Repetition in math class

Practice makes perfect! or Perfect Practice makes Perfect!

These, and others, are comments I hear as to why we need practice in math classes.  This "practice" can be seen by worksheets, flash cards, and multiplication tables.  I, however, disagree with this notion.

The problem occurs when we look at what the students are supposedly practicing when they complete the above tasks. 

These tasks promote the idea of efficiency over understanding.  I remember back to when I used to administer "Mad Minutes" (basic questions which have to be completed in a minute or less, and their mark was based on only the ones which were answered correctly.  If a student did not answer it, or did so and was incorrect, this student would lose marks).  On multiple occasions, I saw students writing down numbers which made no sense, simply due to the pressure put on them during this timed exam. 

Of course, how can students complete deep math questions if they don't understand their basics?  Well I have a great story against this...and the main character in this story is me!  I still to this day, 30 years old with a bachelor degree in Mathematics, and 3 courses left in my Masters of Mathematics, cannot recite the multiplication tables.  I struggle deeply with my 7 and 8 times tables.  Does this make me a weak math student?  Does this imply I will not be able to answer deep questions?  I would hope not one person would answer yes to either of these questions.  However, the way I used to assess math, through repetition, would never allow myself to succeed in my own courses. 

If it was not for my own mother, who strongly refused to use flash cards at home, I would probably have grown up hating mathematics.

As a math teacher I needed to understand that the beauty of mathematics does not come from memorization of basic facts, but instead the use of basic facts to solve problems which a person may encounter on a daily basis.  Does understanding basic facts allow for students to solve problems quicker? Of course, but should we judge the quality of answer solely based on the time given?

I have given tasks to my students, some of which are upcoming blog posts, where students have chosen to complete multiple questions, of similar types, to come to a conclusion.  The difference in these tasks, however, is the word "choice".  If we allow students to decide how many problems he/she needs to solve, to demonstrate higher level thinking, then I guarantee your students will start to see the beauty of mathematics as a wonderful, sometimes chaotic, subject which is not limited to solving petty details.

Providing no answers

Recently, I have tried to provide little to no answers in my classes.  If a student asks a question I would simply pose another question back.  This has caused much frustration in some but in others

Prime numbers and Cicada

Lost on how to find meaningful ways to introduce prime numbers?

Why don't we look at Cicadas 

These are winged insects that evolved around 1.8 million years ago.  What is interesting is that their life cycles follow prime numbers.  They emerge, mate and die quickly during the spring of either the 13th or 17th year.    On these such years, they build an exit tunnel where millions quickly exit and overcome any predators, such as birds, by using their vast numbers to their advantage.

Why every 13 and 17 years?

This way, it will be impossible for any other life cycle to line up with the life cycle of the Cicada.

For example, lets suppose they emerged every 12th year.  This would have animals with life cycles of 2, 3, 4, and 6 years to line up perfectly every time they emerged.

The life cycle being a prime number is, what scientists predict, what has been their greatest strength in their survival for over 1 million years.

8th grade student creates a standardized exam

A 13-year-old eighth grader in upstate New York woke up on Sunday and decided that it would be funny if she designed a standardized test that made fun of standardized tests.  Below is her letter to the state:

Dear New  York State,

I am not fond of your tests. They do not show you who I am, or who my teachers are. For example, if a student is a bad test taker, you would look at her test and think she is a bad student. What happens if a kid is just having a bad day? You would only see that one test and and think he was an unsatisfactory pupil. Imagine how stressed the teachers are having to rely on their students’ test scores as a form of evaluation.

Not all students are the same,  therefore standardized tests are impractical. Albert Einstein once said, “Everyone is a genius, but if you judge a fish on its ability to climb a tree, it will live its whole life believing that it is stupid.” These tests can lower self-esteem and cause a lot of anxiety. The tests are so long that, by the last day of testing, some kids end up guessing, just so they can be done. How can you put eight-year-old kids through six days of testing over a two-week time frame?.

 

Children with special needs have even greater trouble with these exams. The tests are a total waste for them….

Sophia is a high-achieving student (she has a 97.2 average) at Saranac Middle School in Saranac, N.Y. Her mother said she came up with the idea for this test all on her own. She worked on it for hours, and then realized that it was more than a joke. “She has a great perspective,” Laura Stevens said about her daughter.

Sophia said she normally has no problem with all of the standardized tests she has to take in school, but this new Common Core-aligned exam was harder than the others. “I’m a little worried about this one,” she said.

Here’s Sophia Stevens’ standardized test that critiques standardized tests:

Kohn and Sahlberg Public Lecture

Transforming Alberta schools from good to great

 “Creating a great school for all - an evening with Alfie Kohn and Pasi Sahlberg,” Wednesday, February 20, 2013 at Red Deer College.

For too long Alberta schools have been over-managed and under-imagined. The evening presentations will bring together two of the world’s preeminent educational reformers to
explore the opportunities to improve Alberta’s already high performing school system. Based on their research and experiences internationally, the two speakers will explore timely issues facing educators, parents and policy-makers. Some of the questions they will engage include: What should be the role of homework in a student’s development? Why does testing and comparing schools continue to be over-emphasized ? What is the appropriate balance of local and government in shaping curriculum, instruction and school life?

Alfie Kohn writes and speaks widely on human behavior, education, and parenting. The latest of his twelve books are “Feel-Bad Education and Other Contrarian Essays on Children and Schooling (2011), and The Homework Myth: Why Our Kids Get Too Much of a Bad Thing
(2006) and Unconditional Parenting: Moving from Rewards and Punishments to Love and Reason (2005)."

Pasi Sahlberg is Director General of CIMO (of the Ministry of Education and Culture) in Helsinki, Finland. He has experience in classroom teaching, training teachers and leaders, coaching schools to change and advising education policy-makers around the world. He is an international speaker and writer who has given more than 250 keynote speeches and published over 100 articles, chapters and books on educational change.

Doors open at 6:30 with a reception until 7:00 pm. The lecture will run to 9:00 pm. The evening is sponsored by the Central Alberta Teachers’ Convention Board in partnership with its provincial Alberta Teachers’ Association.

Media are invited to contact David Martin 403-597-3394 to arrange for complimentary tickets
and interviews with the keynote speakers.

Integration of Tech into High School math

Here is the link to my webinar on integration of technology into high school math

https://sas.elluminate.com/site/external/jwsdetect/playback.jnlp?psid=2013-01-16.1456.M.403B68B668E3D3B7DBFA5BC0A10B5C.vcr&sid=2009083\