Jean Lave and situated learning

In chapter 6 Boaler states that one of her aims in this study was to investigate ‘situated learning’ and she cites Lave in her research throughout chapters 6 and 7. Jean Lave is a social anthropologist with a strong interest in social theory. She teaches geography and education at the University of California, Berkeley. A lot of Lave’s work in situated cognition and communities of practice has been done with Etienne Wenger. Lave received her Ph. D. in Social Anthropology from Harvard University in 1968.

In 1991 Lave worked with Wenger to propose the situated learning model of learning. This theory suggests that learning involves social interaction, and that knowledge should be presented in an authentic context. In one of Lave’s projects she compared the way ‘just plain folk’ learned to the way students learned in the classroom and she found that apprentices experienced great learning success through authentic activity without actually being taught to. This is similar to what the teachers at Phoenix Park School were trying to do. They gave students projects that were open ended and similar to real life and allowed the students to work on these projects without actually teaching them the skills and concepts.

When designing learning experiences from the situated learning perspective, one believes that knowledge is acquired through situations and this knowledge is transferred only to similar situations. That the knowledge gained out of context is more difficult to generalize to an unfamiliar situation. Students at Amber Hill seemed to have run into this difficulty. When they were asked to answer a question or solve a problem that was unfamiliar to them, they had difficulty applying the math they had learned in isolation.

Looking at learning from a situative perspective means looking at the group of learners as more important than individual ideas. The individuals in a group consider, question, and add to each other’s thinking so that important mathematical ideas and connections can be produced as a group (Brodie, 2005). According to Brodie (2005) situative perspectives argue that what a learner says and does in the classroom will make sense from the learner’s perspective of knowing and being, from the learner’s identity in relation to mathematics and to the learner’s past experiences of learning math, both in and out of school. She states that if learners have a particular expectation of ways of working in math classrooms and of what counts as appropriate contribution in the classroom, that they will continue with this outside of the classroom.

Situated learning theory seems to apply more to Phoenix Park School where the students are given freedom to work with others at their own pace, using their own constructed ideas and skills to solve relevant, and authentic problems. When they learn this way they are more able to transfer this learning to other situations. Amber Hill School on the other hand seems to be following a more traditional learning method where students are given closed end questions to work on individually using learned formulas and procedures which they find difficult to transfer outside of classroom use.

“Situative perspectives argue that a focus on conceptual structures is not sufficient to account for learning. Rather, interaction with others and resources are both the process and the product of learning and so learning cannot be analysed without analysing interactional systems.” (Brodie, 2005)

References

Boaler, J.(2002). Experiencing School Mathematics: Traditional and Reform Approaches to Teaching and their Impact on Student Learning. Lawrence Erlbaum Associates:Mahwah, New Jersey.

Brodie, K. (2005). Using cognitive and situative perspectives to understand teacher interactions with learner errors. Retrieved from the internet October, 2011.

http://www.lifecircles-inc.com/Learningtheories/constructivism/Lave.html

http://www.ischool.berkeley.edu/people/faculty/jeanlave

http://elpea.tripod.com/jlavebio01.html

GAMES

Games – Just a fun fill in OR an effective instruction and/or assessment activity?

Just last week I had a substitute teach my class for a day while I was away.  The sub worked on equivalent decimals and renaming decimals as fractions. When I returned the next day I realized that after this day my students would have a long weekend and because I wasn’t in class yesterday I didn’t know how well they had grasped the decimal concept. I decided to have them play decimal snap so that I could circulate and get an idea of their understanding of what an equivalent decimal was. Each pair of students was given a stack of cards which had either a decimal number written in the tenths, hundredths or thousandths or a picture of a grid divided into tenths , hundredths or thousandths with part of the grid shaded. The only instructions I gave the class was to share the cards equally with your partner, each person turn over a card and if you get a pair of equivalent decimals say ‘snap’.

Circulating the class it was so much easier to get a grasp on who understood the concept than it would have been if I had given them written text book questions and had taken these in to correct one by one. An added bonus was that the students loved math class and had a ball reviewing and learning a math concept.

