fractal questions

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This graphic of a Koch Snowflake (thanks wikipedia) in some ways describes what has happened to me at Twitter Math Camp (#TMC14).  I started out with just a few questions, but then those questions multiplied, and the new questions multiplied, and so on, until they all started to blur together.  Similarly, Koch’s Snowflake starts simple, but then each replication makes the image more complex, until it finally brings you to that snowflakey image that everyone recognizes.

In my questions, unfortunately, it isn’t that simple.  I wonder, do I need to let them replicate more, before I find that big question toward which they are building?  I think I at least have a feel for where they are going.  I started with questions about how to help struggling students, how to reach disengaged students, how to teach multiple levels in one class, how to use project based learning to get there, how to use standards based grading to report on that learning; unh, I’m out of breath.  But in my mind I can almost see the convergence point, the place where all these questions merge into one big question.  I can’t quite see the shape of it, but I know it’s there.

It is something to do with teaching multiple levels in essentially the same lesson.  So that kids in basic math, pre-algebra, algebra I and algebra 2 are all interacting with the same lesson at the same time, but from a perspective that fits with their level of learning.  The concept of multiple entry points resonate with this question, as do the multitude of rich problem based resources from the digital math community.  So for now, it seems my snowflake is this: how do I make this structure happen?


Number sense certainly seems to be at the forefront of many math teachers’ minds these days.   I know we have talked about it in my math department (high school) several times, bemoaning its lack and wondering how best to remedy that lack.  And it has popped up on twitter pretty regularly.  The most recent reference came from Tracy Zager with this post.


My gut response was that this was simplification of the scope of difficulties that students have in math, but Tracy asked me to look at the whole article and see what I thought.  Although I had homework, I couldn’t stay away from it.  As I read through it, I thought of the students I have worked with and all the different ways they have struggled in math class.  Most of my math students have been identified with disabilities.  The rest fall into that category of having “difficulties” in math.  For many of them, number sense was at the root of their problems.  However, it was often accompanied by complicating factors.

Some students have processing issues. I recall a student who would close her eyes and just think.  If you could wait long enough, she would provide a response that was usually on track, although she couldn’t articulate her thought process.  Another student would work a problem correctly and explain her work clearly.  Five minutes later, she would get totally lost on a similar problem.  Last year I had a student who seemed to have great number sense, as well as a great understanding of how things work.  However, as soon as I tried to move him to the abstract or to generalize, I lost him.  For students like these, the difficulty is more than just poor number sense.

In the article, Nancy Jordan does acknowledge that not all difficulties in math result from poor number sense.  However, her main focus is encouraging early screening and intervention, similar to the screenings that happen for reading.  She references research that supports the importance of number sense, as well as her own research that shows number sense as an early indicator of math difficulties and disabilities.  She also offers some specific tasks that might help develop number sense.

So to answer Tracy’s question…After reading this article,  I do agree that early identification and intervention based on number sense screenings would likely lead to improved results.   I want to read more; I want to see more research in this and related areas.   Further research in this area  would perhaps help isolate and identify other factors that later impact success in math.  And I want to know what the research can tell me to help the students that I have who struggle in math.

Jordan, N. 2007. “The Need for Number Sense.” Educational Leadership 65(2):63-65.



Most of the students I teach hate math and school, thinking both are a waste of their time. They also are pretty certain they have limited ability to be successful, especially in math.  (No wonder they hate school)  Fighting their negative outlook is a frustrating, uphill battle.

Today, I was on twitter looking for ideas (procrastinating) and I saw this post by @trianglemandcsd:


I followed his link to an article about UT Austin’s efforts to increase completion rates for disadvantaged students.  It was an interesting read suggesting success with limited time psychosocial interventions, with David Yeager brought in for implementation. Now I am always interested in new weapons in my arsenal for fighting to change my students’ outlook, so I pursued the article a little further. That lead me to this, http://rer.sagepub.com/content/81/2/267, which I put in my reply to Christopher. It is David Yeager’s and Greg Walton’s description and defense of the use of limited psychosocial interventions.

It sounded like something worth trying with my students at the beginning of next year. My brain shifted into planning mode, thinking about ways I could modify and implement, how I could document the process, and curiosity about its efficacy.

Then I saw this post from @tchmathculture, whose opinion I generally respect. Of course I had to follow her link.

@tchmathculture tweet

It led me to The Eduoptimists Blog (theeduoptimist.com) , who rightly pointed out that this one small intervention cannot possible ameliorate the difficulties faced by students with low socio-economic status (SES). She pointed out that low SES students often face costs way above and beyond the typical room, board, tuition, and books. I can attest to this myself. When I started college I had 4 children at home and we were receiving food stamps.  In addition to the typical costs, I had to borrow to cover childcare.  And I had it easy compared to most low SES students since my husband had some income.

However, while I agreed with The Eduoptimists that the psychosocial intervention was not an adequate response to the problem, I don’t think it should be discarded completely.  Even if all the financial issues were addressed, the students still have the mindset problem to overcome. So don’t throw away a tool that seems to be helpful just because it doesn’t solve the whole problem.

Not enough time

Today was a snow day.  I should have used it to do some planning.  Or grading.  Or something productive.  But instead I reread a book for pleasure, The Circle of Ceridwen. A book with no connections to education at all.  A book to get in the mood for the new season of The Vikings.

But as it gets late, I start thinking about Friday’s field trip to Maine Maritime Academy and all the logistical things that need to be done.  And all the math we haven’t done in that class.  It hasn’t been a very mathy week, because the marine part of the class has taken precedence.  By Saturday, the kids need to know enough to pass the certification course for commercial fishing vessel drill instructor (also none as the cold water safety course).  Some of them (about a third) already have this certification and will be doing other safety related things.

