Scaffolded Math and Science: Learning about Domain and Range

Scaffolded Math and Science: Learning about Domain and Range: This week in my Algebra 2 classes, we began learning about Domain and Range. After first introducing the topic, I got a lot of blank stare...

S-R learning models vs Discovery -

"Educational theorists no longer explain learning with behaviourist theories about stimulus-response connections. More recent studies recognize the role of the student in the feedback process"

I had a class in my masters program on learning and literacy - this was, concisely stated, the point of one of the learning units.

"They study the kind of feedback given and the context in which it is presented. What we now realize is that the message sent is filtered through the students perception as it becomes the message received"

hmmmm - isn't the point of s-r that the response is the result of filtered perception - filtered from the prior knowledge of how a response to given stimulus will be rewarded or punished.. I still stumble on this notion that the s-r folks are ignoring the individual in the model. Making it a black box isn't the same as ignoring it. Indeed, the notion of a block box, in engineering, comes from being able to characterize the function of an item based on what output it gives to input. If all the characteristics of output as a function of interesting inputs can be described then the black box is in fact, for all practical purposes, known. It's not exactly that the box is ignored, it's characterized from the outside.

"The student's job is to make meaning from schoolwork, not to respond to stimuli", well yes ok i would mostly agree. Yet still, I have students that can make meaning out of multiplication but don't respond correctly to stimuli such as what is 7x6. They can make meaning with pictures and groups and yet their lack of fluency causes exploration of deeper problems to get sidetracked by what should be rote knowledge.

The above was all from Brookhart, S (2008) page 3 - How to give effective feedback to your students. ASCD.

Speaking to the above point is this quote from a different source, "Research on expertise in areas such as chess, history, science, and mathematics demonstrate that experts' ability to solve problems depend strongly on a rich body of knowledge about subject matter" (p.9). In other words, experts in their field know stuff and use it make meaning and solve problems. It sometimes seems to me that modern pedagogy attempts to short cut to the meaning and problem solving before there's some stuff to work with.

The above from Bransford, J et. al.(2000), How people learn: brain, mind, experience and school. National Academy Press.

on the occasion of our common assessment planing session

The quality of curriculum is not strained,
It droppeth from gentle clouds of essential knowledge like unto rain.
Upon upturned faces it does fall,
it giveth both tools and skills to those both big and small.
It yields that one thing which can perceive the boundless universe in its all,
a new idea that grows like a vine upon the scaffold of bloom’s taxonomy lifted tall
The proximate reach is made just a little more
by standing upon the shoulders of those who lived and wrote and thought before.

a day at a severly normal school

Report from a day at a severely normal school.

I subbed at a BVSD school on Friday Oct 3. It’s my first sub day this year. I make a few bucks on a Friday and also get to expand my knowledge of how schools other than NAS work.

I LIKE working at my school. The more I do it, the more I like our kinds of kids and the rewards for reaching a student are huge. HOWEVER I do feel like there needs to be some regular update above me about just how different our students and the school environment are. Our ability to teach kids and to show academic progress WHEN COMPARED to a severely normal school depends not on just teachers and pedagogy but also students and environment.

I DO think that because of our special obstacles we have to innovate. I didn’t see one word wall in a BVSD math class, and the school reports only 3% ELLs. It makes sense for us to have word walls and ELL strategies. I got no problems with that – I just got observations about what I saw.

ONE They get almost a whole quarter more learning each year.

a. I had an attendance list from 8/19 that that the office gave me. I also had an attendance list from 10/1 that the teacher left me to record grades on. There was one, exactly one, difference between the two lists out of 5 periods with ~30 students in each class. This means that from the first day of school these students have been able to move through their learning goals as a group.

b. The 2nd week of school, my schools D block had 24 students in it. D block is Algebra 1 and is, for 9th graders, the keystone class for CSAPs. At the end of the 8th week my D block has 28 students in it, of which, 16 were ones that were there during the 2nd week of school. In other words, I have 4 more students then I did the 2nd week and about half of the students now present were not there the 2nd week. We add new students daily from the opening of school till Oct 1, and several ON Oct 1.

TWO - planning time.

The teacher I subbed for had the following schedule. She taught 3 different classes (3 preps) to 5 groups of students. MWF the day has 8 periods and she teaches 5 of them (1,3,4,6,7). T/TH the day has 4 blocks. On T she teaches periods 1,3,and 7 so she teaches 3 blocks and has 1 off. On Thursday she teaches periods 4 and 6 so she teaches 2 blocks and has two off. The master schedule for math showed this to be similar for 8 of the 9 math teachers. One of the math teachers taught an additional section of PE. Planning time is useful for improving teaching methods.

On average the teacher then has 3/8 of her day for planning. Lunch is taken out of these periods as desired by the teacher. The shortest period is 55 minutes, twice our lunch, so one could say that she only has 2.5/8 periods for planning. Also students can come and visit during office hours. One period is considered office hours and students do come.

So let’s say she has 2/8 planning periods a day.
This is 1/4 of a day for planning vs our 1/6 of a day. She does, however, get time during the day for working with students. If we make time like that it is outside of our normal hours.

I’ve gone back and forth with administration on this with their claim that we get more planning time at my school then is the norm. I can tell you that at Monarch, Broomfield, and Arapahoe Ridge they get 2/7 of a day for planning. At Fairview (a well regarded IB school) they get ¼ of a day – or so. However you want to wave your hands at the numbers – these are the facts as I myself have seen and worked them.

