Task Discussion

Maria Droujkova May 3, 2012, 6:52 p.m.

I posted this task to the Math Future email group and here are a few responses. Reposting for the class archives!

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Troy Peterson (benevolent)

To alleviate math phobia, increase engagement and eliminate abstraction henceforth mathematics will be taught in this fashion.

Students will be given an overview of basic concepts of physics including astrophysics and subatomic physics using fun videos and games.

Students will then be allowed access to multitouch games and videos that graphically explain the fundamentals of archs and curves.

Students will then be allowed access to interactive games and videos describing fractal geometry, geometry and trig.

Students will be taught to draw a Fibonacci Spiral and the basic shapes (triangles, squares and circles)

Only then will students receive their first introduction to integers.

They are then ready for kindergarten. Thank you for your compliance.

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Julia Brodsky (benevolent)

Recently, I made an experiment. I took the same lesson I teach to 6-7 year olds in our math circle ( fun puzzles, dice tricks, matchstick puzzles, paradoxes, etc) and brought it to the "advanced" 6th grade.
Now, my observation of both classes:
In math circle, the young kids are pretty much like puppies - they will chew on whatever they get their teeth on. They are happy to play with the materials, ask all types of questions, build their own puzzles and suggest them to one another, go on side discussions and come back with new ideas, etc. They laugh and roll on the floor.
The six graders were terrified. They were moaning. They were telling me " I never saw anything like this and I do not know what you want me to do", " When I look at these puzzles I get a headache", " This is not in the textbook", " How are you going to grade us?". They were afraid to laugh when the problem sounded really silly, and looked completely out of their comfort zone. It took me half an hour just to get them to be semi- relaxed - mostly by asking them the questions they have already encountered, and then making fun and silly modifications to those. It was very hard to explain them that all I want from them is to play.
Not surprisingly, the younger kids were able to solve more puzzles and suggest more ingenious solutions than the older kids.

By sixth grade, the kids stop playing with the problem. They expect the teacher to model the problem solution, and then re-create the solution to get a good grade. They are conscious of their image, and consider not knowing the answer as a failure. So, they prefer to give up before even trying.

So, as a benevolent ruler, I would:

Get rid of the grades, tests and other sources of external fear
Get rid of external awards - the motivation and pleasure should come from actual playing with the problem
Choose the materials that provoke thinking and desire to play/experiment with them
Let teachers play with the materials ( include this time into lesson prep)
Let older kids teach younger kids, and vice versa
Include role playing, acting and jester courses into teacher educational curriculum
Value teachers by how much they inspire students to explore and create on their own, not how much they make them learn.
Make teachers take the pledge similar to Hippocratus pledge before they start teaching

I could write more, but I have to run..:)

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Mike South (benevolent)

I liked your "like puppies" comparison and it reminded me of a
signature file or saying of the day or something somewhere that said
this, without attribution:

"All mammals learn by playing."

So profound. My inclination is to say that we are born knowing how to
play (or born with the predilection to learn to play and to enjoy it
immensely) and we beat it out of children when we start deciding what
they will be doing for the largest part of their waking hours.

In other words, your "puppies" analogy is spot on, and what you're
seeing is that they are acting like un-damaged mammals.

But I have to also admit that for the sixth grader group, there could
be more than the horribly stultifying ravages of curriculum to
blame--they are also adolescent mammals at this point and as such are
probably going to have a natural anxiety about appearance, acceptance,
etc, no matter what.

Still, I don't think it would be nearly this bad with non-coercively
taught people.

My Supreme Ruler would include in its dictates that no class be
attended except voluntarily. Then those things that Julie suggested
would be stuff teachers would do to try to actually have a class....

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Patrick Vennebush (responding to Julia)

I like your suggested changes, but I had a problem with the one about the Hippocratic oath… I think it misplaces blame. Administrators and politicians are the ones who need to take it, because they’re the ones who often create systems that kill the love of learning. In my experience, no teacher enter this profession with the intent of doing harm. Teachers want to help students learn math. It’s just that the system often makes it difficult to do so, ostensibly for many of the other reasons you list.
Carolyn April 9, 2012, 12:48 p.m.

