2+2 != Maths

April 14, 2012

What do you mean I don’t need a formula?

Filed under: standards based grading,teaching — Numbat @ 14:16
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I have had a very hard time introducing concepts based assessment (aka standards based grading) to my Year 11 General Maths class this year. I have always tried to teach concepts and so assessing this way was a very good fit. I’ve also tried to emulate some of Dan Meyer’s “be less helpful” ideas. To say it’s been a tough task would be an understatement.

My students are all invested in “formula, formula, formula” and copying worked examples from “cheat sheets” onto test papers – these tasks they can do, but ask them to actually think about something, anything, and they run for the hills.

Imagine my pure joy, then, when during marking of my most recent concepts test I came across the following.  Here is a student who is complaining about having no notes, no formula and yet they were able to think the problem through and get the correct answer (albeit with the wrong units)

If only more of my students would actually engage their brains and take a chance to apply some of their knowledge to their work.

Contrast the above to this second student who has clearly found the right formula and put the numbers into the correct spot, but can’t use a calculator properly or recognise that the answer the calculator has given them is totally wrong.  This is a student with very little understanding of the question or of the concept.  A “formula” driven student who has probably experienced some success in the past but is totally out of sorts when asked something outside their comfort zone.

Clearly the first student has a better understanding of the concept and the processes involved, and I would like to think that if a few more students in this class could make the same effort then they would start to see Maths in a different light.

Unfortunately, many of my students would rather expend their efforts attempting to get me to “teach them real Maths”.


P.S.  I must admit to having a chuckle over this student’s comment about the photocopier. 🙂


March 31, 2012

Maths and my Lathe License

Filed under: standards based grading,teaching — Numbat @ 19:57
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When I was in Year 9 or 10 (I can’t remember which) I studied a year of Fitting and Machining. This was the “big leagues” at my school where we were ushered into a room with many grand looking machines and the smell of machine oil permeated everything.

Before we were allowed to even go near the lathes – the ultimate tool in that particular shed – we were all required to get our lathe license. This consisted of being able to name all 108 parts of the lathe as identified by our teacher. Our teacher handed out mimeographed sheets similar to the one shown here, although luckily the ones we received had each part numbered with all 108 names listed in order as well.

The “test” consisted of a sheet with a diagram of a lathe, with all 108 parts numbered, and we were required to write in the name of the part in the numbered lines below. A few of us got together and set about “memorising” the 108 names, in order. We managed to devise a pattern, almost a song, consisting of those 108 names. It wasn’t easy, but after quite a bit of “study”, we managed to memorise all 108 names. Come test time, we regurgitated those names, in order, in writing, and “passed” with flying colors.

Not a single one of us could identify any part of the lathe by sight or by function. All we had managed to do was to learn the words of the “lathe song”, very much like the words to our favorite songs of the time or of the national anthem. If our teacher had walked up to a lathe, pointed to a part and asked us to name it we would have been exposed as the frauds we were, but he didn’t, we had our lathe licenses and were allowed to use the machines.

The parallel between my lathe license and the way that many students are taught or learn Maths has become more and more evident to me this past year. Many students learn a “mantra” for each question. They follow a sequence of steps from start to finish never really understanding what they are doing. They reach a conclusion which they neither understand nor could repeat if the question were presented to them in a slightly different manner.

On twitter recently there was a bit of discussion about how students say they like Math, but what they really like is the fact that they can memorise a procedure and regurgitate that without having to think. I am beginning to realise that many of my students have not been asked to think in Math class too often.

This year in my concept tests I have disallowed worked examples. I am getting huge resistance from my Year 11 students in particular, many of whom have been bought up on being allowed to bring their notebooks into their tests. At parent teacher interviews the other evening I had one particular student announce to both myself and her parents that of course she knew the work and had learned it, but could only “do it” if she had a worked example in front of her. She was quite serious in demanding that I allow her to bring worked examples into tests. Luckily for me, I was able to convince her parents (and hopefully, eventually the student herself) that all she had managed to learn was how to translate a worked example into a test question by substituting the test values. In essence, she has learned her “lathe song” and will quite happily repeat it when requested.

This year it is my intention to actively prevent students from learning “lathe songs”. Hopefully I can get them to actually learn the concept and in doing so get them to engage their brains a little more frequently. It’s hard, time consuming and the students don’t appreciate the efforts yet. Hopefully one day they will.

What about others? Are your students learning “lathe songs” or are they learning Maths?

February 22, 2012

SBG from the Trenches

Filed under: standards based grading — Numbat @ 20:51
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So I’m full swing into my first year of SBG, it’s the third week of the year and I’ve managed two concept tests with two of my classes and have the other class scheduled for their second test shortly.

I am finding that the younger students (Year 7 and 8) seem ok with it (perhaps they haven’t been too heavily indoctrinated into the alternative) but my Year 11 class is very resistant. I am trying new things in the classroom as well to align my classroom practice with SBG and this is also causing me some grief. It seems that these students (Year 11 General Maths) are even less comfortable with change than some of the staff.

