A Geometry Class is Born (Part II)

So what actually happened in The Class that Nobody Wanted?

Encouraged by how intrigued the students were by the Illustrative Mathematics composite figures task on the first day, I decided to continue with the activity the following day, allowing the students to self-select groups.  I created a worksheet to give them more workspace, and brought in the group whiteboards – always a hit.  I also invited my colleague and mentor into the room for suggestions and feedback.   When the students came in, I distributed the worksheets, went over the formulas for area, perimeter and circumference that they would need, and instructed them to select one of the shapes to work on as a group.

UntitledThe level of engagement in the room was complete and palpable.  Because the composites were squares and circles, because the length of each square was a friendly unit of one, and probably because there were no variables or exponents, the task was not intimidating to the students.  Many of them went right for the blue shape, which, to me, was one of the more challenging figures.    They began to debate the correct method for finding the area.  The whiteboards were a great tool for visualizing how the shapes overlapped, and even students who were uncomfortable contributing mathematically could participate in the sketching.  (Markers always  make it better. ALWAYS.)  There were also 3 adults in the room, which was enormously helpful – gently guiding the work, answering and asking questions, and observing the interactions.   The students worked steadily until the bell rang – everyone (myself included) was so absorbed that we ran out of time for sharing.

I met with my mentor later, and through our discussion realized that the challenge for me was to keep these students motivated with accessible, engaging and respectful tasks.  But I also knew that there was a wide range of ability, as well as a range of goals among the students.  There were seniors who needed one final math credit, and  juniors who were on track and wanted to take the Geometry Regents exam.  There were also students who might have previously been in a more quickly paced class, but failed a semester for a number of reasons – attendance, teenage distraction – and were moved into this slower track.  And finally, there were students who were very weak mathematically, who had been pushed through many classes without retaining much.

So I am faced with the task of managing this class effectively, with the end goal of imparting some mathematical learning and appreciation to these students, while simultaneously demonstrating to the administration that this cohort could and should learn geometry.  I need to show my principal that the assumption that these students were not capable of (or would ever need) the abstraction required by the content was not only an erroneous, but also an objectionable assumption by so-called educators.

The following day I brought the iPads into the classroom, having designed (or so I thought) an interactive review on angle pairs based on this blog post by Amy Zimmer.  The app I intended to use (Educreations) didn’t work out quite as planned, so we used the iPads as digital whiteboards as I quizzed the class on sketching angle pairs.  The students were working in pairs (we don’t have a full class set of iPads), which kept things lively.  Again, high engagement, instantaneous assessment and feedback, and some fun.

On Friday, I knew I needed some hard data on the ability of each student.  So I planned a ‘Quickie Assessment’ such photo (5)as the one I read about in Steve Leinwand’s Accessible Mathematics.  I planned on beginning the class with a six question quiz, beginning with a friendly occasion and working up to a problem involving parallelograms, and then spending the balance of the class exploring the Taco Cart problem.  As my mother would have said, “WRONG!”  After the first equation, many students needed guidance and encouragement.   Some students could barely work through the two-step equation, while others zipped through all the problems, and began working on a more course-appropriate review worksheet.  It took 25 minutes for the whole class to go through the six questions.  We collected the papers, but the students wanted to review the problems immediately.  My co-teacher took the lead while I moved around the room, checking in with some of the kids.

I reviewed the results of our assessment, and they painted a daunting picture.  The class is split into 4 levels, as I see it.  There are students who are on track conceptually, who have landed in this class because of a personal screw-up in a previous course, who need to be not only challenged, but prepared for the Geometry Regents on which they can clearly do well.  Next in readiness level is a group of students who, with preparation and hard work on both of our parts, can also complete the course at a Regents level, and hopefully move on to Algebra 2 next year.   The less accomplished students fall into two categories – a group which can do a modicum of geometry, and a group which was, to be honest, lost on Friday from almost the get-go.  Most of the class falls somewhere in the middle (naturally) – a real bell curve of a situation.  But the difference in current mathematical ability between the high and low ends is huge.  This weekend, as I tried to wrap my brain around what I could do to address everyone’s needs, I imagined myself stretching (literally, across the classroom) so I could work with several different students at once.

So after a weekend of thinking, pacing, asking for advice, and consuming mass quantities of Ritz crackers, I have come up with the following plan:  The class will be split into 4 groups which reflect the aforementioned stages of ability.  On three days a week, my co-teacher and I will teach two lessons on the same topic, but at levels which are appropriate for the higher and lower ends of understanding.  Luckily, the classroom is a long one, with a SmartBoard at the front and blackboards across the back wall.  Everyone will be working on the same topic, but practicing the skills at a level from which they can reasonably improve.  Two days a week we will work heterogeneously – one day on a group task, and the other – well, I am still trying to envision that fifth day each week.

I am going to introduce this re-organization of the class tomorrow, and I will be explicit about the rationale behind this plan.  We will do an exercise on Mindset, and I will explain to the students that the goal is that each student gets what they NEED right now, and that each will be assessed and evaluated on the progress they make from where they are RIGHT NOW.   The intention is that everyone moves forward mathematically, and that each student has individual learning goals.  My hope is that they will appreciate the assumption that they can all learn math (I do not believe they have always been treated that way), and that they will be taught in a way that addresses their specific needs.  My co-teacher is on board, and we have set up a schedule of weekly meetings with each other in order to execute what feels like a very ambitious plan to me.

At the end of class on Friday, I took one student aside – a senior who started out being very social, but by the end of the week, was focused [successfully] on tackling the geometry problems.  I told him I was impressed with his work, and that he should definitely take the Regents exam in June.  He looked puzzled and said, “Really, Miss? But I don’t need it.” (Students only need one math Regents – usually Algebra 1 – to get a NYS High School Diploma.)   I said to him, “You are intelligent, and you can do this work, and you should challenge yourself academically.”  He just looked at me for a minute, and then said thoughtfully, “Thank you, Miss.  I’ll think about that.”

I have to make this plan succeed, because I am fairly certain this hasn’t been said to this boy before, and that thought makes me want to cry.  But instead, I will teach.



  1. mrdardy

    A couple of quick thoughts
    1) Good on you for that last conversation. We need to go out of our way to let students know that we are on their side AND that they are capable of more than they might be asking of themselves.
    2) That’s quite a handful of tasks you have set out for yourself. 4 distinct levels of kids to plan for? Is there any logical way to either (a) streamline the prepping to cast wider nets out for these kiddos or (b) set up some groups with representative kids from multiple levels so that they can help each other out regularly? I just wonder whether the class might start to feel fractured after awhile.
    3) Thanks for the link to the Illustrative math activities. Some lovely stuff there!

    • Wendy Menard

      Thanks, as always, for reading. I am not planning on 4 different lessons, but rather 2. They will be on the same topic, but modified to include either more basic skills attention or more challenge. Remember I have a co-teacher who will do some of that work, although I am the lead math teacher. I definitely don’t want the class to fracture and am on the lookout continuously for activities that will work across multiple levels. And the students will definitely be working in heterogeneous groups on those problem-solving days. I know it’s a lot to bite off, but I also know that if I don’t do something along these lines, I will lose the attention of a lot of students, not get nearly enough of them prepped for the Regents, and probably have serious attendance and/or classroom management issues. Now I just have to plan the next 70-something days!

      Thanks again for your thoughtful comments.

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