This assignment I found very intriguing as Math anxiety is not something I experienced much as a student, not english anxiety, thats something I can relate too. However I did decide to be a Math tyrant for this assignment because it is so much easier to "torture" than to make comfrotable, something that I think teachers struggle with. We all desire to eb the nice loving, comforting teacher that we all wish we had, but as the post before me show it is so much easier to be a wicked witch of the west, whereas it takes thought and time to be the nice witch of the east, Glinda (I hope everyone has seen The Wizard of the Oz).

1. Everyday everyone must answer a math problem that is not their strength.

2. Once a year two names will be choosen from every classroom to be sent to The Math Games where they will calculate to the defeat different problems until there is one victor, who will have eternal glory (Hunger Games anyone?)

3. Every math problem that is answered must be said in confident voice as not to say "I think" or anything like it.

4. Students will be permitted to laugh at anyone who answers a question wrong.

5. Along with answering a math problem everyday, who ever does the worst calculations must then present their problem to the kingdom.

6. Teachers maynot provide any help during the "problem of the day" and can choose to give help at anyother time.

7. When students ask for help, say no.

8. The "elite" mathematicians in class will be punished for their intelligence and given problems that are so easy, they may beg you for something harder, but don't give in because you the teacher are supreme.
Keisha April 1, 2012, 11:57 p.m.
This assignment really gets you to think about your past experiences in math and how good or bad it was. Because I had math anxiety in math growing up I'll be a benevolent ruler.

1. First I will assure my students that everybody is capable of having math anxiety and I will share with them my story.

2. My tests will always be on a Friday so that we have a week or so to study as a class together.

3. I will take time during the day to meet with students individually to talk about any concerns they might have about the lesson that they want to discuss privatley.

4. I will use various activities that we introduced in some of our tasks that talked about math play.

5. I will give out a practice test for the first couple of test so that my students know how the test will feel like and the kind of questions that will be on the actual test.

6. I will teach the students strategies and activities they can do to relieve stress and anxiety, for example:
- breathing techniques
- taking a bath the day before the test
- massaging your temples
- writing out your thoughts
- playing a game
- stretching
- laughing
7. In 7th grade my teacher had us make up a test and give it to a partner. It really helped me fear the actual test less. I will use this same technique with my students.

8. I will ask my students to share with the class what they don't like about math and what ways we can make it more enjoyable. I will try to incorporate their ideas throughout the lessons.

9. I will use a popular song like a lady gaga song and we will change the lyrics to make a song that will encourage them and make them feel better about taking math tests.
Carolyn Lesser April 1, 2012, 3:33 p.m.

I also thought this was a fun assignment! I decided to be a tyrant. I thought of all my worst math nightmares and incorporated into what I thought a math tyrant teacher would be like.

1.       Tests will be given out at random every day to only certain students whose names are chosen out of a jar. The students won’t know what material will be on the test beforehand and will be forced to do the test aloud in front of the class.

2.       Classes will be all lectures with no games allowed. During these lectures students are not allowed to leave their seats or speak without getting permission from the teacher.

3.       The teacher will yell at students if they break any rules. If they continue to break rules they will be slapped on the wrist with a ruler.

4.       The teacher will go around the room having students answer problems within a certain amount of time. If they fail to answer in the time or answer incorrectly they must stay standing for the remainder of the day with a sign saying failure on their back.

5.       The teacher will provide no help with math outside of the lectures. The teacher says that if you don’t understand then you weren’t paying attention and that it was their fault they don’t get it.

6.       When students go home they will spend the time from when they get off the bus until they go to bed working on math homework. Parents are not to help with the work but to yell at the children if they get off task.

7.       Students will be forced to compete against each other. The better a student does the less times their name will be put in the jar to take tests. If a student does poorly in homework, tests, and questions asked in class the more their name will be put in the jar giving them a higher chance of taking a test every day.
Kathy Cianciola March 29, 2012, 12:16 p.m.

