Things to work on.

Two things that I hope to work on during summer school this year include talking less and addressing students in private.

Teacher talk is the bane of many a young teacher's existed. I have improved quite a bit over the course of the year, but I still think that my tendency to talk through issues is a major weak point of my teaching. Those who know me know that I believe 98% of all teaching issues come back to planning. Talking less in class will allow me to start more quickly and put more ownership on my students. It will also require me to plan for and structure longer practice sessions and lots of opportunities for troubleshooting and peer correcting.

As for addressing students... it has been important for me this year to become very comfortable confronting students, making examples and calling them out with confidence. However, I believe that my management is strong enough now to take it to the next level. My authority is clear, I don't need to set examples. Just as I 've developed good habits around nipping things in the bud,  I would like to start addressing unwanted behaviors almost exclusively with individual conversations instead of calling them out infront of the class.

Tuesday = Test day?

The recent spate of snow days twisted up my curriculum in such a way that I ended up with two unit test falling on Tuesdays instead of Fridays.  Amidst all of the things I hated about the missed days  (loss of more than a week, canceled after school detention, lazy lazy students)-- this turned out to be my silver lining. Tuesday test are a godsend. Here’s why.

Let’s pretend for the moment that I have only my students’ best interests at heart, and start with why Tuesday tests are good for them.

1) Focus. The kids need monday to get the weekend kinks out, and especially in math -they need to get back into the language. By Wednesday they remember that really the only reason they come to school is to socialize. Thursday comes before Friday and on Friday they are checked out. A test or quiz in every class leaves many of my struggling learners bubbling in at random. In my limited experience tuesday is when they put their best foot forward.

2) Remediation. Giving a test on Tuesday means that the kids still have the material fresh in their minds and care about the grade on Wednesday when you hand it back (I realize this is easier for those of us who give multiple choices tests....). Handing back the test on Wednesday allows me to require/offer tutoring after school thursday for students who failed and to then do a partial retest on friday- still while the material and sense of grade urgency is relatively fresh.

3) Long term retention. You might reasonably fear that testing on tuesday will increase the disastrous effects of the weekend memory wipe. Yes. Sigh. I hear you. But if we are willing to challenge ourselves a bit... as teachers we really should aim higher than ‘process and regurgitate.’ Long term retention is ultimately what will serve them best. Testing on tuesday increases the pressure on us to be teaching our students to internalize the material  and not just cram for tests. (Also a disclaimer: Testing on Tuesday doesn’t mean that monday is a “review’ day-- I usually choose one easy last topic to present- something that will incorporate earlier material but isn’t just “review” which inevitably seems to be a synonym for “I don’t have to work hard today.”) 

So when do you quiz? Fridays. Definitely. The kids are checked out on friday and the discipline of sitting and working independently for high stakes is one of the few ways to make the time productive. (If you haven’t seen it this recent article from the NYT discusses research suggesting that the act of taking a test/quiz is one of the best ways to practice/retain information). At the same time, by quizzing instead of testing on fridays the grade is weighted slightly less.... and... if your quizzes are open note, open response as mine are-- this gives you the weekend to grade.

...which brings us to the benefits from the teacher’s point of view... 

1) Flexibility of curriculum. As a young teacher I often find that the material I want to cover on a particular topic doesn’t fit neatly into a 2 week unit. This leaves me with an unpleasant decision: do I cut it short? or do I let my unit length vary with the material. Either way is less than ideal. Cutting it short inevitably means shoddy teaching or brushing things under the rug which will likely come back to bite later. However, letting unit length vary too much risks loosing a sense of rigor and pace -- not to mention the benefits that students derive from predictable, frequent assessment.  By testing on tuesday I have the option of an extra 3 days if I realize late into the unit that the kids really need more time... and then a logical start to the new unit on the following monday. On the flip side if 2 weeks works fine then starting something new on a Wednesday is still pretty feasible. 

