I write that Mathematics is a Simulacra, what I consider to be a liberating recognition that maths is a human endeavor, it is created by people rather than discovered as an ontological reality.
Andreas Quale wrote a nice paper that allowed me a fun curiosity for the evening.
Maybe it is productive and/or interesting to view this discipline of mathematics as a human-invented game, with a evolved set of rules that have created a wonderful space that is so at the limits of our minds that we cannot recognize it as such--a game, akin to chess, that is fixed, bounded, determined, one of many possible. Basically, that clearly this particular mathematics is relative to its rules, rather than a real thing.
Some other species peers down upon us like rats in a maze. We don't see our own constraints.
Friday, February 8, 2013
Thursday, February 7, 2013
what do I think of the CCSS?
I bumped into a longtime colleague and fellow survivor of the CA Math Wars at the Creating Balance conference a couple weeks ago. She sent me this article and asked my opinion of the CCSS. I sat and wrote back, allowing some anger to emerge. Maybe you'll notice...
http://www.edweek.org/ew/articles/2013/02/06/20commoncore_ep.h32.html?tkn=XWZFeU8Olfm083V0xBy70dDbpDLjBvdWdUAJ&cmp=clp-edweek
Thanks for sharing this. I have strong, but unreconciled opinions about the CCSS (and CCSS-M). Some unedited thoughts, maybe sequential, maybe nonsensical. [maybe I needed to attend school when there were standards for writing]
This sums up my general feeling about them, "Through the common core, public schools will be used to foster "economic fascism" in education, charged former U.S. Rep. Bob Schaffer, a Republican from Colorado." [dare I agree with a republican?]
The ideal of standards as they first emerged in math ed during the 90's reflected my values of what they might offer--a vision, an opportunity for professional discussion / learning, an opportunity for serious and focused debate over what to teach (e.g. NCTM's 1989 standards for curriculum & evaluation), how to teach (e.g. NCTM's 1991 professional standards), and possibly more.
But they turned away from professional guides to a hammer of accountability, at about the time of the 2000 NCTM Standards. By then, NCTM was viewing itself as a corporation that needed to give its customers what they wanted, rather than serve as a vision for the profession. They sidled up with corporations (the first I noticed, and called him on it, was Lee's connection with Duke Energy. Now, the drive for a "national curriculum" seems to only meet the needs of corporations (textbook publishers, test publishers, we'll come fix your school yokels, we'll run our own schools, etc.) who will be able to create a greater profit margin. This corporate agenda, rather than one about the health, happiness, and welfare of children, as well as our citizens. The hammer of accountability works efficiently to cleanly carve up a radically classist society.
What is more insipid is the propaganda behind efforts for standards, learning math, etc. We need math and science for our economy. That said right after saying our schools are failing in teaching math--while the UCA (United Corporations of America) is by far the wealthiest and most powerful nation in the world. The propaganda machine also sends the message, Math is Power (recall this NCTM campaign?). Well, logic might not say that implies no math means no power, but that is how humans, worse--children, interpret that message. A message that is if not directly stated, the undercurrent in virtually every school in this amerika. We have our success-stories in mathematics, often times a girl or a black boy, held up by white oligarchs' EXCEPTIONAL underclass child-the model to follow if blacks want to achieve this Amerikan Dream.
I guess I am losing focus on the CCSS. How might they be good (maybe)? By providing opportunity for professional discussion. At this time, I see teachers either being pressed to wonder, how will I teach kids "mathematical practices" - or thrilled to feel relieved of that crap they've felt they had to drive into the heads of kids for a decade, none of which was meaningful or fun to teach or learn. To quote a pair of Vista school district teachers who survived the Math Wars here in north county San Diego, "you mean, we are allowed to use these materials (IMP) again?" -- said to their district math specialist.
But, I hate the accountability and associated punishment and threat, as well as the carrot-dangling (the way money plays in this is sick).
