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.

DISCOUNTS
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.

Sample

[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]

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

meanwhile, in Britain

State schools admit they do not push gifted pupils because they don't want to promote 'elitism'


As many as three-quarters of state schools are failing to push their brightest pupils because teachers are reluctant to promote 'elitism', an Ofsted study says today. Many teachers are not convinced of the importance of providing more challenging tasks for their gifted and talented pupils. Bright youngsters told inspectors they were forced to ask for harder work. Others were resentful at being dragooned into 'mentoring' weaker pupils.

In nearly three-quarters of 26 schools studied, pupils designated as being academically gifted or talented in sport or the arts were 'not a priority', Ofsted found.Teachers feared that a focus on the brightest pupils would 'undermine the school's efforts to improve the attainment and progress of all other groups of pupils'.


Read more: http://www.dailymail.co.uk/news/article-1234906/State-schools-admit-push-gifted-pupils-dont-want-promote-elitism.html#ixzz0ZWqSe4TI

Everyone has won. All must have prizes. (fixed.)

From Russia with love: real wor[l]d problems

A friend of mine discovered this paper, Word Problems in Russia and America, by Andrei Toom. Quite a find. A long read, but worth it if you need any moral support in your personal fight against fuzzy math. Here is an excerpt:

The high-school part of [ed. American NCTM 1989, I think is being referred to]“standards” contains a list of topics to increase attention, where the first place is given to “the use of real-world problems to motivate and apply theory” (p. 126). What is a “real-world problem”?

Browsing through “standards”, I found quite a few statements about these mysterious critters. On p. 76 (middle-school part) it is said:

“The nonroutine problem situations envisioned in these standards are much broader in scope and substance than isolated puzzle problems. They are also very different from traditional word problems, which provide contexts for using particular formulas or algorithms but do not offer opportunities for true problem solving.”

What? What did they say about traditional word problems? What a nonsence! With their narrow experience the authors pretend to set standards! Are they aware of the rich resourses of excellent traditional word problems around the world? Let us read further:

“Real-world problems are not ready-made exercises with easily processed procedures and numbers. Situations that allow students to experience problems with “messy” numbers or too much or not enough informations or that have multiple solutions, each with different consequences, will better prepare them to solve problems they are likely to encounter in their daily lives”.

Pay attention that the author uses future tense. This means that he or she has never actually used such problems in teaching and never observed influence of this usage on his or her students’ daily lives. He or she has not even invented such problems because he or she does not present any of them. Nevertheless, he or she is quite sure that these hypothetized problems will benefit students. What a self-assurance!

After such a pompous promise it would be very appropriate to give several examples of these magic problems. Indeed, we find a problem on the same page, just below the quoted statement. Here it is:

Problem 48: Maria used her calculator to explore this problem: Select five digits to form a two-digit and a three-digit number so that their product is the largest possible. Then find the arrangement that gives the smallest product.

This is a good problem, although rather difficult for regular school because having guessed the answer, Maria needs to prove it. But the author never mentions the necessity of proof. What does the author expect of calculator’s usage here? It can help to do the multiplications, but it cannot help to prove. It seems that the author expects Maria to try several cases, to choose that one which provides the greatest product and to declare that it is the answer. But what if the right choice never happened to come to her mind? This is very bad pedagogics. Also let us notice that Maria is expected only to “explore” this problem rather than to solve it. According to my vision, exploration is the first stage towards a complete solution. Do the authors expect Maria ever to attain a complete solution? Do they want children to solve problems or just to tamper for a while?

But let us return to our main concern: so-called “real-world problems”. Notice that this problem has none of the qualities attributed to these mysterious critters on the same page: there is neither too much nor not enough information and there are no multiple solutions, each with different consequences.

One colleague noticed that the book still contains some problems described on page 76. Indeed, there are, but in another document. Here is one of them:

Problem 49: You have 10 items to purchase at a grocery store. Six people are waiting in the express lane (10 items or fewer). Lane 1 has one person waiting, and lane 3 has two people waiting. The other lanes are closed. What check-out line should you join?

