Cooperative Learning and Reinforcing Effort

Cooperative Learning:

A few years ago, I created an assignment that involved students cooperatively building a bridge made of popsicle sticks, string, construction paper and elmer’s glue. The ultimate goal of the assignment was to show students how algebraic formulas work and what factors (variables, mathematical operations and their locations in the formula) influence the output of the “bridge equation. So I developed a formula that I thought encompassed all of the parameters. In a flash of inpiration, I included an aesthetic multiplier in the formula. This aesthetic multiplier was an average of a rating each student assigned to a finished bridge by secret ballot.

I arranged students in groups of 3 to 4 members. One of the problems that I encountered was too few jobs for too many people. What I mean by that is, I found in some of my groups the vast majority of the work was done by 1 or 2 of the group’s members. I enacted this lesson in a class that some students have excessive absences and I although I clearly spelled out the points awarded to the group for the finished product, I did not address how individual grades would be affected by absence(s).

Where the assignment was effective:
In the formula that I developed as the assessment tool, I placed the length of the bridge (minimum 24 inches) and the load (weight in pounds) it could support “cubed” in the numerator and the number of popsicle sticks “squared” times the number of bottles of glue “to the fourth” times in the denominator (I didn’t buy alot of glue and did not wish to have the students douse their bridge with glue prior to presenting to the class, a practical lesson in the cost of materials). The students were witness to how the materials in the denominator (to various powers) would detract from their “bridge index” and how strong their bridge was and its length would increase the index. Before construction began, I introduced the formula to them and gave them example numbers to “plug in” to the formula to see how the output index was calculated. After showing example pictures of bridges I stressed how aesthetically pleasing the bridges were. One of the best outcomes that I did not foresee was how honest (and critcal) the aesthetically pleasing factor played out. The ratings by secret ballot were from 1 to 5 with 5 being the most pleasing to the eye. The ratings were very uniform even when the students rated their own work.
The stress test was an exciting day for the groups presenting as well. I hung a 5 gallon bucket with dumb bell weights from the center of their bridges to find the maximum load sustained by their bridge. The student were witness to how their efforts and attention to detail in construction paid off in finding the critical load and ultimate failure of their bridge.

Where the assignment broke down:
Since individual job titles were not defined or assigned, I did not account for how the students would be individually affected by lack of effort or absence. If and when I choose to use this lesson again, I will have job titles assigned by the group’s members and address the absence issue. Clearly defined titles, responsibilities and an individual post stress test evaluation form will promote active engagement and learning by all.

Reinforcing Effort:

After writing so much for the cooperative learning prompt, I'll keep this short.

During my teaching career, I have always tried to put myself into my students shoes and try to remember what was occupying my thoughts while a high school student. I must admit it wasn't always on my studies, but school came easy for me for the most part. In reading the first part of the reinforcing effort chapter, there is a scenario in which a student blames his genetics on the fact that he is not succeeding in mathematics. In particular, he says his mom wasn't good at math either. (My mother was not the best math student either, but she did instill in me the importance of education.) I believe some of the problem with this student could also be that neither the student or his mother see the importance of learning math. This defeatist attitude and indifference to learning math that occurs more often than I'd like to admit is all the more reason for me to reinforce any effort put forth.

Feedback that Fits and Strategies Reactions

Reaction to "Feedback that Fits"

I must admit of a couple of things that jumped out at me while reading the article. In particular, had I assigned the Dog/Cat paragraph assignment to the 4th grade student named Anna, it is most likely that I would have corrected her paper in the exact manner as the example showed. Also, it would most likely be the only personalized feedback she received from me for that work.

Another thing I noticed was, the author stated several times to try to put yourself into your students position. When and how would you like to receive feedback and so forth. I do try to put myself in their shoes. I try to remember what was going on in my world when I was at the age my students are and what was important to me.

Before reading this article, I finished correcting the 1st Trig test I gave for this academic year. I have 26 in my 6th hour and 30 in my 7th. The average score in 6th hour was a 74% and a whopping 65% in my 7th. I thought I had them prepared. I need some feedback! And I need to give some group feedback to both classes. I may be posting an addendum tomorrow night - post feedback.

Cues, Questions and Advance Organizers

From a few years back when I taught Geometry...

I can think of a time that I asked my students to explain the number, Pi (3.1415926535...), to me. I began my lesson by quoting one of my college textbooks of the values for Pi that ancient civilizations believed. The oldest approximation being 3, of course, and getting more and more accurate as the centuries passed. I recall them laughing at the approximations (which was somewhat unexpected the 1st year I used the lesson, but played into my favor). After the laughter subsided, I asked "What gives you the right to laugh, have you ever proven what Pi is? And how do you know what you believe about its value is correct?" I proceeded to show them a Powerpoint presentation (that took me an incredible amount of time to create, but reaped benefits for the several years that followed, as I said, when I taught Geometry). The presentation was created using the classic example of finding the perimeter of regular polygons starting with an equilateral triangle and dividing it by 2 times a "psuedo" radius, then increasing the number of sides. The result for Pi converges to its accepted value as the number of sides approaches infinity. The students loved it. I believe its success came from using their knowledge of beginning trigonometric functions, but also from the visuals I provided to finally see why Pi is Pi. Also they enjoyed something out of the "norm", as I said I used a presentation in Powerpoint which isn't my normal "Modus Operandi".