I hate the standardization of thinking. The discipline of math does itself a disservice by trying to create a singular way of knowing, a narrow view of mathematics and of mathematical knowledge. It closes itself off to opportunity for knowledge creation. Further, it shuts out potentially more mathematicians by FAR than it invites in. (I suppose this serves mathematics and mathematicians well, however. The pinnacle of knowledge-power in amerikan society, if not $, its perceived intelligence, where mathematicians reside on the highest of thrones.)
I hate the soul-crushing message they send to children who can't/don't.
It is practically comical these are written seemingly without any awareness for who amerika is. Seriously, remove the schools from the nations wealthiest 25% counties/districts and re-consider what the goals of education ought to be. Take out the corporations need for workers. Take out the classist societies' need for a mechanism to delineate haves and have nots. Take out this seemingly human need [i don't believe this] to be better than another. Take out the governments' need for an emasculated citizen. Look at the child.
Every child is mathematical. No child NEEDS to learn mathematics--the discipline. Why are we as teachers so confused about what we should do?
Because we are each a success of a system that told us not to listen to our heart, not to listen to our body.
No grand conclusion for you. Just and end to my ramblings.
-brian
http://www.edweek.org/ew/articles/2013/02/06/20commoncore_ep.h32.html?tkn=XWZFeU8Olfm083V0xBy70dDbpDLjBvdWdUAJ&cmp=clp-edweek
Thanks for sharing this. I have strong, but unreconciled opinions about the CCSS (and CCSS-M). Some unedited thoughts, maybe sequential, maybe nonsensical. [maybe I needed to attend school when there were standards for writing]
This sums up my general feeling about them, "Through the common core, public schools will be used to foster "economic fascism" in education, charged former U.S. Rep. Bob Schaffer, a Republican from Colorado." [dare I agree with a republican?]
The ideal of standards as they first emerged in math ed during the 90's reflected my values of what they might offer--a vision, an opportunity for professional discussion / learning, an opportunity for serious and focused debate over what to teach (e.g. NCTM's 1989 standards for curriculum & evaluation), how to teach (e.g. NCTM's 1991 professional standards), and possibly more.
But they turned away from professional guides to a hammer of accountability, at about the time of the 2000 NCTM Standards. By then, NCTM was viewing itself as a corporation that needed to give its customers what they wanted, rather than serve as a vision for the profession. They sidled up with corporations (the first I noticed, and called him on it, was Lee's connection with Duke Energy. Now, the drive for a "national curriculum" seems to only meet the needs of corporations (textbook publishers, test publishers, we'll come fix your school yokels, we'll run our own schools, etc.) who will be able to create a greater profit margin. This corporate agenda, rather than one about the health, happiness, and welfare of children, as well as our citizens. The hammer of accountability works efficiently to cleanly carve up a radically classist society.
What is more insipid is the propaganda behind efforts for standards, learning math, etc. We need math and science for our economy. That said right after saying our schools are failing in teaching math--while the UCA (United Corporations of America) is by far the wealthiest and most powerful nation in the world. The propaganda machine also sends the message, Math is Power (recall this NCTM campaign?). Well, logic might not say that implies no math means no power, but that is how humans, worse--children, interpret that message. A message that is if not directly stated, the undercurrent in virtually every school in this amerika. We have our success-stories in mathematics, often times a girl or a black boy, held up by white oligarchs' EXCEPTIONAL underclass child-the model to follow if blacks want to achieve this Amerikan Dream.
I guess I am losing focus on the CCSS. How might they be good (maybe)? By providing opportunity for professional discussion. At this time, I see teachers either being pressed to wonder, how will I teach kids "mathematical practices" - or thrilled to feel relieved of that crap they've felt they had to drive into the heads of kids for a decade, none of which was meaningful or fun to teach or learn. To quote a pair of Vista school district teachers who survived the Math Wars here in north county San Diego, "you mean, we are allowed to use these materials (IMP) again?" -- said to their district math specialist.