On the subject of the staff, overall I think that SBG has been received well. There are those who see it as a whole lot of work for no reason (thankfully in the minority) but mostly the staff see it as a positive and other staff are reporting their students are happier with the idea.

The biggest issue my Year 11’s have is that I’m not interested in the “yard of work”. They want me to tell them do Ex 3B Questions 1 to 7 left hand side. This is what they’re used to, they will then have something to aim for and they will have pages of worked questions (or hastily copied answers) to which they can point and say “Look, I’ve done my work” (or not as the case may be).

I am reaching for something more than squiggles on pages. I’m telling them “Look, do a couple of questions, if they’re easy and you understand them then skip to the harder stuff. If you’ve got this concept nailed, go back to those concepts you don’t understand and brush up on those.”.

Perhaps I’m aiming too high, but at the moment giving the students this freedom to work at their own pace and set their own goals is too far removed from the norm for them that they simply can’t cope.

Hopefully this will change soon.


December 19, 2011

Our first attempt at SBG

Filed under: classroom,teaching — Numbat @ 16:01
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I make this post with some trepidation. Opening up our first attempts at converting to SBG is a little daunting. How will others react? Are we on the right track or have we completely gone bananas?

A few months ago I blogged about how I’d presented SBG to my Maths staff and how they’d started to think about and adopt the ideas in a small way. Since then we’ve been making some progress and have spent many hours going over our existing “work related” courses and coming up with a list of concepts.

We still have a ways to go but we have mostly finished the concepts list for our Year 7 course and would like comments from those of you who have been down this road previously. Please be gentle – this is our first attempt and I know that we have much to improve upon.

My own thoughts are that we have too many concepts, but I’m not really sure how to condense them any further. I think I’ll figure out some of that throughout next year but perhaps others can help.

So, without further ado, here is our list of Year 7 Concepts for 2012. Please make comments below.


September 6, 2011

SBG takes little steps

Filed under: teaching — Numbat @ 17:33
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A few weeks ago I stood up at the Maths staff meeting and made my pitch.  “This is SBG,” I told them, “I think it’s the way we should be heading.”  Overall I thought the session went as well as can be expected when someone they don’t usually associate with “change” gets up and tells them we all need to change the way we’re doing things.

Since then there has been some progress.  A few of the staff are starting to introduce smaller concept type tests.  While not truly SBG concept tests, they have trialled shorter more frequent tests with the same concepts being repeated.  And in almost every case they’ve found that the students are responding.  The students are engaging with these tests, they’re attempting more questions and are investing in their performance.  Some students are even staying back and making up time to improve their results.

While this may not be news to many who have implemented this previously, it is certainly a surprise that such a small shift toward SBG can produce such a significant change in attitude. Whether this is just a fad that the students will tire of or whether they will have the stamina to last a whole year only time will tell, but the initial signs are good.

What is also very interesting is that some of the teachers who have made the switch, and perhaps seen the biggest response, are those who I would not have considered the “strong” teachers.  This begs the question whether an SBG based approach may help some teachers more than others?

The last thing I’d like to comment on today is that we’ve now had two sessions working on creating the concepts list.  There have been many interesting and very useful discussions on how we generate our final list and how many concepts we need.  Some teachers have even remarked how we might reasonably need a large number of concepts to accurately identify a years worth of Math instruction….

I haven’t had the heart to point out the irony in those statements.  As it stands, our “concept list” is 10 items long.  It starts with  Chapter 4 Number Patterns; Chapter 3 Lines and Angles; and ends with Chapter 13 Maps, Coordinates and Directions.  If nothing else this work has caused the staff to think about exactly what concepts we’re teaching our students and to put those concepts into greater perspective than just Chapters 1, 5, 9.


August 17, 2011

Just what is my job after all?

Filed under: teaching — Numbat @ 20:12
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I presented Standards Based Grading to my colleagues in the Maths department yesterday.  I was pleasantly surprised by the reception as I was expecting a very cold one but found quite a few of them nodding their heads in agreement at stages.

I was also surprised by the questions being asked.  Thoughtful questions which indicated that they’d accepted the premise and were asking about implementation.  That probably surprised me the most.

However, I was still struck by some of the firmly held beliefs of many of my colleagues.

In particular, I made a statement that I was no longer concerned by what a student had DONE, but rather I was very interested in what a student KNEW.  This differentiation appeared to be lost on most of the staff.  Having come from a background where the “yard of work” was the main focus of the entire department and the measuring stick we drummed into our students, I suppose I shouldn’t be too surprised.

In times past our “curriculum” consisted of a detailed list of questions that the students were required to complete. I suppose the theory was that if the students completed all that work then they must have learned something, right?  Unfortunately the answer was more than often, WRONG!

As I have explored implementing SBG I have come to realise that what a student DOES is perhaps irrelevant.  It’s what a student learns or knows that is relevant.  So now I need to unlearn all those skills I’ve developed that allow me to make a student DO something, and learn a whole new set of skills that will allow me to make a student LEARN something.


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