2) Beat the Sunday-Monday Blues. This is the big one for me. The weekend is never as productive as I want it to be. Inevitably sunday night sees a big pile of “oh i guess i’ll grade that later” and “well, they really don’t need more grades this week.” Try as I might my saturday morning ‘sketch for the week’ almost never turns into hard and fast materials for more than Monday and Tuesday. Then, to make matters worse, Mondays are always 2x more exhausting than I expect- like walking into a wall. By testing on Tuesday, your tuesday lesson plan is instantly done AND requires no prep on monday night. Thus, I can use monday afternoon to 1) finish the grading that I had wanted to finish on Sunday 2) Make materials for the rest of the week or 3) go to bed at 8pm. I found these past two weeks, that the knowledge that tuesday was going to be an easy day of proctoring and review games helped me be more excited about planning the rest of the week.

And so I rest my case with an apology for a mundane post... although in some ways these practical discoveries are just as true to this experience as any of my more theoretical musings.

Looking back, looking forward. (Content Methods Reflection)

For this week’s blog I’d actually like to reflect on the first “creative teaching strategy” that I tried out-- way back at the end of September. At the time I considered it a total failure-- for reasons that I will explain shortly.  I return to the experience now because I’ve been thinking a lot about unit planning recently, and this early experience changed the way I use so-called ‘creative activities.

Ideally a unit plan should maximize content delivery, provide a lot of independent practice, attract and retain student interest, provide easily graded and logical assessment points... etc, etc, etc and the list goes on. The activities in that we’ve been practicing in our Content Methods class are a great way to get student interest and independent practice. However in general, they don’t for direct-instruction -- that is to say these activities are great for a 2nd day work period or a review lesson before a quiz but not always appropriate for the first instance where students are practicing a certain type of problem.

I learned this lesson the hard way. Our second full unit this year in Transitions was on polynomials and we started with a week of exponent rules practice. On wednesday of that week I could tell students were getting a bit restless with the notes and practice routine so I decided to shake it up and try the matching activity that Dani modeled for us in an early lesson. Her version had us sorting through stacks of colored cards creating piles that match a function table to its equation and graph. In mine, students had to match an exponent rules problem (eg. x^2 * x^3) to its expansion (x*x * x *x *x) and the relevant rule (multiply bases = add exponents).

Making the cards was quite a bit more time consuming than I expected-- mostly because of the cutting and assembling piles with the appropriate assortment of cards. I was happy with the product. In class however, everything that could go wrong did. To start with, my instructions were ineffective. I did have written instructions on the board that explained what each color card was and what each pile would look like in the end. The difficulty was that the kids didn’t know where to start and they quickly became rowdy and off-task.

In retrospect I think that the trouble was because 1) I didn’t adequately model the thinking process that they could use to assemble a pile and 2) they were not strong enough with the background skills (simplifying exponential expressions and writing the expansion of an exponential expression) to have the sort of recognitions that would help them see how different cards belonged together. I probably could have solved this had we done some straight forward simplifying practice before trying the activity. 

To return to the question of unit planning and the appropriate placement for ‘creative teaching strategies’ the struggle is to have time to provide a strong enough foundation and practice before  the activity. It’s as if for any given topic you need a day for instruction and then a whole additional day for the activity... but than I always feel pressured to simply move on to the next subject. I hope to continue to use creative activities but only after we have already learned and practiced the skills in a straightforward manner. 

Chapter 3 Reflection (Content Literacy)

Chapter 3 of our Literacy textbook is dedicated to an examination of the term “comprehension.” The text reveals the naiveté in thinking that ‘comprehension’ is a simple matter of ‘ just understanding what is written’ and unpacks the many layers and indicators of comprehension as they apply to content area instruction. In particular the text reveals comprehension as the combination of decoding literal meaning of words and sentences, identifying the context of information conveyed through the written medium and processing and applying this informations. In the book’s more succinct, though also more ambiguous words “ Comprehension of print and other forms of text is a   meaning-making and  meaning-using process” (RAND reading study group as quoted in text p 45)

I am reminded of a story I heard my first night in Mississippi. Some second year teachers were sharing inclusion teacher horror stories. One described sending a struggling resource kid to take a reading test in the inclusion room only to have the inclusion teacher return later in the day saying “I don’t know what the problem is because when I read the test to him M----- does fine!” At this point the gen. ed teachers all laugh a little helplessly, knowing as we do that yes, if our students could just read they would be fine-- both on reading tests and i suspect in content areas. 

