Grade 9 math - Part Deux - Improving Retention through Spiraling and Descriptive Feedback

Every year I complain to myself quietly about two things:  1)  lack of retention and 2) kids at this school only care about marks, and not about learning.

Yes, yes, I know - at least they care about something.  I am lucky to be at a school where they care about school, whether it's extrinsically about marks or intrinsically about learning.

However, these are two problems that I would like to solve.

Retention

Quite often, what I taught in September was entirely forgotten about by the time January came; I saw this in some of my 9 academic/11 university-preparation students who did their homework everyday.  For 9 applied students who are less likely to do their homework, retention would become a bigger  issue in my class.  I looked around online and found that some people were also trying to solve the problem of lack of retention through designing the curriculum in a spiral.  Unlike the linear curriculum that I still prefer to implement for my academic/university prep students (maybe it will change), this style of curriculum allows my applied students to see math concepts a couple times repeated throughout the semester, sometimes in a different light  or through a different problem.  The hope was that by seeing the concepts repeated tweaked in a slightly different way after a few times with weeks separated in between, retention would increase.

Learning vs Attaining Marks

This year, while I am still spiraling, it led to the use of descriptive feedback only.  I had a discussion a couple of years ago with a colleague at Trudeau about a situation where if a student scored better on their exam than their term mark, I should consider making their final mark their exam mark.  Their argument was that if a student can demonstrate their learning by the end of the course, it doesn't matter that they couldn't do it in September.  I still am not fully convinced, as I believe that throughout the term there are other pieces like "thinking" or "communication" which are more fairly evaluated when there is more time than a 1.5 hour exam.  However, the colleague still had a key point that I could not shake off - the learning cycle ends with an exam and if students can demonstrate their knowledge and understanding by that time, that should be all that matters.   

Quite often when my students receive a their test, they always look at the mark first before any descriptive feedback.  While the majority of my students react to the actual mark first, there are fewer students that can get past that initial reaction to read the descriptive feedback and actually learn. This makes sense for a student because the test is a natural end and judgement to the learning cycle of a unit or a spiral.

So, I decided to try descriptive feedback only for the first half of the semester to extend the learning cycle.  This emphasizes to them that the first 1 or 2 spirals through the curriculum would be about learning only.  As a result, the principal and the superintendent have given me permission to give "I" as opposed to any marks on the report card for my students for both the interim and midterm report cards.  This has given its own sets of problems as my students really want to know how they're doing in terms of a mark.  I am trying to emphasize to them that learning as much as you can is all that you should be worried about at this time.

I just want to leave you with this final quote from my student.  The context was this - it was September when I was having trouble convincing my own students that there wouldn't be any marks.  There was a general consensus among the twenty of them that they would actually want marks just to know where they are.  I was about to lose them when one of my students said: "I get it now...school becomes more about learning than it is about passing."  All the students had an 'aha' moment given to them from another student.  It was one of the more impressive 'aha' moments I have witnessed in my 10 year career...and I wasn't the source of it.  What's more interesting, is that this 'aha' moment was more rewarding than any other.  

Iterations Improving the Proficiency of my 3-Act Math Delivery

NOTE:  This is a late post - supposed to have been published last month but I've only recently found time (during exams) to post it.

For today's lesson, we turned to Dan Meyer’s video question on which cup contained more juice.  Here's my powerpoint that goes with it:  

It is a splendid 3-act problem that inspired some interesting questions.  However, the quality of their questions has decreased since September; the questions had more depth, and their observations keen.  Now, they are just giving me the question that I am looking for.  Wasn’t the whole point to emphasize the questioning to clearly define problems a little more?  It looks like I’ve fallen hard into my habits and have prized THE answer as opposed to prizing the question and problem definition. 

Wow, blogging really forces me to reflect more than usual.  It just dawned on me that the reason why the question quality has been decreasing since September is that I don’t answer all of their questions.  There were so many quality math questions that were generated by the students from the videos in September but I ignored the most quality ones because they would probably take a day to answer. 

I have placed 100% more importance on following my scheduled spiral curriculum than their curiosity. 

Looking back, I should have made more of a compromise, and actually followed through with at least a few of their questions.

It would show a lot more teacher willingness to venture into the unknown and really value their questions.  Following through to try and answer their questions would actually demonstrate how I learn – one of the most important things to model.   Instead, I’ve trampled on their curiosity and lost that opportunity to be a role model of a real learner. I feel really badly now. 

But, can’t be ruminating now, can we?  I’ll just change it for next semester.

So I’ve digressed.  Going back to the 3-act question:

After receiving their questions, I specified the question that we were going to answer today.  Which cup has more, and by how much? 

Here are their guesses as a completion to act 1: 

It’s interesting to see how many of them chose that cup A and cup B had the same amount. 

Nevertheless, act 2 came along, and with those measurements and the conversion ratio the students went about to work. 

After about 15 minutes of discussion and hard work on large whiteboards, the students put their answers on at the front.  Only 10% of them got the right answer:

 The stumbling point for many students was the CONVERSION!  I have to find another way of teaching conversions as I have been repeating it throughout the year and it still hasn't sunk in. 

In truth, the fact that many of my students weren’t able to complete this question in pairs disappointments me. 

I made this question into an entrance card to repeat for tomorrow in hopes that the students will get it during their second try.

I will take it up and repeat a similar question as an assessment on the next Friday. 

Update:  They did very well on their assessment.  I wonder if they’ve gained any ‘permanent’ skills along the way in this process or if they've just memorized the process.  I will only find out later I guess especially with that EQAO coming up soon.  

Old Style Education vs the New Style Education

We are at a crossroads for learning. Students are very good at informal learning;  their interests lead them to finding resources on the internet to learn more about their interest.   This is in contrast to the formalized learning that happens in school sometimes.  Some students can bridge these two styles of learning; other students aren't successful at formal education or don't see the point in school.

Many teachers prefer the traditional method of education with the teacher at the front leading the classroom.  Students don't know what they don't know and it's important that the teacher impart some of the perspective, experience and knowledge through interesting media.

However, there are more and more voices from the progressive teachers (which are mostly online) with this view that I found on flickr:

Others prefer student lead learning with teachers as facilitators.  The epitome of student led learning and teacher facilitation is depicted in the makerspace below:

Content doesn't matter as much, as we now have access to knowledge all the time with the internet.

Skills matter more.  With the makerspace, students are creating things.  With this higher engagement, the important skills of initiative, collaboration, and perseverence are all practiced at a much higher level.  Developing these soft skills will enable them to succeed at whatever job they are placed in.

It essentially boils down to this: do we try and give students a base knowledge to start with or do we just let them lead their own education?

The answer is always the same to these new initiatives: mix i the old with the new.   I will do both because students will benefit from both.  I just hope I know how to balance it and if the time allocation is done correctly.

Very often, students don't know what they want to learn because they haven't discovered it yet.  For these students, it is my job as a teacher to show them the amazing parts of this world.  Once their interest has been captured, then it's my turn to facilitate and lead from behind and let the students lead the way.