A couple of things I noticed that I had not planned to assess or ‘look for’ happened that I found interesting.

1)      A student of ‘lower ability’ became bored with the game and decided not to play after a few minutes. She spent the rest of the class just ‘wandering’ while others played. This was similar to the students at Phoenix Park who were off task.  I wonder, would I allow this to happen in all my classes if this student decided not to participate? I wonder how my administrator would react to this?  I don’t think this would fly as a continual practice in elementary especially and not likely in high school at my school.

2)      I was pleased with the number of different ways my students chose to play the game. As I circulated the 12 groups I noticed that about half of the groups had devised another method of play. Some had combined rules from other games they had played such as ‘go fish’ and others had decided to only deal out half the cards and keep a center base pile. In the end it didn’t matter how the played the game, only that they were reviewing and learning about equivalent decimals while having fun.

Boaler, J.  (2002). Experiencing school mathematics:  Revised and expanded edition.  New York:  Lawrence Erlbaum Associates Inc.

Thoughts on Schoenfeld's article - Good Teaching Bad Results

It is important to be able to accurately complete computations in an adequate time frame but also important to understand. In Schoenfeld’s article Good Teaching, Bad Results, he gives a couple of examples of how students were able to answer mathematical problems using procedures and operations but without a deep understanding of the ‘underlying substance’. (p.5)

In one example students were given problems such as

274 + 274 + 274          or        812 + 812 + 812 + 812 + 812           (p.5)

3                                                          5

A lot of the students who could use all four of the basic arithmetic operations solved these problems by working out the addition and then dividing rather than looking at the problem and seeing that the number they had to divide by was the same as the number of addends and the addends were the same numbers. If they had used their number sense and understood the problem being asked they would have completed the problem without having to work out all the operations. “By virtue of obtaining the correct answer, the students indicated that they had mastered the procedures of the discipline. However, they had clearly not mastered the underlying substance.” (p. 5) Schoenfeld explains that this shows that being able to perform the appropriate operations does not necessarily indicate understanding.

The second example Schoenfeld gives is Wertheimer’s example of ‘the parallelogram problem’. Students had been taught how to find the area of a parallelogram by cutting off and moving a triangle to change the parallelogram to a rectangle which they could easily calculate. The students could easily do this problem but when they were asked to find the area of a parallelogram that was not in a standard position they couldn’t do it. The students had memorized a formula but did not understand the reasoning.

Understanding why we do the steps we do in math and why they work is a very important aspect of understanding mathematics. From my own experience in school I remember doing ‘long division’ where I knew how to put a number ‘into’ another and how to bring down the digits until I got the correct answer but didn’t really understand what division was. This made it more difficult when given a ‘story problem’ in which I needed to figure out what operation to use to solve the problem.  

In our provincial curriculum in Newfoundland and Labrador I am proud to say we do now teach our students to understand division and not rely on step by step formulas to do computations only.

Pondering ability grouping- a new thought....

I’m very interested in learning from the findings for the study of the two schools and the different approaches to teaching mathematics in the text by Boaler (2002). I’ve been questioning the effects of ability grouping with students and through my readings have come across some interesting ideas and findings. Marsh (989) interpreted such findings as “big fish little pond” (BFLP) effect: An individual’s self-esteem is strongly influenced by the group that individual uses as a reference.” (Kemp & Watkins, 1996).

I’d been aware of how low-ability students may compare themselves to high-ability students in a heterogeneous classroom and how this may affect their self-esteem. I’ve also been aware of how low-ability students develop high self-esteem when they get to work with students who have a similar ability to theirs and them working at a level which brings them success. However, in reading this particular article this week I have for the first time began to think about how students in a high-ability class have only high-ability students to compare themselves to and therefore, “views their own academic competence less highly than they would if they were in a class with students of varying ability levels.”  (Kemp & Watkins, 1996). I'd never really thought that grouping high-ability students together would affect 'their' self-esteem. Something new to ponder.