3) Students get a period off during the day. I had 3 free blocks to walk about and observe classes and the campus. I observed groups of students talking – and usually working – and when I asked them they said it was their study period. Don’t know that this would work for us, but with students and teachers having time off during the day it allows for learning to take place.

4) I walked around and looked in classes. Every class was teacher centered with direct instruction and guided practice. I mean each and every class (math classes). We can argue about the validity and reliability of learning measures – but – every school in the country would kill for the following results:

Overall Academic Performance on State Assessments
Excellent


Academic Growth of Students
Stable
Winner of a John Irwin School of Excellence Award for the 2006 -


The teacher I subbed for has a website that talks about a quarterly project. I talked to the students – these are projects done outside of class and would seem to compare to the “webquests” in our glencoe text books. Daily class activities are lectures and problems.

5) Students were used to working together in pairs or threes on their homework. I observed mix results. Since it wasn’t my class I was more relaxed about just watching. Sometimes I wonder about co-operative learning.

a) when I tried to help a student the student lost patience with me trying to help him ‘discover’ the answer. The student dismissed me and sought help from a group behind and to his left. The help he received was “oh, just use this formula”. I dunno….does that sound like peer to peer beats teacher to student? Probably I’m just clumsy when I try to help.

b) I heard two girls that could have been an advertisement for co-operative learning. They got to the end of the problem, “ok, let’s check our answer (in the back of the book). Oh boy, our answer is nothing like theirs. Let’s see where we went wrong….(a few minutes)….there it is!”

c) LL, a pleasant young girl with a head covering had finished all her work and asked for an ok to do her geography work. She was on call to a group of 3 girls in front of her. When asked, she delivered direct instruction on how to solve the given problem. Good for LLs learning for sure. She didn’t do a terrible job, but she was more direct about just giving an answer than a teacher would have been.

multiple literacies - reading and righting?

I went off on a quest to try and define terms like; language, reading, literacy, multiple literacies, discourse and traced the coining of the term “multiliteracies” to this 1996 Harvard Education Review.

http://www.hepg.org/her/abstract/290

an unprotected copy of the work is at:

http://wwwstatic.kern.org/filer/blogWrite44ManilaWebsite/paul/articles/A_Pedagogy_of_Multiliteracies_Designing_Social_Futures.htm#11

According to both Wikipedia and the authors of the review itself, mulitliteracies was coined here.
From the abstract we read, “a new approach to literacy pedagogy that they call "multiliteracies."”

Discourse is described and defined. It presents many of the ways our CU program as been prompting us to think about language, literacy and culture.

HOWEVER when I get to the bottom of the article and try to figure out what they are suggesting in terms of what it would mean for the classroom – I’m lost. This is in spite of such promising topic headings as “What Schools Do and What We Can Do in Schools”.

There’s a very appealing view of multiliteracies as including more than print, it includes digital media, hyperlinks, multimedia and such. That’s something I can grasp. Literacy as print in many other forms and extended forms makes good sense.

What they seem to be calling for schools to do is to constantly design delivery of instruction to leverage cultural resources in our classroom.

Good grief. That image is fine if you give me a few hours of prep for every hour of class. I’m schooled in design. Engineers design, however, they also implement. At some point the design is frozen and the product built. Design is time consuming and error prone. In a real classroom with real constraints of time and numbers of students I mostly need to implement.

What’s possible within economic limits?
Much of what we study is focused on the maximum we can do for our students. How high can we set our expectations? What would we possible for every student under optimal conditions.

How about some focus on the floor as well as the ceiling? What are the minimum mandatory expectations we should have for a student – what are the public school exit criteria? Not the entry into MIT criteria – but the minimum madatories.

How about knowing how to read and write English?
Want to make that English or some other languages too? It’s ok with me from an educational standpoint, but I think that question is beyond the scope of an educational stand. It’s a political question. Educators can be part of the discourse, but not the final decision makers.

If a student meets the minimum mandatory requirements, let’s say, reading and writing English, then let’s look at where we can go beyond that – let us then think about getting the student ready for Stanford or MIT.

Treasures found on You Tube

My assignment included reponses to postings by classmates on literacy and diversity issues. Someone wrote that not every one could be taught as if they came from "cookie cutter white middle class families" and so I posted the following:

Goodness we are hard on ourselves!"not the cookie cutter, white middle class family."?

There is at least a little bit of character from family to family on the cul-de-sac I live on, or the surburb I grew up in.

Cookie cutter could be applied to other groups as well, any group that tends to have things in common.cookie cutter seems judgemental somehow - maybe I'm just too sensitive.

What else could be used?
"not the cool, white middle class family"
"not the enviable, white middle class family that the world covets to create in it's own national boarders"

then again Malvina Reynolds agreed with you when she wrote "little boxes", I like that song - maybe I'll just chill and agree that cookie cutter is an ok description. Check out one of the early protests against cookie cutters:Malvina sings little boxes on the intro to Weeds:

http://www.youtube.com/watch?v=b9s-KYMxjMs&feature=related

You can see who Malvina was at:

http://www.youtube.com/watch?v=4sooNNv9qHg

Differentiation, accomodation and social promotion

I took the rant I had below and processed it into a thesis.

Social promotion is when we move students up a grade level when they haven't earned it.
(sorry - slipped out of eduspeak - let me try again)
Social promotion is when we move students up a grade level in spite of the fact that the teacher has failed to allow them to uncover the current grade content.

I submit that at least one enabler for social promotion is slippage between differentiation and accommodation. The line between the two is clear and broad in theory, but not so much in practice.

For more discussion see my rant below.