But, I hate the accountability and associated punishment and threat, as well as the carrot-dangling (the way money plays in this is sick).
I hate the standardization of thinking. The discipline of math does itself a disservice by trying to create a singular way of knowing, a narrow view of mathematics and of mathematical knowledge. It closes itself off to opportunity for knowledge creation. Further, it shuts out potentially more mathematicians by FAR than it invites in. (I suppose this serves mathematics and mathematicians well, however. The pinnacle of knowledge-power in amerikan society, if not $, its perceived intelligence, where mathematicians reside on the highest of thrones.)
I hate the soul-crushing message they send to children who can't/don't.
It is practically comical these are written seemingly without any awareness for who amerika is. Seriously, remove the schools from the nations wealthiest 25% counties/districts and re-consider what the goals of education ought to be. Take out the corporations need for workers. Take out the classist societies' need for a mechanism to delineate haves and have nots. Take out this seemingly human need [i don't believe this] to be better than another. Take out the governments' need for an emasculated citizen. Look at the child.
Every child is mathematical. No child NEEDS to learn mathematics--the discipline. Why are we as teachers so confused about what we should do?
Because we are each a success of a system that told us not to listen to our heart, not to listen to our body.
No grand conclusion for you. Just and end to my ramblings.
-brian
Friday, November 9, 2012
Math & Jazz: Learn by Doing or by Training?
Healthcare professional's first pronouncement when beginning study in the field is to do no harm. Could we teach mathematics if we asked teaching students the same question?
more to follow...
more to follow...
Wednesday, August 15, 2012
A Constructivist's View on Teaching Mathematics (for Social Justice)
This post is a long reply to Bryan Meyer's April 22, 2012 post at Doing Math.
Bryan, you won't be surprised in what I say. I think you've made a fundamental error of seeking to compare two very different issues, a theory for knowing (constructivism) with a theory for teaching (discovery learning). If you address constructivism as a method for teaching, there is no core base for which to make decisions on how to act. What seems to exist in the literature are no more than others' grievous misunderstandings / bastardization of constructivism.
If you treat discovery learning as a theory for knowing/learning, I would say you are much more strongly aligned to a segment of learning theorists who may not fully embrace the "radical" component of constructivism, that we have no access to reality and thus could not "know" in a manner that had been previously taken for granted. These sorts of more modern theory for knowing, that seem to be taken for granted in this "discovery learning" idea, do embrace a similar principal--that the learning mind is an active one--and thus are often labeled constructivist in some way. However, these constructivisms are "trivial constructivism."
Moving beyond the initial problem of your comparison--the titles of the two columns--I find your questions intriguing.
1. The point you attribute to Social Constructivists (SC) is what they believe to be what distinguishes them from (Radical) (Piagetian) Constructivists (RC). They are in error. In fact, Piaget gives great emphasis to the role of social interaction. SC's actual distinction from the RC is the manner in which they fail to deal with this "reality", what the RCist names "intersubjectivity" -- a taken as shared way of knowing. The response to this question, to me as a RCist, is that this is fundamentally not a question I would ask. As someone interested in SJ, I would argue that as soon as you ask the question, you have created an unjust space between people--there is no way that one could be deemed not correct, nor more correct. Each is assumed to be "correct," i.e. viable, for that other autonomous being. That to me is the healthy way of interacting with the other.
To pursue this question, briefly, in greater detail--I wish to deconstruct the portion of the question, "when students agree upon an ontological reality." I read this to mean that the students recognize themselves as several autonomous agents (cf. Maturana & Varela) have knowingly come to an intersubjective agreement about what they are intentionally thinking of as an "ontological reality." I take the students to be RCists in terms of their personal epistemologies; I assume they have agreed to intentionally give an "existence," albeit it unknowable or otherwise, to some mathematical construct. (I state all of this because it is how we most often operate in mathematics--we assume some entity to exist, and then operate on that notion as if it were an object.)
