Thursday, November 26, 2009

Virtual Museum Webinar Today

Not completely math related, but an excellent resource none the less, is the Virtual Museum from Heritage Canada. There is a brief 15 minute webinar today at 3pm to provide an online demonstration of the resource. i believe it's all free and basically gives you access to a variety of museums across Canada, if not the world!

Wednesday, November 25, 2009

Statistics Can Prove Anything!

If you haven't had the discussion with your class about bias in data management, and how stats and graphs can be altered for bias effect or to mislead readers, try this on for size:

Danger! Bread Kills (Or How to Lie With Statistics)

  1. More than 98 percent of convicted felons are bread users.
  2. Fully HALF of all children who grow up in bread-consuming households score at or below average on standardized tests.
  3. In the 18th century, when virtually all bread was baked in the home, the average life expectancy was less than 50 years; infant mortality rates were unacceptably high; many women died in childbirth; and diseases such as typhoid, yellow fever, and influenza ravaged whole nations.
  4. Every piece of bread you eat brings you nearer to death.
  5. Bread is associated with all the major diseases of the body. For example, nearly all sick people have eaten bread. The effects are obviously cumulative:
  6. 99.9% of all people who die from cancer have eaten bread.
  7. 100% of all soldiers have eaten bread.
  8. 96.9% of all Communist sympathizers have eaten bread.
  9. 99.7% of the people involved in air and auto accidents ate bread within 6 months preceding the accident.
  10. 93.1% of juvenile delinquents came from homes where bread is served frequently.
  11. Evidence points to the long-term effects of bread eating: Of all people born before 1839 who later dined on bread, there has been a 100% mortality rate.
  12. Bread is made from a substance called "dough." It has been proven that as little as a teaspoon of dough can be used to suffocate a lab rat. The average American eats more bread than that in one day!
  13. Primitive tribal societies that have no bread exhibit a low incidence of cancer, Alzheimer's, Parkinson's disease, and osteoporosis.
  14. Bread has been proven to be addictive. Subjects deprived of bread and being fed only water begged for bread after as little as two days.
  15. Bread is often a "gateway" food item, leading the user to "harder" items such as butter, jelly, peanut butter, and even cold cuts.
  16. Bread has been proven to absorb water. Since the human body is more than 90 percent water, it follows that eating bread could lead to your body being taken over by this absorptive food product, turning you into a soggy, gooey bread-pudding person.
  17. Newborn babies can choke on bread.
  18. Bread is baked at temperatures as high as 400 degrees Fahrenheit! That kind of heat can kill an adult in less than one minute.
  19. Most bread eaters are utterly unable to distinguish between significant scientific fact and meaningless statistical babbling.

In light of these frightening statistics, we propose the following bread restrictions:

  1. No sale of bread to minors.
  2. A nationwide "Just Say No To Toast" campaign, complete celebrity TV spots and bumper stickers.
  3. A 300 percent federal tax on all bread to pay for all the societal ills we might associate with bread.
  4. No animal or human images, nor any primary colors (which may appeal to children) may be used to promote bread usage.
  5. The establishment of "Bread-free" zones around schools.

Tuesday, November 24, 2009

Authentic Assessment

Here is another interesting harangue by a fellow OCT:

What are the characteristics of an authentic assessment?

In the past, student assessment and hence achievement was based solely on tests and exams. However, I feel these types of tests do not provide an accurate picture of what students know.

Instead, these types of traditional assessments only provided a snapshot of what students know at one particular time. It was more of a matter of teaching to the test than anything else and not allowing students to demonstrate what they truly know or even relating it to skills and knowledge that students would be applying the "real world".

The advent of authentic assessment changed all that. Authentic assessment are tasks given to students that are designed to assess their ability to apply knowledge and skills to real-world challenges.

Some characteristics of authentic assessment are:

1) Performance Tasks: students are asked to perform more complex tasks that are more meaningful. These tasks require complex, higher order thinking skills.

2) Time: the process of authentic assessment is ongoing so it is gathered, analyzed and shared with the student, parents, teachers, and support staff. This would be collected in the form of portfolios.

3) Construction of Knowledge: authentic tasks require students to synthesize and apply what they have learned instead of recall of facts and learning by rote. In this way, students construct new meaning along the way, as they learn while performing these authentic tasks.

4) Student-Centered: authentic tasks tend to be student centered. By this I mean that the teacher is not the one constructing the test or exam. In authentic assessments, students are given a choice or more of a "leeway" into demonstrating their knowledge. Teachers give students more flexibility in HOW they show WHAT they know.