I have never read any report about usage of this problem. Also I have never read any solution of this problem. Irresponsibility again!

What about problems with too much or not enough informations, they attract much attention in Europe lately, but European scolars want children to treat them critically and in many cases to refuse to solve them! Take for example that famous problem, after which Stella Baruk named her book [Baruk]. In the late seventies, the following problem was given to 97 second and third graders of primary school in France:

Problem 50: There are 26 sheep and 10 goats on a ship. How old is the captain? [Baruk], p. 25

76 children (out of 97) presented a numerical answer obtained by tampering with the given numbers. For instance, they might add the numbers and declare that the captain was 36 years old. Educators of several European countries (France, Germany, Switzerland, Poland) are very preoccupied by the fact that children “solve” unsolvable problems. The European educators would be very pleased if children refused to solve such problems with a comment like “It cannot be solved”. The European educators are quite right. But the same is true of what the “Standards” call “real-world problems”.

The most sound reaction to the problem 49 is “I don’t know”. But what a grade will an American student get after that?

TIMSS Advanced 2008 International Release

Hi,

The data were released yesterday in Norway: http://timss.bc.edu/timss_advanced/ir-release.html

Too bad the U.S. didn't participate.

Patsy

Ideologically-motivated intellectual gatekeepers

What Climategate and Discovery/Constructivist math have in common.

Narrow intellectual gatekeeping is omnipresent in academia. Want to know why the government wastes hundreds of millions of dollars on math and science programs that never seem to improve the test scores of American students?[3] Part of the reason for this is that today’s K-12 educators—unlike educators in other high-scoring countries of the world—refuse to acknowledge evidence that memorization plays an important role in mastering mathematics. Any proposed program that supports memorization is deemed to be against “creativity” by today’s intellectual gatekeepers in K-12 education, including those behind the Math and Science Partnerships. As one NSF program director told me: “We hear about success stories with practice and repetition-based programs like Kumon Mathematics. But I’ll be frank with you—you’ll never get anything like that funded. We don’t believe in it.” Instead the intellectual leadership in education encourages enormously expensive pimping programs that put America even further behind the international learning curve.

I like it. This will be widely distributed to our local educators.

Perhaps I should picket like this Climategate picketer (I have no idea who he is) at the entrance to NCAR (National Center for Atmospheric Research) in Boulder.

Imagine, that could be me!
Change title to "Discovery Math Protest Longmont, Colorado Day 1

Testing Shows Improvement in Shoe Tying

Recent testing has shown improvement in shoe tying by fourth and eighth graders over the past two years, although the growth has been stagnant in some districts. Urban school activists, however, can be encouraged by the statistical improvement in areas with populations of 250,000 or more. This continues an upward trend that started 6 years ago when this testing began.

Urban districts still face enormous issues of poverty and large numbers of English language learners. Forty-eight percent of 4th graders tested nationwide were eligible for free or reduced-price lunches. In spite of the improvements, many still point to the problem of the large shoe tying gap and the lack of properly trained teachers in urban areas.

Still others claim that they are testing the wrong things. "Kids don't want to tie their shoes", said Sarah Sandala. "The other kids would make fun of them if they did." She said she knows that the skill is important to get ahead in the world, but many kids might just decide to wear loafers. However, those in charge of the testing emphasized that some districts are willing to be held to high standards. "I think we are now safely walking on the right path.", said Dan Foote, chairman of the testing board.

Late, but unique opportunity

Hello,

I apologize for sending this message at such a late date. It is directed toward those flexible individuals in the DC area. ;->

There will be a workshop on fractions presented in DC by one of only two mathematics master teachers in Singapore on Friday, 11 December from 1 - 4:30pm. There are a few spaces available. If you are interested and able to participate, please email me: pwangiverson@gmail.com

Again, my apologies for the late notification.