With this clarification, I would suggest that this opening condition you have created, when students agree on a reality and intentionally determine it to be different from that of the teacher or the mathematics community, I would suggest that is the pinnacle of educational success: when the child refuses the oppression of other's ways of knowing.
2. This question to me is fundamentally Dewey's in The Child and the Curriculum. In considering your question, first I encourage both you and myself to recognize your role as an observer in considering the various portions of the inquiry, such as "more consistent with that of the mathematics community" -- that is a statement made by you, the observer. It says you see what you think to be the knowing you as teacher press towards to be that of the knowing you attribute to the mathematical community. Ultimately, what your question says, as a RCist, is that you are pressing the students to know as you to.
I simplify the dilemma posed here for myself in such a way that the dilemma simply no longer exists. Basically, there is no other way of interacting with the other. We always "draw" them toward our ways of knowing. It is our mind's way of seeking to maintain equilibrium.
Getting back to my basic read of your Question #2: Does the Constructivist learning theory imply a "Discovery Learning" pedagogical theory? I say no; it is dependant on the teacher's personal epistemology. If the teacher is a Constructivist, they would recognize the decision they make about accepting or rejecting the ways of knowing of others. A Constructivist who acted in socially just ways would value other's ways of knowing, and not seek to use to their advantage power relations to preserve the self-proclaimed superiority of their knowing.
Dewey concludes, "The case is of child." "The formulated wealth of knowledge that makes up the course of study...says to the teacher: Such and such are the capacities, the fulfilments, in truth and beauty and behavior, open to these children. Now see to it that day by day the conditions are such that their own activities move inevitably in this direction, toward such culmination of themselves. Let the child's nature fulfil its own destiny, revealed to you in whatever of science and art and industry the world now holds as its own."
3. I think my responses to 1. and 2. provide my answer to question 3. It is "agreed!" provided the teacher sees those content standards as anything other than what Dewey recommends. This allowance for "measuring against a greater authority" is some perverse myth, if not a blatant bigoted oppression. It is my believe that there are MANY powered structures, including those of racial status, economic status, and intellectual status, that all benefit from mathematics being the pinnacle of the truth regime.
What is the purpose of mathematics education, and how can it be socially just?
- What is the purpose as math education is presently conceived? It is to replicate the racist society.
- How can it be socially just? Adults can respect children's ways of knowing. A teacher can conclude their days by observing the child's ways of knowing, and deem them to be mathematics. In fact, it is certain that they are mathematical; and there is no way of knowing otherwise.
I do think it is quite neat to have come to a very similar questioning by Luis Radford in his paper "Education and the Illusions of Emancipation." He seems to have limited himself, however, to a world of math education as it seemingly operates now; rather than what I have offered above.
Tuesday, July 17, 2012
My sister's can of worms
My sis, a Montessori teacher, asked Why do we need to invert the second fraction when we are dividing? I told her to go to the Kahn Academy!
Actually, here is her email. This has become an interesting curiosity for me. What can I "teach" "online" ? Why not jump in with the hairiest possible question, fraction division.
On Jul 16, 2012, at 4:08 PM, Mary Halase wrote:
So I have this question that I believe you could answer. Why do we need to invert the second fraction when we are dividing? so if I have 1/4 and you divide that by 1/3, why do we need to do the invert 1/3? I had an 8 year student ask me this question and for the life of me I could not answer that question, I just told him that is a rule that I have learned when I was young. He is the first student that has asked me that. I googled it and got some answers but the answers that I got seemed more confusing. So I would like you to help me with that question so that I understand it and that way I can go back and explain it to this young student. I am actually getting the answer to this question thru my montessori training. We are going into division with a fraction. Thanks for you help.Love,Mary
So, I made an attempt to respond to my sis (Mary). Oh, that is her real name. Please don't mis-treat her! She is a fabulous teacher--imagine, she actually asked the question "why is that?"!