5) Proof of Knowledge: Authentic assessments, offer more direct evidence of the construction and application of what students know.
For example, I remember having many multiple choice exams when I took Psychology courses in university. I don't believe this really demonstrated what I knew. Instead, I relied on my memory which really didn't show that I could apply my knowledge to real life situations.

To make my Psychology exam more authentic, I believe my professor should have given us "real life" scenarios of patients, so more clinical examples and see if we could apply the theories of Psychology in helping the patients.

Here's a quote I found which I can really relate to:

“Fairness” does not exist when assessment is uniform, standardized, impersonal, and absolute. Rather, it exists when assessment is appropriate.

I truly believe in this statement because I have often said to colleagues: "Equality is not treating everyone equally. Rather it is treating students differently according to their needs".

Having the exact same assessment for all students is not fair. Just like every teacher has their own teaching style, every student has their own unique skills, strengths, and weaknesses. As teachers, we need to design assessments which will showcase their strengths and knowledge at the same time challenging their weaknesses.

Authentic assessment helps us do just that; allows students to demonstrate what they know in various ways :-)




Monday, November 23, 2009

Understanding Math

At the ECOO conference i met a man by the name of Rudy Neufeld. He has created a math resource software series called Understanding Math. It is very well designed, very user friendly, and most importantly, he envisions the software being used to COMPLEMENT the teacher's instruction and students' use of manipulatives. It truly is an enhanced learning experience, as opposed to a "stick a kid on a computer with this math game and leave me alone" kind of resource.

For more information, visit his website. You can view sample lessons, templates and other resources, as well as download samples of the software for classroom use.

Friday, November 20, 2009

October Numeracy Meeting Minutes

These were just passed and approved at yesterday's Numeracy meeting:

Six Nations District Numeracy Committee Meeting Minutes

Thursday, October 1st, 2009

JC Hill (12:30 – 3:30)

Agenda Items



Present: Carrie Froman, Luanne Martin, Alice Anderson, Sandy Hill, Janis Thomas, Joe Restoule General

Absent: Judy McNaughton

Review of last year’s committee and any unfinished business

Robin Staats asked the question of inviting an LSK rep

Newspaper space for numeracy was discussed last year (see Tammy Claus);

PD involving whiteboards was discussed (see Marlene Martin)

Math nights were planned last year; JAM currently planning a math workshop for parents; ECG did some planning as well

Numeracy Assessment Selection

Overview of assessments was conducted

PRIME was discussed at PAC as too expensive

CAT was considered a similar option as EQAO; it was suggested that should this assessment be explored it be used in Grades 2, 5, and 7 to not coincide with EQAO, but rather give an indicator beforehand

KeyMath workshops are being planned; all schools have a kit

ONAP for grades 4 to 8 to be explored

Numeracy Nets for grades 3 to 8 to be explored

Imperial Oil dollars were raised as a possible source to fund exploration of these assessment tools

Math contest (Caribou)

Contest was explained and viewed

Schools were asked to encourage participation

Gr. 7/8 students in modified programs (LM)

This was brought up to help us develop grade 8 programs better suited for students possibly entering Locally Developed stream

Toni Martin’s name was mentioned in regards to knowing about a Life Skills program

Joe to follow up with Cam McDonald from GEDSB about the Math Connections poster

Comment was made that our high school students have said that once they enter high school they find that the teachers “teach completely different” from the way they were taught previously, meaning no hands on activities.

K-8 Curriculum Continuum from Niagara DSB

This was shared with the committee to share with their respective school staff

It was mentioned that T.I.P.S. has a continuum as well for grades 6 to 10 approximately

The Grade 7-9 continuum put out by Grand Erie (LM)

Question was raised about the origin, implementation and future avenues regarding the Math Connections poster.

Joe to follow up on this with GEDSB

Access to Grade 9 Math Scores (LM)

Question was raised about our ability to access grade 9 EQAO math scores

Joe to follow up on this

Review 3 Year Plan in Draft Form

The committee felt that we could begin implementing this plan as a work in progress; this would mean begin working towards the goals and getting perspectives from the Six Nations staff

In order to do so, it was decided that we needed to revise the original to make it more reader friendly (copies were cut off)

Joe to revise and redistribute for next meeting

Question was raised regarding the number of strands to report for each term

Joe to follow up with GEDSB on this

Numeracy Committee Goals for 09-10

The number one goal was to try and determine a common assessment tool or tools for the district

Future Meeting Dates and Times

Committee determined that Mon to Wed was not good for future meetings

Thursdays were decided upon; request was made to not have meetings the same week as the Literacy committee

Joe to complete schedule, gather feedback, and distribute final schedule

Thursday, November 19, 2009

Are You a "School on the Move"?