So next week we need to get down and dirty on the math content.  I’ve noticed that some of my “Algebra 1” level kids may still be at a pre-algebra level.  I think I’m going to have to split that group, somehow.  And I am switching my only stats student to a better book.  Almost two weeks in, and we haven’t covered half of what I was hoping for, so I will have to look for ways to make up the time.

Speaking of time, I have noticed that it flows much differently in my MSP class.  Out of a two block period (150 minutes), I usually only get 40-50 minutes.  It is forcing me to really think about my priorities and objectives and really tighten things up.  This unit has been focused on the marine industry certification related to cold water safety.  I was able to pull some good unit, scale, and measurement learning targets out of the activities they did last week, but this week it has been harder.

On Tuesday, I did a short, DI type lesson on functions vs relations.  We also delved into domain and range, but I had some students really struggling with that.  Also, with my Algebra 2 group, it was review for some, but new for others. Because of our snow day today and the field trip on Friday, I probably won’t get them for math again until next week!

 And they all asked what functions vs relations had to do with fishing.  I told them I didn’t know of any connection, but it was a standard we had to cover.  (I hate giving that answer, especially when I suspect there is a good reason that I am too dense to see).  Ah, well. There will be other standards that do flow nicely out of their marine content.  

1 down, 17 to go

Tomorrow is the second Monday for this semester.  That means I made it through the first week.

Good stuff that happened…

Kick off was mostly successful in spite of the weather.  We took the kids to the Town Dock and split them in two groups.  One group went on a local fisherman’s boat and surveyed it for safety hazards (pre-test for marine studies) and the other group stuck one hand in 33 degree F water for a minute (if they could stand it) for the science teacher, then we used an infrared surface temp reader to compare wet hands and dry hands at regular intervals (for the science teacher).  DATA!  Then the groups switched places. The kids were miserable in the wet, but at least it wasn’t actively raining. And they weren’t in the classroom, hooray!

We used their data to work on graphing and analysis skills in the following days.  We also used the data sheet from the marine trades instruction about the rate of water flow when a boat has a hole below the waterline.  More data and more graphing. In the end, we had the chance to discuss units, scales, variability, quadrants in the coordinate plane, axis labels, domain, and range.

Tonight I read Gregory Taylor’s post on SBG, http://mathiex.blogspot.com/2014/02/my-grading-iep.html?spref=tw which  led me to Michael Pershan’s post on other things, http://rationalexpressions.blogspot.com/2012/06/4-things-more-important-than-sbg.html, which led me to believe I need to have an assessment. Soon. So I’m think I will give them a data set and a graph and ask them what’s wrong with the graph (formative).  Then I will just give them some data and ask them to graph it (summative).  When I have the assessments built, I will post them here.

For now, I need to take the time to sketch the upcoming week.  I use a simple table, write in just a word or two, and keep it on a clipboard (with bell schedule and school calendar, so I always have them even if the ‘net is down).  WeeklyPlan-12

Four more days

It’s Thursday and first semester is almost done.  All that’s left is the make up exams and grading. Then we start the new semester on Monday.  I have been really stressed about the new Marine Studies class, but now I also have concerns about my other class.  Sigh.

I teach a special ed science class that alternates between physical science and life science year to year.  I have tried to have it follow the content of the regular ed classes in the past.  But the new physical science teacher is throwing in a lot of chemistry this year.  Yet another topic about which I know little.

My motivation to become a teacher had a lot to do with my preference for a high learning curve, but I didn’t expect it to be near vertical. Between chemistry, SBG, PBL, co-teaching, and marine studies I feel like I’m in an 18 credit semester while carrying an outside job. I don’t know when I will have time to breath.

And I am still. not. ready. for the marine studies pathway beginning on Monday.

(Forgot to post this, so I will now, even though the semester started a week ago Monday).

Time’s getting short

Marine Studies Spring 2014 starts on the 27th. I am not ready. We are not ready.  We are insane.  Three of us will be teaching a two block class.  In two consecutive blocks, students need to learn content for Ecology, for ½ of their grade level language arts (the writing half), math, and marine industry standards.  I am in charge of math for 16 students whose levels range from pre-algebra to post-algebra 2 and share responsibility for writing standards for four grade levels.

We have promised project based learning, which I have never done before this year. We have promised standards based grading (whew, I tried that last year, so it’s not completely new.)  We have the first project planned, sort of. Last summer we talked about other projects, but it is feeling very nebulous at this point.  We have weekly meetings, but otherwise only talk when we catch each other in the hallway.  There is a facilitator to help, thank god, but we just haven’t put enough time in.

I have my algebra 1 standards.  Kids at pre-algebra will get supplements to catch them up.  I have my algebra 2 standards.  Kids who might have taken geometry will get algebra 2.  Geometry can come next year.  But I don’t know what to do for my one post-algebra 2 kid.  It looks like stats.  Stats would be a good fit, since every project we do will involve looking at data. But I don’t have a scope and sequence for stats; and my text is not core aligned; and I have never taught stats.  Twitterverse, I hope you respond to the plea I posted.

I have until the 27th to wrap my head around the stats and generate a list of standards for the student (and me). Or maybe the 28th, since the first class is a planned field day. I really don’t want to have to make it up as I go along, but I can’t just follow the text either. Not in a project based setting. Did I say we were insane?

I hope to document this semester of insanity.  I’m afraid the load is going to be too heavy to allow time for reflection, but I think the reflection is going to be critical to keeping the course moving forward. At the least, I will be able to look back and say hey, remember when we tried that crazy course?