What the inclusion teacher meant to explain, I think, is that she had identified the student’s problem as one of decoding and not of comprehension. The student could not make meaning out of the symbols on the page, however if given that meaning the student could use that meaning to apply and analyze information contained in and implied by the text.

As a content area teacher I think that it is important to be cognizant of this distinction but    I am also challenged to know what to do with this information. In this example, yes it is very important for the teacher to know that the student’s ability to analyze/summarize the text would earn him a passing grade... but at the end of the day if the only situations in life and school that the student would be required to perform such analysis also require that he read the passage in the first place... well, then, how do we grade the kid? Based on our privileged knowledge/believe in his partial abilities and in the complex factors which explain(though not excuse) his poor literacy...? or by the same standards that a job application would hold?

Luckily, as a math teacher I can minimize the impact of poor decoding skills on my students; performance on assessments. However, comprehension is still a hugely important and relevant skill. The textbook discusses a number of strategies for building textbook reading skills (eg. bridging text ideas, mapping strategies, charts, opinionaires). Since I rely very little on the textbook these strategies interest me less. However, the discussions about developing a language of process through justifying content statements and group strategies like reciprocal teaching were of great interest.

As I have mentioned in previous blogs I believe that the main forum for literacy strategies in my high school math classroom is in the way that I employ “steps” to teach problem solving strategies. For each new topic that I introduce, one of the early lessons will be devoted to taking notes on key vocabulary and steps that describe a systematic approach to tackling this particular problem. For more complicated subjects we may spend up to two weeks getting to know the same steps or adding on new steps to the same sequence. To conclude this post I would like to briefly re-examine the use of explicit written “steps” in light of the text’s structural analysis of comprehension-- namely that it may be divided into 4 dimensions: 1) Cognitive, 2) Textual, 3) Personal, 4) Social.

1. The Textual Dimension to Using Explicit Written Steps in Algebra Instruction.

This is the simple one. The “textual structure” of my steps are always the same: numerically ordered steps in the form of direct imperatives sometimes with sub-bullets that describe different cases or outcomes. We acknowledge this structure in practice by reading and checking off the steps as we work through a problem.

1. The Cognitive Dimension to Using Explicit Written Steps in Algebra Instruction.

One of the challenges from the teachers’ perspective in writing the steps is to find a balance between detail, clarity and brevity. If the steps are too long, then students are reluctant to use and internalize them. However, if the steps are really short there is more work to be done to ensure that students correct interpret the written reminder. Our textbook discusses the ‘cognitive’ dimentson of comprehension as drawing together the students skills and background knowledge. To increase the effectiveness of “short steps” we can rely on words that may not have the exact mathematical meaning, but which we know are familiar to the students and convey a memorable concept. (eg. in dividing fractions instead of saying to “exchange the numerator and denominator” we just say “flip.”

1. The Personal Dimension to Using Explicit Written Steps in Algebra Instruction.

A key piece to using steps is to have the student themselves reading and speaking the steps aloud- both using the language of the generic instruction ( eg. “next we have to flip the fraction”) and in application to a particular problem (eg. “that means instead of 2/3 write 3/2”). To make this process more personal, and perhaps as a way to tackle the challenge described in section 2 would be to have students use their own words to articulate the steps as they think of them.