This is really meant as an experiment to me, to begin to consider Sal Kahn's challenge--to communicate/develop understanding(?) of mathematics "online." I totally know it isn't a greatly designed experiment, nor do I have any idea where it will go. I am just (quickly) giving something a try, with my patient sister.
Here is what I wrote back:
This is really meant as an experiment to me, to begin to consider Sal Kahn's challenge--to communicate/develop understanding(?) of mathematics "online." I totally know it isn't a greatly designed experiment, nor do I have any idea where it will go. I am just (quickly) giving something a try, with my patient sister.
Here is what I wrote back:
My answer is that you have to make sense of this one for yourself. It is complex because a lot of operations (relationships) must be understood. Give this a try... (let me know!)
1. First, you must deeply understand division... both sharing and grouping ways of thinking. Do you? Play with that until each is second nature. Start with easy numbers, then use numbers that yield a fractional answer. Understnd what the fractional answer means.
2. Wait, why don't you go watch the Kahn Academy video <http://bit.ly/O5CWsa>?
3. OK - totally kidding. Might be a joke you don't get, but in the land of math teachers and math ed researchers, this stuff is the bane of our existence. Back to really trying to help...
4.a. After really owning division, now its time to really know fractions. Here are a few ideas, then problems. Begin by drawing some line segment. Call that one unit of length. Now split it into three equal parts. Notice each is the exact same size, and that when all three are put together, they create the "whole"--the one unit of length. For naming purposes, call each of those pieces "one-third". (You know the fractional symbol.) Etc. for all other "unit fractions" (a fraction with a "1" in the numerator)
4.b. Take "one-third." Match that with one more one-third, so you have 2 one-thirds. OK? [with kids, a teacher should repeat this kind of naming over and over, i.e. 5/7 is five one-sevenths]. Imagine 3 one-thirds. The same as one whole, right? 5 one-thirds? OK?
4.c. Note that might be written 1/3 + 1/3 + 1/3 + 1/3 + 1/3 , which is equal to 5/3. What is 2/3 + 1/3 =? 2/5 + 4/5 = ?
4.d. Next equivalent fractions. Split each of your 1/3 (from 4.a.) into four pieces. How big is each piece? It is one-fourth of the one-third, yes--but what portion of the original whole is it? That is, how many do you need to make the whole? Your reasoning should go, I need 4 of these to make one-third. And 3 one-thirds make one whole, so I need 4 x 3 = 12 of these new pieces. [Aside: when a kid can reason in this way, they know multiplication. Until then, multiplication is simply a modified addition for children. This is a profound way of knowing multiplication, some children do not develop this as a result of school- (or life-) based activities until early teens, or later. It seems that children around 10-12 typically can.] So the new piece is called a one-twelfth. Given this, children can create and identify equivalent fractions. When teaching, they should be allowed to be extremely creative, such as arguing that "three and one-half one-sevenths is the same as one one-half." OK?
4.e. Addition next (which is the same as subtraction). How much is 1/2 + 1/3? Figure this out, and why--with no algorithm. Keep in mind that you should be able to justify any renaming of a fraction through the rules of equivalence developed in 4.d. Notice the answer is five one-sixths. 5/7 + 3/5 = ? Answer is 46 one-thirty fifths. Children do this stuff, with lots of time andp lay, they get quite fluent at it... Subtraction is just as easy/hard (because subtraction is the same operation as addition, for the child--maybe not for the mathematician.)
4.f. Back to multiplication, which is easier than addition actually. What does 3 one-sevenths look like? Write this either as 3 x 1/7 or 3/7. So it is true that 3 X 1/7 = 3/7. (again, equivalence being emphasized).
_______ _______ _______ (I begin with 3, that is 3 one-wholes.)
------- ------- ------- (this part is two simply create/show the
length one-seventh)
After many whole number times fraction, where the first number means "for every unit in that first number, I must have the named number of units of the second number." Better said with the example. "For each of the three 'ones' I must have one 'one-seventh'." So 5 x 2/3 is "For each of 5 ones, I must have 2 one-thirds." So that is 10 total one-thirds, i.e. 5 x 2/3 = 10/3.
