kitchen table math, the sequel: 12/13/09 - 12/20/09

Friday, December 18, 2009

truth in advertising

My copy of the district newsletter arrived the other day.

On the back:
SAT scores on the Rise
Over the last three years, our students' SAT scores have been rising in all categories.

Do you wonder what happens when you back that up from 3 years to 5?

(properly formatted version)

Steve H on speed, mastery, & understanding

I remember being very discouraged (in the old traditional math days, no less) trying to understand mixture problems because the book we used approached it using tables and grids. When the problem changed a little bit, I couldn't figure out which numbers went into what boxes. I finally learned to approach the problems using governing equations and defining variables.

That understanding didn't come from solving one or two problems. I had to work at it. There were so many times when I thought I understood what I was doing only to feel completely lost when I tackled the homework set. That's when the real lightbulb goes on. Look at any proper math text book and you will see homework sets that give you all sorts of problem variations of the material in the section.

I also want to make a case for speed in helping understanding too. As you move along to more complex math, you need this speed or else you will be completely bogged down. In high school, I got really good at "seeing" right triangles in word problems, even if the triangles weren't explicitly drawn. I was very fast at finding any side or angle given "enough" information. I could state that a length was something like d*cos(theta) just by looking at it. I didn't have to draw a picture and stew over which leg is for sine and which leg is for cosine.

The mechanical monkey paradigm leads to all sorts of wrong conclusions. It also conveniently fits in with their predisposition to equate mastery with rote learning and drill and kill. When they talk of balance, they really don't mean it. They still think it's just for convenience rather than understanding.

This position might seem reasonable when it comes to the basic algorithms of arithmetic, but it falls completely apart as you head into algebra.

Reading this post makes me want to go do, right this minute, two things that cannot be done at the same time:
  • fire up ALEKS and finish the geometry course I was taking before my mom fell last summer
  • finally write my post on just exactly how much money Response to Intervention (pdf file) is going to cost us once RTI gets going in public schools with a) lousy curricula and b) no focus whatsoever on deliberate practice (pdf file) & mastery
Maybe I should spent 10 minutes de-cluttering my desk before I do either of those.

shoot me

highest ever

(current per pupil spending: $28,291)

learned disability

from the Comments thread on Paul's post, Creating Learning Disabilities,

Exo wrote:
I think you are right, Paul. Learned disability - and it's almost impossible to correct in later years.

I see the same in my HS science classes. Elementary computations, numbers make them look like the deer in headlight...They ARE afraid. The ones that are not are either my ESL students who recently moved to the US or "math kids." And please, we don't do anything higher than what in Soviet schools would count as 6th grade... Maybe even 5th.

It's just that immediate "I don't get it" as soon as the numbers are involved.

I think the psych term for this phenomenon is learned helplessness.

According to this woman, it takes about 5 minutes to induce learned helplessness in a 20-year old.

Unfortunately, the teacher ends up saying girls are specific victims of learned helplessness.

I'm pretty sure the person operating the camera doesn't agree.

Alternative to Common Core

What are your thoughts on this post from Jay P. Greene's blog?

Thursday, December 17, 2009

links for Barry's Education Next articles

The links to Barry's Education Next articles have gone missing on Google, so here they are (I'll get them linked on the sidebar, too):

An A-maze-ing Approach to Math (2005 and now a classic--)

Miracle Math (about Singapore Math)

I'm giving both articles to folks here.

Wednesday, December 16, 2009

Beyond Singapore's Mathematics Textbooks


The winter issue of American Educator will be available online (I believe) on 18 December. In the meantime, I have received several boxes, as this issue contains an article I co-authored, Beyond Singapore's Mathematics Textbooks: Focused and flexible supports for teaching and learning.

If you are not a member of American Federation of Teachers (AFT) and would like to receive a hard copy, please email me privately ( with your mailing address.

Happy holidays to all!



Tuesday, December 15, 2009

Creating Learning Disabilities???

This quarter our school established three cohorts in the 7th grade and three in the eighth that are based (primarily) upon academics. We also split our math blocks in half with one half dedicated to our grade level curricula and the other half dedicated to remediation of core number sense skills. The core skill blocks are further homogenized such that there are six distinct groupings that are independent of grade level. If you are in the seventh or eighth grade you are in one of three groups attending normal curricula for your grade and in one of six groups attending remediation, independent of your grade. These splits are the best we could do based upon scheduling, teacher, and room considerations. Our goal was to create the most homogeneous groupings possible.

After about five weeks with this schedule I've come to the conclusion that there are two kinds of learning disabilities. There are those that are inherent to the child and there are those that we have created. Each of my grade 7 cohorts are about a third of the class, with the highest being no more than one year below grade level, the middle group being 2 or 3 years below grade level, and the lowest group being more than 3 years below grade level. The really interesting feature of this schedule is that I see most of my kids in two entirely different academic settings.