Patsy

letter to the editor, part 2

11/30/2009

To the editor:

On November 24 I attended a school board meeting at which Renay Sadis, principal of Dows Lane Elementary School,^* gave a presentation she had rehearsed before superintendent Kathleen Matusiak earlier in the week.

Ms. Sadis’ report to the board did not mention student achievement. Focused entirely on “new initiatives” at the school, Ms. Sadis’ remarks were so empty of substance that one board member called her presentation a “commercial.”

During the time allotted to the audience for questions and comments, I asked the following questions:

How many remedial reading teachers does Dows Lane have on staff?

Answer: 3

How many general education students need remedial reading instruction?

Answer: Ms. Sadis did not know.

How many special education students - students with Individualized Education Plans - are enrolled in Dows Lane?

Answer: Ms. Sadis did not know.

How many of our students would score “Advanced” in reading on the National Assessment of Educational Progress (NAEP), the federal test known as “The Nation’s Report Card”?

Answer: Ms. Sadis had not heard of NAEP.

Finally, and most importantly, what are our plans to reduce the number of students who need remedial reading instruction?

Ms. Sadis, who last year commanded a salary of $165,000, had no answer.

I’d like to suggest that, going forward, the district consider recruiting teachers and administrators who have worked in successful charter schools here or in states where charter schools have been founded to teach high-SES student populations. A charter school is simply a public school with accountability and a tight budget; no one who has worked in a charter school would show up at a school board meeting not knowing how many struggling readers are in her school.

Educators who have come up through the ranks of the charter school movement have a different philosophy from those who, like Ms. Sadis and Superintendent Matusiak, have worked exclusively in traditional public schools. Where traditional public schools focus on compliance with state and federal mandates, charter school teachers and administrators concentrate on performance. Charter school educators are committed to the success of the individual child.

That is for the long-term, of course. In the short-term, I would like to suggest that the Board require administrators to devote themselves — and their presentations — to student achievement.

Catherine Johnson

The Rivertowns Enterprise
Friday, December 4, 2009
p 21

^* enrollment: 493; district per pupil spending: $28,291.

Teaching How Science Works, by Steven Novella MD at Neurologica Blog

Dr. Novella discusses particular curricula, and then makes an observation based on his childrens' experience.

Another way in which a good sounding idea for science education has been poorly executed on average is the introduction of hands-on science. Ideas are supposed to be learned through doing experiments. However, textbook quality is generally quite low, and when executed by the average science teacher the experiments become mindless tasks, rather than learning experiences.

I have two daughters going through public school education in a relatively wealthy county in CT (so a better than average school system) and I have not been impressed one bit with the science education they are getting. Here is an example – recently my elder daughter had to conduct an experiment on lifesavers. OK, this is a bit silly, but I have no problem using a common object as the subject of the experiment, as long as the process is educational. The students had to test various aspects of the lifesavers – for example, does the color affect the time it takes to dissolve in water.

The execution of this “experiment” was simply pointless. They performed a single trial, with a single data point on each color, and obtained worthless results that could not reasonably confirm or deny any hypothesis. By my personal assessment, my daughter learned absolutely nothing from this exercise, and afterwards complained that she was becoming bored with science.

Evidence in Education

As I've visited this blog over the past year or so, I've learned a lot about different viewpoints regarding education. It's been enlightening to say the least.

One thing has struck me lately: There is almost no reference to evidence when education is discussed. When I'm speaking about evidence, I'm talking about trials with the following characteristics:

1. The whole curriculum is tested, not just elements. Too often, we hear about curricula based on "research". Unfortunately, individual program elements, even if they are based on good science, don't translate into effective programs. For a curriculum to work, *all* the elements must work together to provide a positive result.