1. The Social Dimension to Using Explicit Written Steps in Algebra Instruction.

Ultimately my goal in using steps is to get student to think of math as a problem solving process and not just a race to the answers. Thus the goal is for students to be able to help themselves and their peers by giving hints and instructions instead of just giving away the answer. This social process both reinforces their mathematical knowledge and is a huge motivator/ ego-boost.

Chapter 4 Reflection (Content Literacy)

As a math teacher I have struggled to find an appropriate integration of our literacy strategies in my classroom. It’s not that I disagree that improving literacy is my responsibility-- not at all-- rather I struggle to fit literacy in when a) there is so little time and so much math to begin with and b) for many of my students my “in” is the little wedge of confidence that they have in the one class where low reading skills don’t immediately single them out--- well not as much that is.

Coming from this perspective I appreciated how widely applicable most of this chapter is. “The goal of literacy assessment” the authors write  is to encourage students to become “reflective, active, and purposeful learners.” This could just as well be the goal of any other type of assessment or educational strategy.

In taking this ‘goal’ literally I am slowly developing a niche for reading/writing in my classroom routines: namely, I am trying to make a habit of asking students to read out and write out steps and justifications of their thinking process and problem solving strategies. Not only is this just a general good practice, but I believe it has the dual benefit of 1) bolstering students with strong verbal skills and 2) challenging students who may already know what to do mathematically but not how to explain their own knowledge.

I was particularly interested by this chapters’ discussion of strategies to involve students in the assessment process. I love the idea of having students give input into the creation of rubrics. However I disagree that this type of engagement relieves teacher workload-- if anything it seems like facilitating this type of ‘mature’ student involvement would take a lot a lot of advance thought and planning. As a teacher I really struggle to draw out reflection or self-criticism on the part of my students.

A related struggle that stretches across discipline with implications for literacy is the challenge of getting students to use their own notes effectively. Of course in order for this to be possible their notes must be ‘usable’ i.e. ‘legible’ in the first place. However even those students who copy clearly must be explicitly taught how to look back and find answers to their own questions. It is a habit of self-reliance that sometimes seems impossible to build up in students with low confidence and low motivation... a crucial life skill that should be the goal of education in any discipline, but which in some ways seems more elusive that the most baffling phonics or factoring. 

Points of Comparison (Content Methods Reflection)

My green-book planner was great fun in the first months of school. “Function wheels” is scribbled in along a margin in mid-September between “Functions Test” and “start Unit -III.” There was, theoretically a 30min gap to fill. Needless to say, by the time that day rolled around between make-up work and management battles and piles of paperwork “function wheels” didn’t actually happen. 

Mock-teaching this activity the following saturday for our Content Methods Class then was bittersweet. I hate it that the few times I’ve tried creative activities have become management disasters; but I am also invigorated by the reminder that there are creative ways to represent material and engage students’ abstract thinking... something to aspire to.

Basically the activity was to build a manipulative that was the math-equivalent of a function table. We cut concentric circles of colored card stock and attached them in the center with a paper clip. We wrote input values around the outside circle and cut windows in the top disc so that the window would show the corresponding output as we rotate the outer circle.

In the ‘protected’ setting management was fine. Clear directions were super important. I’m glad that I had pre-copied the circles and also that I had students do the cutting instead of spending that time myself. In a larger class I probably would have a harder time walking around to check that people were folding and cutting correctly but that might be helped if I found a way to get students helping each other or have a visual of different stages of the assembly process.

Two strengths of the activity I think were that the “wheel” draws out the distinction between dependent and independent variable, and the “output windows” helped me to clarify f(x)-notation ( during my ‘traditional’ lesson this was a major point of confusion... the idea that f(x) isn’t itself an expression but rather the ‘name’ for an expression and which simultaneously represents an output). At the same time, I wonder about the pay-off of spending a whole 20 minutes on what really amounts to a single function table’s worth of calculations. Still, I could envision extending the activity to have partners composing their functions which I think would be powerful conceptually. I look forward to modifying the activity to try when I introduce functions in Transitional Algebra.