Non-linguistic Representation

The first idea that came to mind while reading the chapter dealing with non-linguistic representation was an idea I try to work into my classes each year. It is the idea that mathematics is a language full of symbols, syntax rules and order that represents bigger concepts. In fact, I inform my students that the physical sciences are basically the study of using mathematics to describe the world around them. And the last point I make is to ask my students, "If aliens from another world landed on earth tomorrow, how do you think we would communicate with them?" It would not be with any language from earth; the only language that is universal is mathematics. So if mathematics is a language then it is a linguistic representation and I must come up with some more non-linguistic representations, such as, "stomping my foot" at 4:4 time, then stomping whole note beats to represent the idea that 4 quarter notes comprise one full note just as 4 quarters equal 1 and so forth. This representation would address kinesthetic, audio and visual learners (very crudely yet effectively).

Summarizing and Note Taking

Being a math teacher, I have to say I am already in tune with summarizing the topics introduced to students. I think the best information that I learned from this chapter is the different tools and features that I did not know existed within Microsoft Word. The summarizing tool and configuring templates among others will be learned by this user.

Some thoughts after the 1st night of class and the Meta-Analysis

I will admit, somewhat reluctantly, that while taking classes to become certified to teach, I looked at most of the information as a lot of “fluff”. With phrases used, like “every student can learn and succeed”, I said to myself, “Yeah, yeah, give me something I can use”. I don’t know if I have reached a turning point, but some of the information I now read, which is related to improving my strategies and techniques, is beginning to make more sense.

Two points resonated with me as I taught classes the 2 days after the first class of CEdo525. Those are: 1) the best way to improve student understanding of material is to show similarities and differences to what they already know. 2) communicate not only what the goals are for the entire class, but from day to day.

With so many great ideas to consider of how to introduce myself to students and what to do the first day, I wish I had read the article the week before school started instead of the week after.

Quite often - in years past - after being done with a class I have “taught” I felt like I went through the motions. This year I am becoming more cognizant of what I need to improve upon. It seems so obvious in hind sight that I haven’t shared the daily goal often enough with my students.

After reading the Meta-Analysis (and before reading the intro to Using Technology with Classroom Instruction that Works):

Keep in mind upon reading the following that the book intro explains some of my misunderstanding below:

If reading this article and posting a response was a means to “find a cynic”, here I am. I prefer the term "skeptic", however.

From the abstract:

“…The mean of the study-weighted effect sizes averaging across all outcomes was .410 (p < .001), with a 95-percent confidence interval (CI) of .175 to .644. This result indicates that teaching and learning with technology has a small, positive, significant (p < .001) effect on student outcomes when compared to traditional instruction.”

and

“On the other hand, the mean study-weighted effect size for the 3 studies that contained behavioral outcomes was -.091, indicating that technology had a small, negative effect on students’ behavioral outcomes.”

What is the study-weighted effect size, what does it measure?

I get the feeling spending all the money that districts do on computers isn’t justified if the results show just a “small” positive significant effect. I wonder what spending the money to hire more teachers, thus, changing the class sizes would do in comparison? And just what does a small, negative effect on students’ behavioral outcomes mean?

What was measured?

The article also states:

“Swan and Mitrani (1993), for example, compared the classroom interactions between high school students and teachers involved in (a) computer-based instruction and (b) traditional instruction. They found that student-teacher interactions were more student-centered and individualized during computer-based teaching and learning than in traditional teaching and learning.”

Am I missing something? The preceding sentences from the article state something that is as obvious as the following. Let’s say you only eat food with a knife and fork. The more you use the fork, the less you will use the knife…

Am I cutting my own throat here?

A couple of things I had to research and/or look up: Meta-analyses is a big study made up of a bunch of little studies (which by the way, the article says originally 200 little studies were retrieved and only 42 of them were used, the others were thrown out for various somewhat ambiguous reasons). Effect size is the output of a meta-analyses. It involves a weighted average based on sample sizes of the smaller studies. (How is the weighted average set up? Who decides how to weigh things? Or is there some agreed upon way? And what about those studies that were "thrown out"?)

The last paragraph of the conclusion is:

“There are, of course, many unanswered questions about the effects of teaching and learning with technology on students’ outcomes. We maintain, however, that research can play a critical role in answering some of these questions. Policymakers, however, will need to invest more money on research in technology. The findings from this research synthesis suggest that more and better research needs to be funded and conducted by researchers in this area. Although recognition of the uniqueness of each school and classroom situation will always need to be considered, the accumulation of research evidence over time and across studies may provide consistent findings that enhance our understandings of the role of teaching and learning with technology.”

What I read between the lines:

unanswered questions = disclaimer so if part of our study is disproved, we are not responsible

Policymakers will need to invest more money = We need a new study cause this one is over and we’re out of grant money (kinda getting hungry)

…findings from this research synthesis suggest that more and better research needs to be funded… = We don’t want to eat at anything less than a 4 star restaurant.

Having been an analytical chemist, I know how to use statistics to prove something. I am well aware of what the 95% confidence interval means, that is, within ±2 standard deviations of the mean (95 out of 100 times the next bit of data will fall within that interval). I have no idea, since I didn’t see it specified in the meta-analysis, of how it is justified that technology integrated in the classroom is better than without. After all, how are students from the United States falling behind students from other countries in academic achievement that certainly don’t have the money for technology in their classrooms?

I do, however, believe students can achieve more with technology, but how much technology? Yet another study...