2. Many classrooms. I once spoke with an administrator about the need for evidence. His response was "well, there are just too many elements in a classroom to figure out what is working and what isn't." This is true if you're talking about a single classroom .. . we don't know if its the classroom teacher, those particular students, or some other factor. However, if we involve multiple classrooms at multiple schools, we start to get somewhere, as random factors start to cancel each other out. While this is expensive, curriculum developers, like drug manufacturers, should bear the burden of testing their curriculum *before* they introduce it to classrooms.

3. Beginning and end points. Often, medical researchers will talk about "end points" in a study. This refers to end outcomes that they are going to measure. In academia, this means 3rd party tests that make sure students know the material. These tests should be administered at a minimum before and after the "treatment" (i.e., the curriculum in question). To make sure the curriculum developer is dealing honestly, multiple 3rd party tests should be used, to make sure curriculum developers aren't gaming the trial by using tests that favor their curricula, and so outside parties can figure out which measure they trust if results are vastly different.

4. Controls. In medical trials, one group will get a placebo while the other gets the medicine. This doesn't apply directly, but curriculum developers can simply let schools either implement whatever curriculum they like, or they can stipulate a specific curriculum they'd like to test theirs against. Since the curriculum developers are claiming that their curriculum is better, then it should handily beat the other curricula, and this should show up in greater net achievement in beginning vs. end testing no matter what other curricula is chosen. If the chosen curricula can't achieve this result on the average, then the curriculum just isn't better.

This approach could change the whole game. One could imagine, for example, an FDA-like body for curricula. Publishers would have to submit their testing results to prove efficacy before the curriculum would be used in schools. So rather than testing the "treatment" on the next generation of children (e.g., whole language in CA in 1987), curricula would be tested *before* kids are subjected to them.

Nonjudgmental arenas for discovery

I'd love to know who the education writer is at the Onion.

"At Montessori, we believe dentistry is more than just the medical practice of treating tooth and gum disorders," school director Dr. Howard Bundt told reporters Tuesday. "It's about fostering creativity. It's about promoting self-expression and individuality. It's about looking at a decayed and rotten nerve pulp and drawing your own unique conclusions."

"In fact, here at Montessori, dentistry is whatever our students want it to be," Bundt continued.

If you feel yourself getting ill, just remember, the article is satire. It's supposed to be humorous.

A Potential Promising Venture by Some Education Schools

...and a few other entities.

Read about it here.

Precision Teaching In A Fuzzy World

Ever since I wrote the post "Do You Only Get What You Measure", I've been thinking about the impact of precision teaching and measurement as detailed in the links provided by PalisadesK . OT, but I would like to see an entire post sometime on where PalisadesK gets the time to find this stuff. If you're reading this, let me just interject here that you are an amazing resource, sort of like the Wikipedia of education without the half truths. Kudos!

Anyway, I've struggled with why such a common sense, obvious truth (precision measurement and teaching) seems to hit such disproportionate resistance to any such implementation by the education establishment. I'm so old that I have all sorts of ancient oblique anecdotes to sift through, and as I sifted through my old warehouse of stories, it hit me. I've been through this exact scenario before. I just never recognized the connection.

In the late seventies I was a test engineer for a computer company. In those days testing was pretty much an end of the line event. Hundreds of people built stuff, then threw it over the wall to a test system that found defectives and fixed them before shipping to customers. I'm over simplifying of course because there were always interim tests of subunits, but the important point to this discussion is that testing was, culturally at least, a post manufacturing event. Defects were intentionally passed on to others to resolve.

As products grew more sophisticated it became more and more difficult to build a high percentage of good units on your first try and the hypocrisy of passing on defectives became a problem. Eventually, most of what was built in its first pass was in fact bad. Simple probability worked against us as circuits went from tens of thousands of components to tens of millions of components. The cost of test machines skyrocketed to over ten million dollars a copy and the programming costs to bring one of these beasts on line soared along with the purchase price. A point was reached where it was physically impossible to test-in goodness as a post build event.

