Data Management, Geometry, Measurement, Number Sense & Numeration, Patterning & Algebra

Another One About Reporting

As the end of Winter Break approaches, it’s time for me to sit down and do some planning for the coming weeks.  Reports cards are due at the end of the month and I need to get all of my assessments up to date and my comments organized.  The report card should reflect what the child is capable of at that time, not what they were doing 2 or 3 months ago. I last formally reported on everyone in November. I know there has been growth for everyone, some big and some small.

For math assessment, I am going to re-do the interview I used in September.  I know that for some children I can start in a different place because they have shown mastery in areas I previously assessed.  I will have to go beyond where I left off with them because they have shown growth toward the end of year goals. I also need to add in some geometry and data management questions so I can report accurately on that as well.  I have a lot of anecdotal notes to draw from, but I want to be really sure of what they can do now.

As I have been reflecting on this, I am struck once again with how hard it is to divide math into 5 strands.  I suppose it is easy in the Primary grades to do that with Geometry, Data Managment/Probability and Measurement.  But even at this point they are all starting to blend together. Everything we learn in Number Sense is related to everything we learn in Patterning and Algebra.  I can hardly decide how to mark everyone sometimes because I’m not always sure if the things they need to build understanding about exist in one strand of the curriculum document or another.  I have to consult it every time because in my mind it’s all mashed together into “math”. Everything we do in Number Sense is related to what we do in Measurement too, but it’s a little easier to seperate out the skills that will be reported on.  Same for Geometry and Data Management/Probablity.

Here is one example of this from the Grade 2 curriculum document (2005):

  • identify and describe, through investigation, growing patterns and shrinking patterns generated by the repeated addition or subtraction of 1’s, 2’s, 5’s, 10’s, and 25’s on a number line and on a hundreds chart (e.g., the numbers 90, 80, 70, 60, 50, 40, 30, 20, 10 are
  • count forward by 1’s, 2’s, 5’s, 10’s, and 25’s to 200, using number lines and hundreds charts, starting from multiples of 1, 2, 5, and 10 (e.g., count by 5’s from 15; count by 25’s from 125);
  • count backwards by 1’s from 50 and any number less than 50, and count backwards by 10’s from 100 and any number less than 100, using number lines and hundreds charts (Sample problem: Count backwards from 87 on a hundreds carpet, and describe any patterns you see.);

Two of those are from the Number Sense strand and one is from P/A.  But I teach them simultaneously. And if a child is having trouble with skip counting is it because s/he isn’t understanding the patterns associated with the skip counting, or is having trouble memorizing the order, and if they seem to not be having any trouble is there some rote counting, or is the child processing the numbers and thinking about the patterns?  It’s tricky to assess sometimes. And sometimes it isn’t. For instance, if a child can say, “2, 4, 6, 8, 10” but then stops and can’t figure out what comes next, I know the first 5 terms are acutally just counted by rote. Or if a child can count by 2’s even further, but then isn’t able to do this when there are actual things to be counted, I know there has been some memorizing. And if a child gets to ten, then pauses to work it out in his head, comes up with 12, then slowly with 14, and so on, I know there is some understanding.  It’s tricky to boil all of that down to a letter grade.

Someday when I open my own school and can make my own rules, I am not going to assign letter grades to Primary kids ever. The report cards at my school will be all about the comments.  And I will definitely not divide math up to strands!  But for now, I’ll sit down and go through my assessment and the curriculum documents, then I’ll sit down with everyone in the next 2 weeks or so and ask them the questions I’m wondering about.  And then I’ll sit down and give them all a grade that reflects what they can do.  Easy, right?

 

Geometry, math, Measurement, Number Sense & Numeration

I’m making a plan!

This is the point in the Winter Break when I have started to think about sitting down to do some lesson plans. Instead, I just spent 30 minutes on social media reading garbage, and am now writing.  My lesson plans will wait until Sunday night, right?

I have started to work on report cards this week though.  This always gets me in a reflective mode.  Mainly I am asking this:  Have I covered something from at least 4 strands of the math curriculum in a way that will allow me to write a good report card?  I still have 4 weeks to go, so if the answer to this is “no” then I have time to make up for that.  I know we have done plenty of Number Sense and Numeration, and lots of Patterning and Algebra.  I think we have done enough Geometry, if I spend another day or 5 (or 6) on that, and I am going to comment on Measurement this term too, but will need to spend a few days doing some of those activities.  We did a lot of measurement in science, but I haven’t asked them do anything lately.  I want to make sure I have done something recently that I can comment on.

That leaves Data Management.  We have done quite a few things that are part of Data Management, but I don’t feel like I have done enough to comment on this strand yet. One of the things I have been working on this year is integrating math into other parts of our day.  We did lots of measurement in science, for example.  I wanted to do more data management in science as well, but we got side tracked.  I have not taught a single measurement lesson during math though, so I feel good about that.