If I were the Mathematics Princess of the Universe, my overall goal would be to teach my subjects to love math. I would accomplish this by finding math in all sorts of wonderful and unexpected places, and by making math fun. My subjects would be willing to participate because I would allow them many opportunities to follow their interests, so that the motivation and rewards would be intrinsic. If we were engaged in mathematical problem solving I would always try to be encouraging. In my kingdom we would crochet, knit and do macrame. Not only do these have aesthetic and practical values, but hidden within the beauty of the created object is the basic process of counting and making patterns. Everyone in my kingdom, young and old, would be invited to The Paper Chain-Making Festival. At this grande event, we would create colorful paper chains with repeating patterns that seem to continue on into infinity. These beautiful creations would adorn every street and village in the kingdom. Collaboration and learning from eachother would be encouraged, and activities would be so engaging that it would often seem as though time did not even exist. The mathematics would be so much fun that no one would ever stop smiling, and this would make the Dark Lord of Math (Laura) very angry.

1)Teach them to love math 2) find math in wonderful unexpected places

3) let them follow their own interests 4) be encouraging 5) collaborate 6) give ample time

7) have fun
Laura Haeberle March 29, 2012, 3:14 p.m.
In Reply To: Kathy Cianciola March 29, 2012, 12:16 p.m.

This sounds like a great system. I think the people of your kingdom would have a very positive, engaged attitude towards math! My kingdom is jealous!
Denise March 28, 2012, 4:19 p.m.

I'm a firm believer in keeping things as simple as possible. If I were an evil math overload, I would need only one rule: Make sure that elementary math is taught by adults who hated math when they were students.

If I were a benign ruler, I would have two rules: (1) All students will be taught math by a personal tutor/mentor. If they experience personality or style conflicts with their mentor, they may freely change to another until they find one from whom they can learn. (2) And no one can become a math tutor/mentor unless they enjoy learning math themselves and have a conceptual/relational understanding of mathematics.

But that wouldn't be very helpful in the present school system, and in reading the Wikipedia article, I think most of their recommendations would also be either outside the teacher's control ("Refraining from tying self-esteem to success with math") or not really helpful ("Making math relevant").

Individual teachers cannot change our test-oriented system or the math-phobic culture their students grow up in, but they can:

(1) Emphasize the process of figuring things out more than the production of correct answers.

(2) Ask for and encourage alternative methods.

(3) Explain math procedures relationally, rather than just giving steps to follow.

(4) Encourage mental math skills, which usually rely on deeper conceptual understanding than is required when following memorized steps of a pencil-and-paper algorithm.

(5) Do plenty of word problems in class. See point (1) and (2).
Maria Droujkova March 30, 2012, 7:32 a.m.
In Reply To: Denise March 28, 2012, 4:19 p.m.

Denise, I think your message is very profound. Love is the critical variable here! It also charts the way for professional development: help people love math.
SandyG March 28, 2012, 9:33 a.m.

This was a fun assignment! It made me think about things that caused me so much math anxiety.

    If you want to be a benevolent ruler, name 7-10 measures you will take to eliminate math anxiety and to create the atmosphere of math happiness, well-being and productivity.

1) Differentiate instruction- It’s a fact that students learn differently, and it seems to me that math does not take that into account as much as some other curriculum areas do. Not only are students on different academic levels, but students have different learning styles. My benevolent rule would take these differences into consideration and tailor class size, demographics, and even the lessons to suit the needs and preferences of the students.

3) Allow sufficient time- There is nothing worse than feeling the pressure of a time crunch when you are trying to help students understand. For my students, I would allow as much time as they need to understand a concept. We would not be held to any deadlines and curriculum guidelines, so we would be free to explore math in interesting ways until the children understand the concepts.

4) Do not put kids on the spot- For me there was no situation that raised my anxiety more than the teacher who would randomly call kids to the board to complete a problem. I would never put my students on the spot. Instead, I might utilize technology such as Activote which would allow students to privately input their answer and the only one to know if their answer is right or wrong would be I and my student. Not only would this allow me to provide the appropriate remediation for the student but also it would preserve their self-esteem.

5) Provide assessments in different formats- Just as students learn differently, so, too, do they test differently. I would assess my students in a number of different formats, and I’m not sure I would use exams at all.

6) Make it fun- As we’ve learned in this class, bringing art and games into the classroom can make a huge impact on students. I would take the fear out of math. I would take away the performance anxiety and the fear of being right or wrong. My class would be a place for exploration and discovery.

7) Encourage- My class would not focus on what kids do wrong; rather, we would celebrate what the kids did well. I would use only positive behavioral supports and would recognize effort (even if the answer is incorrect). I would work hard to build my students’ self-esteem.