The forces of stasis in this culture were huge. Entire buildings had been erected to sustain this post test culture but in private enterprise stress causes change. You change or die without a monopoly position. In order to address this increasing complexity, testing evolved from a post build culture to one that was integrated into manufacturing. Instead of testing products after they were assembled you tested people, parts, machines, and processes before and during the process of putting them together. We found that if you perfected the front end you didn't have to test on the back end (as much) and ultimately some products had such high yields that if they were found (at some final system check) to be bad, this was such an infrequent event that it was economically unsound to fix them. Test engineering went from 'find and fix' to 'find and prevent'. This was an enormous paradigm shift that took a decade to complete.

In education we have a very analogous paradigm shift to work through if we want to get to precision teaching.

Today, we have a 'post build' culture. Kids are tested after being 'built' to see if they've gotten it or not. Where this process gets dicey is when it bumps up against the physical infrastructure of the ordinary school. Schools are a collection of rooms. There are 1st grade rooms and 2nd grade rooms and on and on. There are 1st grade teachers and 2nd grade teachers. There are 1st grade students and 2nd grade students. You get the idea. The infrastructure is entirely designed as a sequential set of processes in an assembly line with the kids passing though the system like little computer parts .

Once you understand this locked in, sequential infrastructure it's easy to see why you can't teach with precision. Teaching with precision creates 'rejects'. It creates students with identified deficiencies that need to be fixed. The most effective (for the status quo) testing system in this infrastructure is one that leaves deficiencies in a fuzzier state, otherwise how can you justify passing the 'part' down the line to the next assembly station. Only fuzzy measurement can possibly support this sequential structure. This is exactly like the old computer manufacturing. It knowingly passed defects down the line to the next step in the process. In this culture you don't hang a sign on the defective parts telling the world you just built junk. You just don't mention it.

Precision teaching would blow up this infrastructure!

Precision teaching tests to find out what to do next, not to produce a grade. So if you want to measure and teach with precision, the implication is that you must also build an infrastructure that is responsive to what you learn in your measurement. To navigate a paradigm shift from today's post test culture to a pre test culture, a culture where testing is designed as a prerequisite screen for 'the next step', the infrastructure has to have components equipped with a finer edge than the blunt sword of grade levels, teachers in rooms, and monolithic curricula.

The challenge for precision teaching is to devise an infrastructure to support it. If you do the testing right and uncover lots of little defects that need to be remedied before passing on the 'parts', then you need a structure that has a great variety of paths that can accommodate what you uncover with your precision. Instead of a sequential set of processes you need a web of processes that can provide for all the twists and turns that are the inevitable detritus of human interactions.


I'm convinced that precision teaching can not happen without fundamental change to the infrastructure and it is fear of this fundamental change which creates the illogical resistance to precision measurement and thus precision teaching . It's far easier to pretend that Johnny can add and pass him on, than to prove he can't and then have to do something about it.

"Practical Differentiation Strategies in Math"

I recently had the opportunity to attend an professional development seminar for elementary school math teachers. The topic was Practical Differentiation Strategies in Math.

It was a dinner-and-talk event. Several schools sent several teachers, and occasionally an administrator, to socialize and the listen to a 90 minute presentation. There were somewhere around 3 dozen people in attendance.

The talk was given by Liz Stamson, a math specialist with Math Solutions. You can see a related set of slides for a talk by her here. Those slides are for the webinar at this link to differentiation.

Stamson's talk was more specifically geared to engaging the math teachers. She spent most of her time talking about creating lesson plans and assignments that met the goals of differentiated instruction.

Stamson's talk assumed the full-inclusion classroom. She began the talk by saying that teachers were already needing to address students that could have vastly different "entry points" into the math curriculum. No mention was made of whether this was good or bad, whether grouping by ability was a help or hindrance. Full inclusion was a fact for teachers, not a point of argument.