___ ___ ___ ___ ___ (this sketch shows the 5 ones)
--- --- --- --- --- (I redraw each of the ones with something
↓ ↓ ↓
- - - (the problem 3 x 1/7 states, for each of the
- - - (the problem 3 x 1/7 states, for each of the
original unit, I take 1 one-seventh of that
unit)
After many whole number times fraction, where the first number means "for every unit in that first number, I must have the named number of units of the second number." Better said with the example. "For each of the three 'ones' I must have one 'one-seventh'." So 5 x 2/3 is "For each of 5 ones, I must have 2 one-thirds." So that is 10 total one-thirds, i.e. 5 x 2/3 = 10/3.
___ ___ ___ ___ ___ (this sketch shows the 5 ones)
--- --- --- --- --- (I redraw each of the ones with something
equivalent, 3 one-thirds for each one the ones
seems helpful here)
↓ ↓ ↓ ↓ ↓
↓ ↓ ↓ ↓ ↓
-- -- -- -- -- (for each of the 5 ones, I take 2 one-thirds,
collecting 10 one-thirds in total)
What then, is 1/7 x 3? "For each of the one 'one-seventh' I must have three 'ones' (i.e. one wholes)
_______ (this sketch for initial reference, my initial whole
What then, is 1/7 x 3? "For each of the one 'one-seventh' I must have three 'ones' (i.e. one wholes)
_______ (this sketch for initial reference, my initial whole
(unit), to build my 7 one-sevenths)
------- (this is 7 one-sevenths)
- (this is my starting one-seventh. Next, for each of these
units, I take 3 (whole) of these units.)
↓
- - - (so, compared to the original unit, I have 3 one-sevenths.
1/3 x 1/5 = ?
_____ _____ _____ (this sketch for initial reference, to build my 3
_____ _____ _____ (this sketch for initial reference, to build my 3
one-thirds)
----- ----- ----- (this is 3 one-thirds)
----- (this is my starting one-third)
Next, for each of these units, I take 1 one-fifth of these units. That is for the one one-third, I need one-fifth one-thirds. So split this into 5 parts.
- - - - - (pretend that is the same length as the one-third
above. I will take one of these one-fifth of one-
third.)
↓
↓
- (compared to the original unit, what portion is
it? Well, I know I need 5 to make one one-third.
And I need 3 one thirds to make one unit, so I
need 15 of these pieces to make one whole; it is
one-fifteenth)
Work that out for:
1/2 * 1/5
3/5 * 1/2
2/3 * 4/7
5/4 * 1/3
11/7 * 5/3
5. Write a division problem. Re-read it as a grouping or sharing task. Solve it--with the sketches. This will allow you to argue WHY for your answer when you divide to fractional numbers. A key: remember, fractional numbers are just another number... (instead of 3 one-wholes, it may be 2 one-fifths)
Some examples that may help:
9 ÷ 3
12 ÷ 7
3 ÷ 5
1/2 ÷ 3
2/5 ÷ 8
1 ÷ 1/3
6 ÷ 3/5
5 ÷ 2/3
1/4 ÷ 1/3
3/4 ÷ 2/3
3/4 ÷ 5/3
6. After lots of playing, practicing, doing... kids may be ready to analyze what happens for any a/b ÷ c/d and generalize a rule like what you know.
7. Next problem for you is to write a contextualized (i.e. "real") problem for 3/4 ÷ 2/3.
I am sure you'll write me with a question, at some point...