                If you want to be a tyrant (in this task), name 7-10 measures you will take to increase math anxiety and to create the atmosphere of oppression and fear.

1) One test- There would be no differentiated instructions. It wouldn’t matter what students prefer. What I say goes, and I would provide one test, with no accommodations, no hints, helps, or consultations.

2) Pass/Fail- Along with that one test, I would set up my exam so that kids would either pass it or fail it. I would provide only one question per concept in the unit, worded the way I think the students should understand it, and if they don’t get it right, it would be an automatic F. My goal would be to scare the material into them.

3) Pressure them into learning- Teaching through intimidation would be the name of the game in my class. I would expect my students to perform at any time without volunteering, and I would constantly ask them to do so. If I pass the students in the hallway, I could ask them a random math question and expect them to have an answer. They would think mathematically all of the time because they would never know when it would be their turn on the hot seat. All wrong answers would, of course, be held against them, and there would be punishment for too many incorrect answers.

4) Foster a competitive environment- Pitting one student’s strengths against another’s weakness would be a great way to scare them into learning. Perhaps I could have races at the board for figuring out problems, or I could keep a leaderboard for students who have done the best. That way, the students who are struggling will use their embarrassment and sense of failure to turn things around. They would work harder, right?

5) Book work- There would be no games, no art, no discussion, and no fun. I would lecture. They would cypher. There would be no fun activities or worksheets. We would not use computers. All students would need would be their textbook, a pencil (no eraser), and paper.

6) Grades- The focus of my class would be performance and grades. Every test, in-class assignment, and homework would be graded—and I would not give half credit for the process but incorrect answer or vice versa.

7) Homework- Students would receive homework every night, and their parents would simply be an extension of me. We would work as a team to make sure these kids can do math. No calculators or any accommodations would ever be allowed because the kids would be doing math for hours and hours a day. It would become second nature.
Laura Haeberle March 27, 2012, 8:10 p.m.

For this task, since it's the closest I'll (probably) be to becoming an evil overlord, I decided to be a math tyrant.

Here are the laws of my kingdom.

1. All students must answer math questions in the front of the class. If they answer incorrectly, the other students are required to laugh at them.

2. Students struggling with math must be taken out of class to complete math assessments in the school dark, dank basement.

3. There will be no math games, activities, or group work. In fact, if any student smiles while doing math, they automatically fail and need to stand in the corner for the rest of class.

4. Math tests will be timed, growing exponentially in difficulty. Questions will be partially based off what is taught in class, but mostly based on out-of-class knowledge, obscure applications of math, and math that I haven't taught yet.

5. The last person to finish their math test will be kicked out of the kingdom and fed to grizzly bears.

6. Math homework will be at least 6 hours a day. If a student fails to turn in homework (or if they get any homework questions wrong), they will be given double homework the next day.

7. Parents will be encouraged to stand over their children while they complete their homework, laughing maniacally when they get anything wrong.

8. There will be no erasers provided in class. Mistakes are unacceptable.

9. I am the lord of all math. Every answer I say is automatically correct. Opposition will be crushed.

Okay, so I may have gotten a bit carried away with this week's assignment, but this was fun! I based most of these off of what I believe stresses children out the most. For example, my law about students laughing at wrong answers is based off the fact that children don't want to appear dumb to their classmates. They don't want to admit when they're struggling in math, which only hurts them in the long run. Overall, I believe that if I do the exact opposite of most of these tyrant suggestions, my classroom should be pretty math-friendly.
Kathy Cianciola March 29, 2012, 10:27 a.m.
In Reply To: Laura Haeberle March 27, 2012, 8:10 p.m.

Laura,

Just reading about your ruthless tyranny, I'm literally trembling from head to toe!
Maria Droujkova March 30, 2012, 7:28 a.m.
In Reply To: Laura Haeberle March 27, 2012, 8:10 p.m.

Laura, as you say, your points are hyperbolic and satirical, but they represent very widespread practices.

You say the opposites would work well for supporting kids. What would be a good opposite to this evil rule: "The last person to finish their math test will be kicked out of the kingdom and fed to grizzly bears." Would you encourage slow work, and if so, how?