Given that, she said, differentiation (that was the phrase, not differentiated instruction) was a way to help teachers engage all of their students. She stressed that differentiation could occur in content, process, and product. Her main ideas in how to differentiate content were to create "open tasks": questions that didn't have set answers, but had a multitude of answers. For example:

"what is the perimeter of a rectangle with length 10 and width 3", is a "closed" task. It has one answer. Such closed tasks, with one solution, and no critical thinking, does not lend itself to a differentiated classroom.

Instead, she promoted "open tasks" and "choice." What she meant by "open tasks" were problems that don't have one answer. By "choice" she meant allow the students to choose which problems on a problem set they must do. For example, instead of asking the above perimeter question, one could ask "describe a rectangle whose perimeter is 20." Such a task "opens" the problem to more creative thinking, allowing the more advanced students to find their own solutions (or to find a set of solutions), while still allowing the minimally skilled students to contribute. She said she'd offered the following "assignment" to her students, she said : "Do all the problems whose answers are even." This promotes critical thinking, she said, as they must investigate all of the problems to learn which ones fit the criteria.

She illustrated an open task with the "Which Does Not Belong" problem.

She gave the following sets:
2, 5, 6, 10
9, 16, 25, 43
cat, hat, bat, that

She asked the teachers to "work" the following problems. Teachers were seated together by grade (rather than by school), and were asked to collaborate. For each set, remove one item. Find a rule by which all of the remaining elements belong to the set, but the removed one does not. Repeat for all items.

The teachers gave a variety of answers.
Someone said that with the 2 removed, the remaining numbers' words were in alphabetical order. One said that with the 5 removed, the remaining numbers could all be written by 3 letter words. Another said all the remaining numbers were even. With the 10 removed, the remaining numbers were single digits said someone. With the 6 removed, the numbers formed a set of divisors of 10 (or alternately formed the number sentence 2 * 5 = 10.)

Ms. Stamson used this variety of answers to illustrate her point: all answers were valuable, no one had to get the "wrong" answer, even if some students didn't see immediately what the others did. This was practical differentiation--the more complicated patterns were found by the more advanced students, the less in depth by the students with less skills, but all could satisfy the assignment. The later grades could use factors, fractions, or other mathematical terms more appropriate to their lessons, while the younger grades could do this assignment with words or pictures if necessary.

She encouraged the teachers to create their own sets during this talk, stopping for several minutes.

Differentiation of process and product seemed to mean giving out different problems/homework/quizzes to different children. She advocated designing assessments/quizzes with several problems whose values were weighted, and requiring the student to complete a certain total value of problems, but allowing the students to pick which to do. The simplest problems were worth 1 point, say, and the hardest 10, and 15 points were needed for completion of the assignment. She suggested that such choice allowed all student to build confidence. She said also that it allowed a teacher to be "surprised" by a student who did difficult problems when the teacher expected to only do the easiest problems (as well as surprised when a good student did only the easiest). She also offered that the best students would challenge themselves and do all of the problems, so this provided a way to meet their needs for more or harder work.

When a teacher asked whether such choices were really practical, she admitted that such assignments might not be practical for daily practice, but suggested simply offering different students different problems. "Do you actually suggest assigning different problems to each student?" one teacher asked. Yes, she said: just hand out a worksheet, and highlight problems 3,4, and 7 for one child, and 1, 8, 9 for another. "If the culture of your classroom celebrates differences, then it's natural. We are all different, so of course we all have different strengths, and we all do different practice problems."

I could not tell from my vantage point, seated with a few lower grade teachers, if the room generally viewed the talk favorably. I assume the answer was yes, as who would attend such an evening if they were not already so inclined? The teachers at my table were quite dutiful at doing her assignments to us during dinner, and took very seriously everything she was saying. There were few questions from the audience, though. I couldn't tell, but perhaps that's just the style of talk, or the general behavior of a Minnesotan audience.

What is new with the science on math disabilities?

Wednesday, December 02, 2009

Atypical numerical cognition, dyscalculia, math LD: Special issue of Cognitive Development

A special issue of the journal Cognitive Development spotlights state-of-the-art research in atypical development of numerical cognition, dyscalculia, and/or math learning disabilities.