One setting, the grade level curriculum, is fairly conceptual so you get to see kids working with new concepts and from that you can assess their prowess with connecting the dots in their zone. The other setting, core skills, is not big concepts or word problems. It is simply raw calculation of rational numbers in all their various forms. This skills component lets you see more of what they bring to the table from lower grades.

Here's the nut… My highest group is making progress in both grade level curriculum and their core skills training. My middle group is making progress in their grade level curriculum (subject to the limitations inherent with their lack of core skills) and little to no progress in the core skills block. My lowest group isn't making progress in either curriculum or core skills.

My observational shock is not so much with the lowest group as they have clearly identified, documented learning disabilities. The highest group is making progress across the board so they're not a big concern either. The real conundrum is the middle group. In their grade level curriculum they appear to have no problem attacking new material (as long as the computation is simple) but their core skills are every bit as resistant to improvement as those in the lowest group. For these kids in the middle, it's like they have two personalities, one of which has a learning disability.

One more relevant point of reference is that this middle group has a normal amount of enthusiasm and energy level in the grade level work but in the core work they have all the inherent joy of a glazed doughnut. They sit in the core class with obvious boredom and do not apply themselves at all. In this class you could easily mistake them for the kids in the lowest cohort.

I would argue (perhaps foolishly) that this middle group is capable, based on my assessment of their grade level work, but disabled when it comes to computation. I would further submit that this seeming disability is induced by their prior failure, i.e. we created it. Could it be that after enough exposure to 'failure' in a particular domain, kids simply give up on it, concluding that it is a skill that is beyond them? Remember that this skills stuff is what they've been getting for the six preceding years.

My anecdotal evidence is telling me that these kids have an externally induced learning disability. It's induced by too much early indulgence towards their early lack of mastery and the school's failure to address it before it has damaged them. As a result they level out at a place that is far below their full potential. Is it possible that at some point, the failure to master becomes a built in disability that impedes further progress? Is there a threshold, beyond which a lack of progress becomes viral, thereby blocking future attempts to improve?

Has anyone experienced this?

Am I drinking too much coffee?

6th (actually 7th) grade holiday math project: Just Because I Care About You

A Just - Because - I - Care - About - You MATH PROJECT!

You have been given $2,000 to buy gifts for ten different people in your life. You must decide who you want to give a gift to, what you want to buy them, and why you want to buy them this particular item. You must find a picture of this item with the price. Every item you select has a discount. You must find the discount for each item, calculate how much you will save, and how much the item will finally cost you.

Each student must complete a booklet consisting of 13 pages
Page one is your title page. This must include your name, and title of this project.

Pages 2 - 11 will display:
* A picture of a gift
* The original price
* The discount
* The final price with calculated sales tax ***
* Your math work
* Who the gift is for and why you chose this item for this person

Page 12 will show the price you spent for each item, how much money you spent all together, and how much you have left.
On page 13 you will donate the remaining money to a charity of your choice and explain why you chose this charity.

20% off all major appliances (refrigerator, washer)
50% off all jewelry and clothing

***Please remember, there is a 8% sales tax on everything but clothing.

...Your project will be judged on creativity, accuracy, and neatness.


[Picture of Lamp]

A lamp for my friend Nancy.
My close friend, Nancy, just got married. At the Craft Show last month, she admired a lamp which bears a resemblance to this one. She said it was the perfect lamp for her foyer. I could not pass it up.

[Various calculations]

[Final price]

Sunday, December 13, 2009

Barbara Oakley at ktm-1

Here she is!

ideologically-motivated intellectual gatekeepers

small-d democracy and its discontents

communicating with the public

or not:

11/24/09 Board of Education Meeting Agenda 8E:
Protocol for Information Requests by Board Members

Recommended Motion: “RESOLVED, that the Board of Education of the Irvington School District, approve the protocol for Board functioning that all information requests made by Board members of any District employee must be made to the Board President. If he/she so deems the request might require a significant expenditure of time, the Board as a whole will vote as to whether the request will be approved or not.”

11/24/09 Board of Education Meeting Agenda 8F
Protocol for Request of Information (FOIL)

Recommended Motion: “RESOLVED, that the Board of Education of the Irvington School District approve the protocol for Board functioning, that it is the intention of the District to manage the effective use of District staff time. Thus, it is the intention of the Board of Education that any request from the community for information that requires collection of data, pulling a report, copying, or any work and time commitment should be requested through the FOIL process. To that end, it is the intention of the Board that no individual Board member should directly ignore this protocol by circumventing the FOIL request – by providing information to which a Board member has access directly to a community member without the requested FOIL request.”

On the agenda for December 22 vote.

COOG weighs in.

if you live in New York:
Committee on Open Government