This article popped up in the "Numeracy in the News" sidebar on this blog. i just wanted to post it here for future reference, as the sidebar is a newsfeed that refreshes itself as new articles arrive.

The article is about a school in the HWDSB that was identified as a "School on the Move", an initiative of the Ministry of Education. There is a link in the article to the Min. of Ed. site section that explains Schools on the Move. Basically, schools with similar backgrounds and challenges connect with one another about initiatives that have helped boost student achievement. It's worth a look.

Wednesday, November 18, 2009

Why Use Problem Solving?

Have you noticed a diatribe in my posting? Here's the latest "gem" from an OCT colleague:

While not really a theory, for me one of the most influential ‘models’ in shaping my approach to teaching is of doing so through problem solving. “By learning to solve problems and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding” (Ontario Mathematics Curriculum, p 11). I find it surprising that many colleagues still struggle with this model, uncertain as to implementation and misunderstanding the “time factor” (“that would take waaaaay too much work to do – I don’t have time for that”).

As I learned to follow a problem solving approach to teaching and learning, what was impactful for me was the realization that, by teaching students mathematical concepts through problem solving, I can incorporate many critical skills while also providing opportunities for students to learn, connect, and apply concepts in meaningful and purposeful ways. “Students who engage in problem solving build a repertoire of reasoning skills and strategies…Students who work together to solve problems learn from one another as they demonstrate and communicate their mathematical understanding.“ (Guide to Effective Instruction K-6, Volume 1, p 27) Teaching through problem solving also provides a means to incorporate different strands of the curriculum as well as to integrate math into other curriculum areas. Too, it offers me a flexible framework in which to consider students’ needs, strengths, prior knowledge, and learning styles when planning, allowing me to differentiate based on their individual/common needs.

A problem solving approach also establishes a learning environment that values students’ thinking, communication, and participation, making students feel important, respected, and appreciated as a group member. It supports students in feeling accepted and valued for their different strategies, methods, and perspectives in solving problems, fostering confidence in themselves and their abilities to be successful in math.


Tuesday, November 17, 2009

Math Dictionary For Kids

Here's a site i just discovered (in the same way Columbus discovered America---i.e., it was already there but i ran into it). It is a math dictionary for kids. Everything is interactive. There is a word bank that students can click on, which then takes them to a definition, as well as some interactive content that brings that definition to life. Verrrry handy at boosting the communication side of learning, using and most importantly, UNDERSTANDING math terminology.

Just a word of warning. The site requires Adobe Flash Player, which is a free download, but it may need to be installed on your computer. It doesn't take long and is very handy for all sorts of web based content.

Monday, November 16, 2009

What is important about teaching Number Sense?

George Gadanidis claims number sense teaching is about developing what already comes naturally to the child. It is allowing children to develop their own procedures, not ready made algorithms, so that they strike upon procedures that are most useful dependent on the situation. "It's what they think that matters, not what we tell them to think." (p. 33)

Marilyn Burns would take the position that teaching about number sense is practicing mathematical thinking, which is best learnt through games, especially for K-6. It's not just about getting answers, it's about solving problems and finding approaches to those problems that require mathematical thinking.

Through these games (and the resulting math talk and play) children discover relationships between/across numbers. It is also about making reasonable judgements based on the knowledge of the relationships and comparisons of numbers. This means determining if a solution to a problem makes sense, based on the student's understanding of numbers. In order to arrive at these solutions, students need to use mental math, reasonable estimation, and proper judgement and selection when it comes to procedures or operations.

Sunday, November 15, 2009

Get with the Times People!!!

How uncanny it is that i would be attending an education technology conference and the Globe and Mail for that day has an article exactly on the message of the keynote speaker (more on him at a later date), not to mention the basic premise and theme of the conference. That is, embracing technology in education for the betterment of our students. Take a read of this article and let us know what you think...

Saturday, November 14, 2009

Yet Another Math Site

The sites just keep coming and coming. This one is another math "hub" where links to other sites are organized at one main site. Check it out here.

i will keep adding these to the blog if you want, but your feedback will be the most helpful indicator of which sites are useful and which ones aren't as helpful. The best ones (again, based on YOUR feedback) i can add to the sidebar so they are always available for your access. Leave your feedback by clicking on "comment(s)" below.