-brian
Work that out for:
1/2 * 1/5
3/5 * 1/2
2/3 * 4/7
5/4 * 1/3
11/7 * 5/3
5. Write a division problem. Re-read it as a grouping or sharing task. Solve it--with the sketches. This will allow you to argue WHY for your answer when you divide to fractional numbers. A key: remember, fractional numbers are just another number... (instead of 3 one-wholes, it may be 2 one-fifths)
Some examples that may help:
9 ÷ 3
12 ÷ 7
3 ÷ 5
1/2 ÷ 3
2/5 ÷ 8
1 ÷ 1/3
6 ÷ 3/5
5 ÷ 2/3
1/4 ÷ 1/3
3/4 ÷ 2/3
3/4 ÷ 5/3
6. After lots of playing, practicing, doing... kids may be ready to analyze what happens for any a/b ÷ c/d and generalize a rule like what you know.
7. Next problem for you is to write a contextualized (i.e. "real") problem for 3/4 ÷ 2/3.
I am sure you'll write me with a question, at some point...
-brian
Sunday, May 27, 2012
Cogs in The Testing Machine
I find the conversation below to get at the heart of a problem I face in my "work." My work, I suppose, is often under the guise of serving math teachers, schools and districts, to raise test scores. I accept this rue so that I can do what I define to be my work, work for a social justice. My goal is that children, all children, are schooled in ways that maintain their authority for knowing, acting, and being in this world.
The conversation was sparked by an @AlfieKohn twitter post, which I past to a group of colleagues working HARD to improve the math teaching and learning experiences for students and teachers at a large number of high schools. Names have been changed to protect the innocent (and the damned)--that is, except my own.
Alfie Kohn (@alfiekohn)
5/26/12 5:16 AM
Video of kid being talked at about her scores (“data-based goal setting”): ow.ly/b7UKi. How *not* to do a tchr/stud conference
Hi all,
I share this video because the data factory that education seems to being asked to act as seems to go unquestioned in the schools I visit. Mostly, it seems to make it very difficult to think about how to do work with admin. who see no problem with the activity in this sort of interaction. Maybe said slightly differently, I find myself challenged to work with admin. beliefs acknowledging that they may see no trouble with this interaction.
-Brian
Brian- This video is ironic on so many levels. Watching it I am so appalled and yet I know for sure that in my district we pulled in all our students and did the exact same thing and were lauded for doing so! Watching the video makes me realize how meaningless and impersonal those conferences are. It seems ludicrous to imagine that this student will leave that conference with any concrete ideas for learning more math or with any sense that she is highly valued by the adults around her. I'm also wondering why, in this day and age, they would produce a video that is so blatantly non-diverse.
I think there are many fine administrators with idealistic goals for students and schools. They are being herded down a cattle chute in which the rhetoric about " what works" has centered on data. A few well -promoted successes in using data for school- wide reform resulted in large - scale, half-hearted, blindly executed imperatives that administrators have convinced themselves will help their teachers and their students. I think it only appears that they have lost sight of the real data source: students' thinking based on real work around learning math in class. I think we need to take back the agenda for school improvement and encourage the administrators who are looking for a way to re-gain a student- based approach to step up. We ned to promote and provide alternatives to balance this test score mania. Indeed early efforts in many districts centered on studying students' learning and understanding their thinking (for example re: learning). These innovative ways to look at students may have been ahead of their time but could be re- introduced to people looking for answers. Just thinking...
Happy Memorial Day. Heidi
Heidi, thanks for your thoughts. It is ironic (that may not capture my reactions totally, but at least in part) in many ways--diversity, total lack of relationship between teacher & student, I don't think the student voiced one thought of her own rather was given words and ideas and opinions by the adult, and more. It is also disturbing to me the way the student responds the whole time, as if this is OK, normal.
Yes, fine admin with idealistic goals. Parallel to most every teacher's classroom I experience with idealistic goals--yet their actions don't seem to match their beliefs. A challenge to me, someone who hopes to provoke possible realization of this incongruency, is to figure out how to create the space for the teacher or administrator to see differently their actions.
To paraphrase Neil Postman, children come with excellent crap detectors. How do I tap in to those still functioning mechanisms in adults, especially when the crap to be detected is tied up in their own identity?
