hard for me to think about how to use this to help students "Make sense of problems and persevere in solving them."  But I've been thinking about it a lot after that challenge...maybe I will post again about what I decide to do and how it goes.  Going to be a big risk!

Presenting our Plan

We were asked to present our plan for implementing instruction at three levels at our Day 3 meeting.  Not sure why us or what part of it most people are interested in, but we met after school today to look over our plan again and discuss our presentation.

There are two main aspects of the plan:  assigning students and scheduling classes.  I will give some highlights of each below.

Assigning students to the Tier II and Tier III courses:

• Students who have addition math instruction as a requirement of their IEP will receive Tier III instruction
• Students will be identified for intervention (Tier II) using a variety of sources:  Algebra Aptitude Test, IA Assessments, Previous Course Grade, Teacher Recommendation.  We will likely choose a cut off for each of these and then flag students who are on the list for 3 of the 4 identifiers.  This may include IEP and non-IEP students.
• Our principal, the math team, the special education instructor, and AEA representatives will all participate in selection process
• Currently we have no official universal screen or progress monitoring in place

Scheduling, Planning, and Instructing Tier II and Tier III:

• We are on a 7-period day, with 51-minute class periods (and a 17 minute homeroom)
• As the Algebra teacher, I will give up all my non-Algebra classes next year (currently consisting of 2 periods each day) to provide tier II instruction.  So I will teach 4 periods of universal instruction and 2 periods of intervention.
• I have requested that the tier II classes be schedule at the beginning/end of the day so that all students in the class will have had same universal instruction
• My dropped courses will be taken on my the 2 other mathematics teachers we have by increasing enrollment in advanced classes and no longer offering Pre-Algebra
• Tier III will be given to students during their Guided Studies time.  It will mean of their 51 minutes of GS, 30 minutes each day will be Algebra instruction given by the Special Education instructor
• I will be planning (with the help of all my peers in this project) the universal, tier II, and tier III instruction
• We have requested 1 day each week to collaborate on the instruction for tier III students
• Students will receive elective credit for tier II and tier III algebra.  Will be unable to shift in and out of course as needed (not seen as a potential problem).
• We have a special education associate who will be able to facilitate instruction during universal, tier II, and/or tier III

Why?  I honestly think that is what some people want to know.  "Why are we willing to go to all these lengths to provide something like this?"  I would have to say because I can see that my students need it.  I have many students in Algebra currently that I desperately wish I could provide this opportunity to.  I see the need and I address as good as I can, but without the additional time and the smaller class sizes I cannot do all that is necessary.  

These are the ideas we are going to try to get across within our 10-minute time frame, as well as providing an opportunity for others to ask questions.  I hope this will help others find a way to make this successful in their schools as well.

Day 2

Our second meeting (also known as "Day 2") was packed full of thought-intensive analysis of multiple things. We started by discussing "Understanding by Design" lesson planning, where focus begins with the desired result.  There are 3 stages of this planning method:  the Desired Results, the Assessment Evidence, and the Learning Plan.  This process can be challenging because only after a long time looking at the standards and choosing an assessment method can the instruction planning actually begin.  As teachers it is hard to wait so long to plan instruction!

After discussing this method, we broke into groups and began unpacking various standards from Unit 1 of Algebra 1 as defined by Appendix A of the CCSS with this template to guide us.  This is really challenging!  At first we were supposed to base it off of our professional understanding of the standard (which is not always clear), and discuss our understandings.  Then we could look to some other documents, but there are few resources available from the authors of the CCSS to help us unpack them.  We spent all morning doing this!  It felt very unproductive to me for two reasons.  First, because we were working in groups with people we didn't know very well, and so it was hard to respectfully critique each others' ideas.  And secondly, because we did not define "understanding" and "knowledge" prior to getting started.  All in all a challenging morning for me.

We were actually supposed to do one more thing before lunch.  Choose one of the practice standards to focus on for the rest of the year--yikes!  I remember hearing someone say that the first four are the most important, so we chose to go with #1:  Make sense of problems and persevere in solving them.  Then we had the opportunity to change the rubric for it.  The rubric we were given was not structured the way I like to have rubrics structured, so I redesigned it with the help of my coworkers present at the meeting.

After lunch we created a proposal for how our district should implement Tier II of the instruction.  We had already had quite a few conversations with our principal and other math teachers in our district, so I felt as though the proposal was just formalizing all of those conversations.  The goal/plan is for me to teach only Algebra next year.  Four periods of Algebra (tier I) and two periods of Strategies (tier II), while a special education teacher would teach the students receiving tier III instruction during their guided studies time.  My hope is that I can have the "strategies" courses at the beginning/end of the day, so that the students have had the same instruction from the Algebra class.

Once we completed that, we discussed the benefits of standards based grading.  My district is already in the process of developing standards based grading, so we have an idea of what it is, what it might look like, the benefits, and the drawbacks.  However I still found this conversation to be very rewarding.  I jumped into standards based grading this year without all the background work that teachers in my district have done, so it was good for me to step back and remember why they chose to move in this direction.

The last thing we did is to split off as Algebra teachers (special education teachers did something else) and look through 7th and 8th grade standards that we might have to teach during the transition to the common core.  These are the standards that are necessary to meet the Algebra standards, and may not get mastered in 7th and 8th grade.  I think it was important to acknowledge that it is a transition to the common core, because at times I feel pushed to move my students over to it too quickly.  It is important to get there, but we also have to remember that we are in a transition time.

So when I left Day 2, my brain was working in many different directions, but I felt that all were beneficial for the future of our students and their mathematical learning.  I sometimes just wish that it didn't take so much work, but in the end it really does.  In which case it is important to remember the purpose--student learning!