Category Archives: Learning

When is a Line Not a Line?

3rd Grade Line Plot

3rd Grade Line Plot (From K12Math Passion Third Grade Written Assessment)

After a long hiatus, I am finally getting back to my assessment project.  The end of the third grade assessment is in sight!  As I work to understand each standard and turn it into an assessment question, I do a fair amount of checking to make sure (1) I’m using appropriate levels of problems and (2) my assumptions are good.  (I don’t always succeed, but that’s another story!)  This check is particularly important with elementary topics because my credential and most of my experience is with secondary math.

Two of my favorite sites for checking my assumptions are IXL Math and Illustrative Mathematics.  They are both very organized and easy to use.  IXL Math has lots of practice problems for each standard and Illustrative Mathematics has amazing tasks and a great interactive graphic showing the domains across grade levels.  (I’ll be using both of these sites over the summer with my 3rd and 4th grade tutoring students.)  There are others, of course, and I also use Google to research topics.  (If  you have a favorite site, please share it in the comments!)

Thank goodness I checked my assumptions about line plots (3.MD.B.4).  I don’t know about you, but when I think of line plots my brain constructs an image of coordinate pairs connected by line segments.  You know, something that has lines in it.  So, I was a bit surprised when I Googled “line plots for 3rd grade” and images of stacked X’s came up on my screen.  (See example above.)

Okaaaay.  Hmm.  Well, the making-a-line-plot standard doesn’t have an image of a line plot.  So, I did a little digging and discovered that, apparently, in the 3rd grade world a line plot looks like stacked X’s.

Don’t get me wrong.  I think the stacked-X’s-as-line-plot is an outstanding stepping stone between bar graphs or pictographs and traditional line plots.  I understand it’s an important bridge, which will greatly help students make the transition.  In fact, I hope teachers facilitate this transition by eventually asking students to draw a dot at the top of each stack of X’s and connect those dots with line segments.

It’s just the name that gets me: line plot.

I realize I’m a very literal person, and third grade was a LONG time ago, but I think even third grade me would be confused.  “Where are the lines?”

When is a line not a line?  When it’s a third grade line plot, of course.  Anyone can see that.


So Much More Than People Think

To educate

Microsoft Office Clip Art, November 2013

The announcement for Mission #7 of Exploring the MathTwitterBlogosphere happened to cross my consciousness this morning.  The mission: to explore a day in the life of a teacher/educator.   (Thank you for including non-teachers!)   It’s Sunday, my big tutoring day, so I resolved to take whatever happens today and write about it.  I wondered if I would have anything to write about.  This turns out not to have been a problem.

This morning, with latte in hand, I continue unpacking my calculus knowledge so I can preteach the next section to one of my tutoring students later today.   I love this concept – can you love a concept? – that as we process knowledge it becomes compressed, and then as teachers we have to go back and unpack our knowledge so we can help students learn.  This model perfectly matches what I feel in my own head as I learn and process new concepts.  BTW my calculus knowledge has been packed for a very long time!

In the middle of all this calculus, I find out my dad was in the hospital last week and didn’t tell me.  (Sigh.)  He blacked out twice recently, and was planning to drive somewhere today.  OMG.  I make him promise not to drive and wish I lived closer to him, or vice versa.

Tutoring session #1 starts out shaky.  It turns out my student is having a personal crisis.  I don’t ask outright, but wait until confided in.  I then spend 10 or 15 minutes responding with my best growth mindset messages:  this happened only one time; you will do better next time; this event does not define you.  Whew!  I’m able to help the student process the event and move on.  This job is so much more than people think it is.  At the end of the session, I strongly urge my student to “step away from the math” for a few hours, and then go back and review each of the problems before submitting the assignment.  Recognizing the benefit of letting time pass so you can tackle a problem with fresh “eyes” is a good life lesson and only one of many I find myself sharing with my students.

Tutoring session #2 starts out great:  I discover my student scored one of the highest grades in the class on the latest test.  You can just see the increase in confidence and a willingness to try more difficult problems instead of sitting back and saying “I don’t get it.”  Gotta keep this positive feeling going!

As I reflect on the day’s educational interactions, I realize (once again) how much the affective side impacts our ability to be effective educators.  This job is so much more than people think it is.  And isn’t that great!

How Does Math Make You Feel?

Session 1 - Concept Map

Well, I hope math doesn’t make you feel like the Stanford University freshmen (see the concept map, above) who were interviewed for the OpenEdX course entitled How to Learn Math.  You might think anyone who was accepted into Stanford would be good at math (and feel good about their abilities), but not so.  In fact, the professor (Jo Boaler) includes in the first class session an interview with a scientist from the UK who, when awarded a medal by the Queen, still harbored feelings of math inadequacy.

Many thanks to Karl Fisch, for his blog post that pointed me in the direction of this class.  One minute I was reading about Karl’s introductory assignment for his students and parents, and the next thing I knew I was signing up for the class.  This is just up my alley and I am really enjoying it.  (Oh, and did I mention, the class is free!)

The concept map is one of my first assignments.  After listening to the students talk about their school math experiences,  I created the concept map to capture the essence of their responses.  I think it came out pretty well.  I’m interested to see what some of the other 20,000 (!) students came up with and if anyone had a different take.  Back to class!