Number Sense and Numeration, as well as Patterning and Algebra, are the areas I have always felt I needed to spend a lot of time on during math.  As a result, I have often rushed through Measurement and Data Management/Probability.  It’s not that I don’t think these are important.  It’s just that I was prioritizing one over the other.  By thinking about how to teach these outside of my regular 60 minute math block, I think I am seeing connections that will help my students build connections and we can all use math in more meaningful contexts.  For science, we were growing plants on the window ledge. For 3 weeks, every couple of days we pulled out the rulers, measured the height of our plants, and recorded that in our journals.  That’s meaningful.  I also recorded the results of a mould growing experiment on a chart as part of our science learning.  But we haven’t taken the next step and graphed any of this, and that is why I’m feeling like I am not ready to report on this yet. I could get there by the first of February if I really wanted to, but I have other plans for this so I’m not going to rush it.

In the coming term, we are going to be learning about Movement, and Strong & Stable Structures.  February and March are really interesting months to track weather in Ontario.  These are things that will give us a context in which to use some data management and probability related math.  I’m not worried about making sure we get enough practice with these concepts.

To get ready to finish first term reports, I guess my math month long plan will look something like this:

Week 1:  Measure things, like temperature & time (January is an interesting time for this, I think.  We’ve talked about time on a clock a fair bit, but need to talk about this human way of measuring the passing of our lives.) (This will also lead us into a social studies connection since we will be learning about Canadian Communities 1780-1850 in Social Studies during the second term.)

Week 2:  Use pattern blocks to measure length, width, area, etc. Talk about why we get different answers when we use different pattern blocks to measure the same thing. (geometry connection…this will give me a chance to check in with a few kids who were having trouble naming attributes of some 2D shapes and see if they’ve met that goal.)

Week 3:  We’ll do this part during our science time: Build 3D shapes using stuff (cardboard, spaghetti & marshmallows, etc.) and start talking about strong, stable structures (science connection for 2nd term)  In math we will start our next Context For Learning math unit (“Measuring for the Art Show”).

Week 4:  By this time I need to be finished with all of my math recording, and should be able to write everyone’s math report card comment.  Should.  🙂  I really want to sit down with each child and ask them some of the questions from our first math assessment in September, but realistically I’m setting an “end of February” deadline for that.  If the Polar Vortex (is that what were are calling it this year?) continues to churn over North America, we’re likely to have some bus cancellation days. This will help me meet that goal since I’ll only have a few students each of those days, but will also hinder me in meeting that goal because I tend to have the same few students each of those days.

math

Reporting and Assessment

Back in April, I wrote about using the Landscape of Learning to assess some students, hoping to do two things. 1) assess where my students were on the Landcape and identify some next steps, and 2) assess were I was in my ability to use the Landscape for assessment of and for learning. I feel that I accomplished both.  (You can read about it here.)  I have continued to work on this, and will probably write some more in a few days about how these students have progressed, as well as how I will use this next year.

In the past few weeks, however, I discovered just how much all of my Landscape learning has effected my report card writing.  I think I have always done a pretty good job of reporting.  I personalize the comments with anecdotal quotes and events, I use up all or most of the 13 lines of allotted space, and I make them easy for parents to understand.  But this time around, I started write things like, “XXX counts forward and backward…” and I realized I could say so much more about the counting than just direction.  I found myself feeling that I had to comment on all the nuances of the child’s counting skills.  Is he counting forward by 1’s, 2’s, 5’s, 10’s, etc. and backward by the same?  Is she using this counting to add and subtract double digit numbers on a number line?  Does the counting happen mentally, or only with a math tool such as counting chips or a Rekenrek?

Adding and subtraction skills were no easier.  Instead of “XXX adds and subtracts double digit numbers”, I had to write, “XXX adds and subtracts double digit numbers using several strategies, such as splitting, counting on, or finding the doubles and near doubles.  He demonstrates an understanding of the commutative property when he starts at the largest addend and counts on.  He draws his own number line to communicate his strategy.  During Number Talks, he clearly explains why he chose to use a certain strategy to find the answer.”

And that’s just for Number Sense, with a little bit of Patterning and Algebra thrown in.  If you were counting, you’ve probably realized that I have used up nearly half of the 13 lines without even mentioning measurement, geometry or data management.

It was hard, you guys! I’ve always felt like I had plenty of room to report on math.  Now I feel the opposite.  In a meeting with colleagues on Friday (you know who you are, Blue Sandals!) I found out that several of my colleagues have felt the same way while writing the second term report.

I also don’t have enough space to report on literacy skills, but that’s another blog post for another day.  If anyone at the Ministry wants to know how I think this should be solved, I’m going to tell them that we should take away all that space in the phys ed section, make a few things like phys ed, health and The Arts pass/not pass subjects where I can write, “Hey!  Your kid tried his heart out and good for him for doing it!”  Because, at the end of the day, I think knowing your child needs assistance counting money because he isn’t able to unitize is way more important than declaring him an A student in throwing and catching.

And I know some people are thinking, “But throwing and catching are so important!!”  And they are.  But do we really need an equal amount of space to report on their PE skills as we get to report on their math and language skills?