-brian
The conversation was sparked by an @AlfieKohn twitter post, which I past to a group of colleagues working HARD to improve the math teaching and learning experiences for students and teachers at a large number of high schools. Names have been changed to protect the innocent (and the damned)--that is, except my own.
Alfie Kohn (@alfiekohn)
5/26/12 5:16 AM
Video of kid being talked at about her scores (“data-based goal setting”): ow.ly/b7UKi. How *not* to do a tchr/stud conference
Hi all,
I share this video because the data factory that education seems to being asked to act as seems to go unquestioned in the schools I visit. Mostly, it seems to make it very difficult to think about how to do work with admin. who see no problem with the activity in this sort of interaction. Maybe said slightly differently, I find myself challenged to work with admin. beliefs acknowledging that they may see no trouble with this interaction.
-Brian
Brian- This video is ironic on so many levels. Watching it I am so appalled and yet I know for sure that in my district we pulled in all our students and did the exact same thing and were lauded for doing so! Watching the video makes me realize how meaningless and impersonal those conferences are. It seems ludicrous to imagine that this student will leave that conference with any concrete ideas for learning more math or with any sense that she is highly valued by the adults around her. I'm also wondering why, in this day and age, they would produce a video that is so blatantly non-diverse.
I think there are many fine administrators with idealistic goals for students and schools. They are being herded down a cattle chute in which the rhetoric about " what works" has centered on data. A few well -promoted successes in using data for school- wide reform resulted in large - scale, half-hearted, blindly executed imperatives that administrators have convinced themselves will help their teachers and their students. I think it only appears that they have lost sight of the real data source: students' thinking based on real work around learning math in class. I think we need to take back the agenda for school improvement and encourage the administrators who are looking for a way to re-gain a student- based approach to step up. We ned to promote and provide alternatives to balance this test score mania. Indeed early efforts in many districts centered on studying students' learning and understanding their thinking (for example re: learning). These innovative ways to look at students may have been ahead of their time but could be re- introduced to people looking for answers. Just thinking...
Happy Memorial Day. Heidi
Heidi, thanks for your thoughts. It is ironic (that may not capture my reactions totally, but at least in part) in many ways--diversity, total lack of relationship between teacher & student, I don't think the student voiced one thought of her own rather was given words and ideas and opinions by the adult, and more. It is also disturbing to me the way the student responds the whole time, as if this is OK, normal.
Yes, fine admin with idealistic goals. Parallel to most every teacher's classroom I experience with idealistic goals--yet their actions don't seem to match their beliefs. A challenge to me, someone who hopes to provoke possible realization of this incongruency, is to figure out how to create the space for the teacher or administrator to see differently their actions.
To paraphrase Neil Postman, children come with excellent crap detectors. How do I tap in to those still functioning mechanisms in adults, especially when the crap to be detected is tied up in their own identity?
-brian
Friday, March 23, 2012
Knowledge as Fabrication
The following is an excerpt from a soon-to-be-published book chapter I wrote a bit ago. It happened across my email just after I made some Twitter comments about constructivism and the fascism of teaching styles that are predicated on Discovery Learning. Many people equate the two--constructivism & DL--mistakenly.
The mistake begins with the idea that constructivism, a theory for knowing and learning, has anything to say about teaching. Or that any teaching theory could be based on constructivist principles. The problem is that no matter how or what is taught, learning occurs. Constructivism helps to account for what is learned, and how it is known. It says nothing about the effectiveness or quality of the teaching.
I am willing to say that if a teacher embraces the ontologically agnostic (i.e. we cannot know whether objective truths exist) status of knowledge that constructivism posits, that her teaching may be quite radically different. Maybe this passage hints something at that, but I have more thoughts on teaching--I may post on those later. I do think Dewey got it right in the Child and the Curriculum (when read of course, as an ontological agnostic).
See more at Why Some Like it Radical.
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