I’ve wrapped up my 1st algebra unit with my 6th graders and I have to say it was an overwhelming success. Student growth from the pre-test about 6 weeks ago to the post-test a few days ago shows a range of 10-50 percentage point gains with an average gain of roughly 30 percentage points.
For many of them, this was their first time actually digging deep into algebra and using it to solve problems. They were able to represent problems verbally, visually, and symbolically. I started on error analysis with them toward the end of the unit. That proved to be a little more difficult than I had hoped, but we still have plenty of time in the year for that.
The culminating activity for them involved having them learn to write secret codes with algebraic equations and functions as an encryption device.
Before jumping into the activity I showed a short clip from “A Beautiful Mind” It was the pentagon scene in which John Nash stares at the wall of code and deciphers it mentally. That isn’t exactly where I was going with the activity but it quickly got me some buy in from a classroom full of pre-teen girls who had never heard of cryptography or used the word encrypt or decrypt a day in their lives.
We began this exercise using simple substitution to “hide” messages. A = 1, B = 2 and so on. They grabbed onto that rather quickly and some of them even made the leap that this was essentially the equation y = x with X being the input position of the letter and y being the encrypted position of the number.
Next, we used one step equation to encrypt and decrypt secret messages. Essentially, if A = 1, B =2, C = 3…we would use the equation 5x = y to encrypt the message. A = 1 became A = 5 and so on. We toyed around with this simple encryption for a day or so and eventually moved up to multi-step equations as encryption and decryption devices.
Finally, we moved into the realm of non-linear functions as encryption devices and the use of tables/grids to decrypt secret messages. This proved to be a little more difficult because developing an equation for the system we used may be about a year away for my 6th graders. This was the most time consuming of all the activities and I witnessed a loss of interest and some burn out on this activity.
I like the idea of using real world application of mathematics beyond using equation to figure out how many people can come to your party, etc.
I have been receiving jokes and little messages from my students in the form of encrypted numeric messages since we concluded the activity and I love it! One disappointment took place yesterday though. We were completing our second review of the last 6 weeks when I witnessed one girl passing a note to another. I was overjoyed for a second because I had hoped that they were using a code to communicate in class. Unfortunately, it was in English and I was able to read it quite easily.
Sigh.
The film with the same title as this post is probably one of my favorites because it begs the question…”Is it ever too late to change?”
I often ask my colleagues at what age or stage in life does a student’s refusal to work to their full potential simply turn into that student just being average or below average. At what age does potential simply give way to actual performance? The answers always vary.
My conclusion is that there is no age or stage of life when the potential of another should ever be given up on. Redemption, change, growth are all continuous variables and as such have no ending point.
Everyone has a 25th hour.
Torture numbers, and they’ll confess to anything. ~Gregg Easterbrook
Statistics and data have always been incredibly vital to public education. However, since the NCLB mandate and the Bush era that defines research as being replicable, generalizable, and quantitatively based. As such, school leaders LOVE data, graphs, and Microsoft Excel. I’m all for data and statistics in schools under certain conditions.
1. Schools employ a pre-test, treatment, post test design: I’ve worked in schools where only benchmark assessments were given. Student and teacher performance were only weighed against absolute standards. Growth wasn’t tracked at all.
2. Assessments must be frequent…but not too frequent: I’m a fan of monthly pre-post test assessment as well as quarterly benchmark assessments. Monthly pre-post tests may seem excessive, however teachers should be assessing AT LEAST that often anyway…
3. The data MUST be used to change instruction: If schools gather data just to have graphs on the walls or in their data rooms the process of gathering the data is pointless. If teachers and schools are not using data to change or improve instruction then they’re essentially trying to make a cow fat simply by weighing it.
1. The students.
2. The students.
3. The students.
4. The students.
5. Summer vacation.
6. The students.
7. The students.
8. The stories that the students tell me.
9. Spring break.
10. The students.
1. When the weekend work/extra credit is expertly done and the in class work and quizzes are all over the place….I know a parent has been doing a little too much helping at home.
2. When students are not held at least partially accountable for their own learning. Helplessness is a learned trait. We must stop teaching our kids to be passive learners!
3. Elementary school teachers who teach some, but not all of a concept, so when students enter the middle grades we have to spend precious time getting them to unlearn bad habits.
4. The question “Is this for a grade?” I would much rather have them ask me, “How will this help me learn?”
5. Persons with no experience managing adults or, any other type of organization for that matter, moving up in the ranks of education.
6. Poor quality educator prep programs. Educator prep programs should include professionalism, time management, organization, document presentation, and a number of other basic skills taught in business courses.
7. The pay.
8. The fact that our primary policy makers have little to no education background. Former lawyers and business owners have no business deciding education related issues.
9. The notion that anyone walking off the street can do what I do at a high level and achieve real results from the students.
10. When kids doubt themselves so much that they talk themselves out of being successful.
The post title is my favorite Einstein quote and the basis of something new I’m trying with my students. Dan has been advocating this for a long time now and I just got on the bandwagon.
I’ll be helping them less. And they’ll be making more mistakes.
I’m trying to transition this class from teacher centered to one that is more student centered. I want the curriculum to be driven more by their curiosity and less by my rigid set of standards and my pacing guide. I find that if the students are more intellectually invested in school…they tend to get more out of it.
This transition isn’t going to be easy though. Helping them less means more complaining, less structure, and ( from the outside looking in ) more chaotic classroom sessions.
I hope the bosses can see and appreciate my vision!
Today was one of those days in the classroom when I just wasn’t sure if I was “doing it right.”
I second guessed, thought twice, and questioned myself all day long. I’m not sure if it was the lack of sleep or the fact that I’m taking a big chance by pushing so much of the middle grades content down to 6th grade.
My students are all terribly bright and can hang with the best of ‘em. They’re full of passion and fire and will argue, question, and push until they get it just right. As soon as they meet my expectations I raise the bar. Everytime I raise it I think they’ll never make it…and then they do.
Today was different. Today I saw a group of tired little girls who may have had enough of the maniacal mathematical man with the impossible expectations.
Do I keep pushing or do I let up ? When they grow into young women and tell their stories I don’t ever want to be remembered as the man who didn’t challenge them…or as the man who killed their love of math with his high expectations and unorthodox teaching style.
Today, I just wasn’t so sure of myself.
I’m doing my budget this morning and wondering if good people make good teachers. Stay with me for a second.
Do people who make the best choices make the best teachers or do people who have made ( and continue to make ) the biggest mistakes make the best teachers ?
I’m sure most parents would prefer the former…but I somehow think we all have more to learn from the latter.
Thoughts ?
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