Article titles and abstracts are available at Kevin McGrew's excellent IQ's Corner blog.



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Joe Elliot on dyslexia:

"Contrary to claims of ‘miracle cures’, there is no sound, widely-accepted body of scientific work that has shown that there exists any particular teaching approach more appropriate for ‘dyslexic’ children than for other poor readers."

I am in agreement with Elliot.

I wonder if the same will be found to be true for dyscalculia and kids who struggle with math.

"deep shift in the makeup of unions"

in the Times:

A study has found that just one in 10 union members is in manufacturing, while women account for more than 45 percent of the unionized work force.

The study, by the Center for Economic Policy Research, a Washington-based group, found that union membership is far less blue-collar and factory-based than in labor’s heyday, when the United Automobile Workers and the United Steelworkers dominated.

[snip]

About 48.9 percent of union members are in the public sector, up from 34 percent in 1983. About 61 percent of unionized women are in the public sector, compared to 38 percent for men.

[snip]

The study found that 38 percent of union members had a four-year college degree or more, up from 20 percent in 1983. Just under half of female union members (49.4 percent) have at least a four-year degree, compared with 27.7 percent for male union members.

[snip]

The percentage of men in unions has dropped sharply, to 14.5 percent in 2008, from 27.7 percent in 1983, while the percentage for women dropped more slowly, to 13 percent last year, from 18 percent in 1983. For the work force over all, the percentage of workers in unions dropped to 12.4 percent last year, from 20.1 percent in 1983.

Economix: Union Members Getting More Educated




The 2002 Census shows that "more than one-quarter" of adults hold a college degree.

Amongst union members, that figure is 37.5%.

Do You Only Get What You Measure

I attended an interesting faculty meeting today. These are once a month affairs where we are tasked to work on a continuing project. The current project was for each grade level team to analyze our state test data and report out on any significant findings along with ideas on what we might do to mitigate any adverse findings.

Math was the first topic. Turns out (no surprise here, we've been doing this since the seas parted) number sense is a big deal. It's the highest percentage test item and also where we do the poorest.

When the elementary teachers made their presentations they described their efforts in this very area of arithmetical calculation, number sense stuff. Since I'm pretty frustrated with my kids' lack of ability in this domain, my ears were perked. They work really hard on this. I know this from personal observation. But, there was one omission.

Someone asked how many kids leave third grade knowing how to add. Crickets! It's not measured.

I posed a question about what is meant by 'knowing how to add'. Crickets! There is no criteria.

Then I was asked what I meant by asking that. My response had to do with objective measurement vs. subjective measurement. Crickets! Nobody has objective measures.

Here's what the consensus answer was (I'm paraphrasing). "We have a pretty good idea what most of our kids can do when they leave us." There you have the big omission. We have a completely fuzzy string of descriptors all wrapped up in one sentence; pretty good, most of, and can do. Not only is there no objective measurement taking place, there isn't even an awareness of what one should look like.

Suddenly the scales dropped from the eyes of this grasshopper. We're getting what we measure! Subjective measures lead to subjective results. We aren't asking for kids to know facts. We're asking kids to get answers and it's perfectly OK if they do this with fingers, toes, and mystical incantations to math gods. We even meet the, by God, state standards with this fuzz as they ask for no more.

I'm of the school that says if you can't measure it then it doesn't exist. Have we reached a point that it is culturally unacceptable to do anything that isn't fuzzy? Am I working in a measurement resistant culture? To me, with my background, uncovering fuzziness is just an indicator that I need to do more work to expunge the fuzz. To my colleagues it seems like fuzziness is not a clue, it's an objective.

Please, just disabuse me of this if you think I've just had too much coffee, but I think it would be really interesting to find out if there has ever been a correlation study in education to see if it's true that "You get what you measure." From this anecdote it sure seems to have some truth to it.