Friday, November 13, 2009

Math for the 21st Century

Yet another gem from a fellow OCT (when i see something good, why not share it?):

The following is a summary of the vision of mathematics in the 21st century, where math is going and how children are going to get there. There has been a paradigm shift in the teaching and learning of mathematics. The movement is towards a more constructivist approach where students learn for understanding they don’t just participate in rote learning. I have found the constructivist approach to be an ideal model to guide my teaching practice.


the changing perspectives of elementary school mathematics and what this means for students;

the new directions being taken to teach and help children learn mathematics;

how children learn and “do” mathematics;

New Methods versus Old Methods

Mathematics used to be a test of your memorization skills and how well you could mimic the teacher’s procedures. Math was about practicing the formulas by doing a set of similar examples. Focus was not on the process involved in solving problems.

Mathematics is now focusing on teaching for understanding with the ultimate goal to produce successful and productive citizens.

Teaching for understanding yields growth for children at all ability levels thus making the goal more attainable.

Having an understanding of the students’ thinking processes helps guide teachers’ instructional practices to meet this goal.

The OLD way of teaching and learning math looked like this:

paper pencil tasks (worksheets,tests)

teacher modelling

one method to achieve solution

one correct solution

rote learning

students saying, “Huh?”

The NEW way of teaching and learning math looks like this:

students working collaboratively

teacher guiding encouraging learning and reflection

teachers providing a positive environment where math is fun and students are confident

many methods to achieve solutions

math journals and logs (to solve problems, explain math ideas and, to write and learn about processes)

math words walls (math terminology, definitions and symbols)

math centres (problem solving groups, journal sharing, peer discussions about math)

manipulatives (hands-on materials to aid in learning new concepts and solve problems)

students reflecting on work (what do I understand?, what am I still confused about?)

reasoning (thinking about why answers make sense)

students actively constructing new knowledge and making sense of ideas

students applying their learning in new situations

teacher read alouds about math

lots of talk (sharing of ideas, learning from peers, presenting new connections)

students saying, “I GET IT!”

New Directions

National Council of Teachers of Mathematics (NCTM) was a major driving force for bringing about change in how we teach math.

The NCTM created a comprehensive set of Principles and Standards for Mathematics Education that has been made an essential part of the curriculum.

Educators are designing their programs according to these principles and standards each of which are objectives for helping students to process mathematical concepts. The universal goals are for them to be actively engaged in learning, questioning, analyzing, predicting and constructing knowledge from meaningful contexts and real-world experiences.

How Children Learn Math

The NCTM Learning Principle states that, “Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge.”

Young children are curious beings and it is therefore important that educators and parents provide them with opportunities to actively explore their environment and construct concepts.

A thorough conceptual understanding is required so that students may use their knowledge to make sense of new problems.

The problems that a teacher chooses for students should be interesting to them and relate to their personal experiences.

Talking with one another helps children to expand on existing concepts and develop new ones.

The best way to learn is to do.

Thursday, November 12, 2009

Why Get a Clicker when you can Poll Everywhere?

i know there was some Clicker training and interest being done in and around our district. Here's a resource that claims to be much much cheaper and is creating a lot of educational buzz (two name drops out of two seminars today).

It's called Poll Everywhere and you can check out some educator FAQs here.

Wednesday, November 11, 2009

The Changing Face of Math

Here is something that came from a fellow OCT:

A worthwhile math task in one that:
•Challenges a student
•Allows for students to collaborate, communicate and share ideas,
problems and solutions
•Involves the use of, or provides an opportunity for the use of technology and /or manipulatives to build and further a student’s understanding
•Is fun and engaging
•Takes place in a positive math environment
•Embraces errors and mistakes to further learning
•Coincides with curriculum expectations (otherwise, why are we doing it? :) )
•Is meaningful and relevant
•Connects math to the “real world”
•Relates to other math strands or other subject areas

A math task that is not worthwhile is one that:
•Does not connect to the curriculum at that grade level
•Does not challenge a student
• Does not engage a student
• Does not provide an opportunity for personal growth and learning
•Is not relevant
•Is “busy work”

An example of a math task that is not worthwhile:

You hand your grade 8 student a worksheet at the end of a lesson. You tell them it’s due tomorrow and you’ll be marking it. On the worksheet, they are required to measure the length of the sides of various polygons and find the area and perimeter each. There are many reasons why this is not a worthwhile math task. Firstly, in grade 8, this does not correlate with the expectations. In grade 8, students are way beyond simple area and perimeter. The focus in grade 8 is surface area of cylinders, circumference, radius and diameter of circles and their respective relationships. Clearly this task does not challenge them, and it’s not appropriate for their grade level (given that they are expected to achieve grade level expectations). Secondly, how can it provide an opportunity for personal growth and learning when they’ve done this in the junior grades. Thirdly, if they are required to take it home to complete, how does it engage them and provide opportunities to collaborate and communicate with their peers? Clearly, this would be a case of “busy work”. Furthermore, if they have to do it at home and hand it in to be marked, how do they learn from errors in their processing if they don’t have the opportunity to ask questions for clarification? Also, if the only access a student has to manipulatives or appropriate technology is at school, it is unfair to send a student home to complete work that may require their use.

Tuesday, November 10, 2009

Environmental Education

Though this isn't solely a math initiative, i wanted to point out that the province has created a document that aligns with the June 2007 "Shaping Our Schools, Shaping Our Future" document on Environmental Education in Ontario Schools. This document is called "A Scope and Sequence of Expectations" which indicates how Environmental Education can be taught throughout the Grade 1 to 8 curriculum in various subjects and strands.

i tried to order some for the schools but the document is only available on line (which makes sense from an environmental standpoint).

Then you can decide whether or not you want to print only the pages you want, print the document in its entirety, or the most environmentally responsible option, bookmark the page so you can refer back to it.

If you have any ideas for connecting Math to the environment, feel free to add them to the blog!

Sunday, November 8, 2009

Need some Fraction Lessons?

Here is a site with some lesson plan suggestions for the almighty difficult area known as Fractions.

Another suggestion for fractions is to use fraction stacks. These may already be in your classroom. Basically, they are stackable cubes that represent fractions in four different ways. One side has a typical fraction (1/2), another side has the decimal (0.5), the next has the percentage (50%), and the fourth may have a fraction over one hundred (50/100). This should help with that tricky converting between the rational numbers.

Finally, here is a webpage that i think will work interactively with SMARTboards or whiteboards (don't actually have one to try it out, so i can only presume it works--please leave a comment if you try it and it does or doesn't work).

Like many things on the internet, you can do this on a regular computer, as a whiteboard isn't entirely necessary to use it.

Saturday, November 7, 2009

Primary Math Games

Here is a site with a number of games more suitable for the Primary division.

Try out the time games on the second page. This might help students with some practice for that difficult concept of learning time.

One downside is the amount of advertising on the site.

Friday, November 6, 2009

Bringing Parents into the Equation

Here is an article on the importance of including parents in a child's learning of math. It is from an excellent site that is simply entitled, It might be something to include or talk about in and around report card day. Possibly post it or relay some of the ideas of the article to the parents you converse with.

Besides the article, the site has a plethora of tutorials and math lessons. Truly, someone from outer space could use the site to teach them everything there is to know about math. (Though, if they found earthling math from the far reaches of outer space, i'm not sure what our primitive math would have to offer them).

Thursday, November 5, 2009

A Suggestion from a class mate

One of the websites I use is I use a game called Railroad repair under the grade five heading to teach decimals. The activity is popular because students root for the train and they are given many opportunities to discover decimals while having a representation that they can drag. I was introduced to it by a retired highschool teacher who works at the University of Waterloo. There are follow-up activities to be printed off. The curriculum requirement that this activity fulfills is: demonstrate an understanding of place value in whole numbers and decimal
numbers from 0.01 to 100 000, using a variety of tools and strategies . It's a great introductory lesson for my grade 5s and works on understanding for my grade 4s.

In regards to calculators, I've used them with success in many of my lessons. My favorite activity is the broken calculator key that I got from a Marilyn Burns book. In this activity, you are not allowed to use specific keys and you are forced to experiment to create working equations. These kind of scalable puzzles always go over well with my class.

Monday, November 2, 2009

Another Day, Another Fun Math Site

We are trying out a new site

It's kid tested. A lot more challenging from a video game aspect, as the action is fast and furious. It brings a little more speed into the math thinking, which is good for the times tables or other areas where quick mental math ability needs to be developed.

Give it a try and leave us some feedback.

Edit: i just went back to the site and noticed the "video" section, where kids send in questions and the answers are explained using audio and visual responses. Really, do students even need teachers anymore?