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Showing posts with label comprehension. Show all posts
Showing posts with label comprehension. Show all posts

Wednesday, October 22, 2014

Rote understanding

Late to the party ---- I've just read Barry's "Undoing the ‘Rote Understanding’ Approach to Common Core Math Standards"!

I love that phrase: rote understanding.

Exactly.

I was interested to see that Barry was taught "making ten" when he was in grade school:
The “making ten” method is included in the math program used in Singapore—a nation whose fourth and eighth graders have consistently obtained the highest scores in international math tests. Specifically, in Singapore’s Primary Math textbook for first grade, the procedure for adding by “making tens” is explained. Of particular importance, however, is that the procedure is not the only one used, nor are first graders forced to use it. This may be because many first graders likely come to learn that 8 + 6 equals 14 through memorization, without having to repeatedly compose and decompose numbers in order to achieve the “deep understanding” of addition and subtraction that standards-writers—and the interpreters of same—feel is necessary for six-year-olds.

“Making tens” is not limited to Singapore’s math textbooks, nor is it by any means a new strategy. It has been used for years, as it was in my third-grade arithmetic textbook, written in 1955...
I have a question about the teacher's explanation of the number 6:
“So if we can partner 9 to a number and anchor 10, we can help our students see what 9 plus 6 is. So we’re going to decompose our 6, and we know 6 is made up of parts. One of its parts is a 1 and the other part is a 5.
How do mathematicians think about whole numbers?

Do they see them as "made up of parts"?

Or as decomposable into parts?

(Or both --- ?)

To me, "made up of" and "decomposable into" seem like two different things.

Another question: if 6 is "made up of parts," is 6 one of the parts?

Is 0?

I bet right this minute there are kids all over America who are royally confused by the ramifications of making ten.

Thursday, March 18, 2010

cumulative practice

I've been meaning to get a post up about this article for years now. I think it's incredibly important (relates to Direct Instruction, too).

No time to write now, but here's the abstract:

THE EFFECTS OF CUMULATIVE PRACTICE ON MATHEMATICS PROBLEM SOLVING (pdf file)
KRISTIN H. MAYFIELD AND PHILIP N. CHASE
JOURNAL OF APPLIED BEHAVIOR ANALYSIS
2002, 35, 105–123
NUMBER 2 (SUMMER 2002)

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.


Note: the effects of cumulative practice on problem solving.

Not "procedural fluency" or "automaticity" or "mastery" etc.

Problem solving.

The path to problem solving goes through a particular form of practice - cumulative practice - not through "do the problem 3 ways" (Trailblazers) or "explain how you got your answer."

Wednesday, February 10, 2010

Yet another thing our education experts may have backwards

Besides their confusion of that which is largely development and shouldn't factor into grades (e.g., organization skills) with that which isn't (e.g., math skills), and their confusion of that which most children learn implicitly without deliberate classroom interventions (e.g., social skills) with that which most children do not learn implicitly (e.g., reading, foreign language) and their confusion of that which is best done outside of school (e.g., board games and movies) with that which is best done at school (e.g., the multiplication tables), there's the issue of text-to-self connections in reading.
Text-to-self connections are highly personal connections that a reader makes between a piece of reading material and the reader’s own experiences or life. An example of a text-to-self connection might be, "This story reminds me of a vacation we took to my grandfather’s farm."
So explains the Florida Online Reading Professional Development site, a site dedicated "to providing quality professional development services and support to Florida educators in effective reading instruction through its online course, expert staff, quality resources, and other professional development services."

The ability to make text-to-self connections, FORPD states, is part of what distinguishes good readers from poor ones (emphasis mine):
Good readers draw on prior knowledge and experience to help them understand what they are reading and are thus able to use that knowledge to make connections. Struggling readers often move directly through a text without stopping to consider whether the text makes sense based on their own background knowledge, or whether their knowledge can be used to help them understand confusing or challenging materials. By teaching students how to connect to text they are able to better understand what they are reading (Harvey & Goudvis, 2000). Accessing prior knowledge and experiences is a good starting place when teaching strategies because every student has experiences, knowledge, opinions, and emotions that they can draw upon.
The cognitive science literature, however, suggests that text-to-self advocates may have it exactly backwards.

Consider, for example, a paper by Courtnay Norbury and Dorothy Bishop entitled "Inferential processing and story recall in children with communication problems: a comparison of specific language impairment, pragmatic language impairment, and high functioning autism." This paper finds inferencing difficulties characterizing all poor readers with the above conditions. What Norbury and Bishop find, however, isn't that these readers weren't able to make inferences, but that they made the wrong ones. For example, when asked, in reference to a scene at the seashore with a clock on a pier, "Where is the clock?", many children replied "In her bedroom."

Norbury and Bishop propose that these errors may arise when the child fails to suppress stereotypical information about clock locations based on his/her own experience. In support of this hypothesis, they cite Morton Gernsbacher's book Language Comprehension in Sentence Building, which provides evidence that adults with poor reading difficulties are less able to suppress irrelevant information. As Norbury and Bishop explain it (emphasis mine):
As we listen to a story, we are constantly making associations beween what we hear and our experiences in the world. When we hear "clock," representations of different clocks may be activated, including alarm clocks. If the irrelevant representation is not quickly suppressed, individuals may not take in the information presented in the story about the clock being on the pier. They would therefore not update the mental representation of the story to include references to the seaside which would in turn lead to further comprehension errors.
Text-to-self connections, in other words, may be the default reading mode, and not something that needs to be taught. What needs to be taught instead, at least where poor readers are concerned, is how not to make text-to-self connections.

I'm neither a reading specialist nor a cognitive scientist, but my gut feeling is that, while accessing general background knowledge helps with reading comprehension, accessing personal background knowledge does indeed lead you astray. Text-to-world, OK, fine; but not text-to-self.

Especially, I imagine, for those most entrenched in the self, for example, children on the autistic spectrum.

Friday, December 18, 2009

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.

Tuesday, January 16, 2007

interview with Willingham

(Cross-posted at D-Ed Reckoning )

EdNews has a good interview with Daniel Willingham posted today on "reading comprehension:
6) What are your three main factors that you see as important in reading comprehension?

Decoding, fluency, and background knowledge. Obviously, if you can't decode, it's pretty much "game over." And if you don't have some degree of fluency, you're so occupied with decoding, that you can't pay attention to the meaning of the text. Finally, if you don't have some background knowledge to which you can relate the text, you may comprehend it, but your understanding will be pretty shallow—it will be closely tied to the text itself, and you won't be able to generalize the message of the text
There you go: decoding, fluency, and background knowledge. Three things that don't get systematicallt taught in your typical balanced literacy classroom.
Here's a question: "To what extent have educators and policy-makes recognized the importance of background knowledge to reading comprehension?" My answer would be "not enough!" I'm specifically concerned about the role of the National Reading Panel report. That Report is becoming crystallized in state and federal legislation as the final word on reading, and the report is great. . . but it's incomplete because it doesn't say anything about the role of background knowledge in reading comprehension. If we're concerned about having students who are good readers we have to recognize that reading is an interaction between the words on the page and the knowledge in the reader's head. Without background knowledge, you can't comprehend a text to a level we would call "understanding." We need to pay attention to developing background knowledge in students from the first day that they are in school, and encouraging parents to do so even before then. It's not a trivial matter to decide what that content should be and how to deliver it. But if we want all children to be excellent readers it has to be done.
Background knowledge: the untaught subject. Read the whole thing.
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