Assessment for and as Learning using the Mathematical Processe

As I was looking for articles and reports about ability grouping and teaching in Mathematics. I came across a really neat PDF file. It's not related to ability grouping however it's something I hope to bring into my teaching practises in regards to assessment!!!

The document contains two charts:

1st chart- deals with reasoning and proving, reflectings, selecting tools and computational strategies, connecting and represents (areas that are always troublesome for my students for sure!)
- it provides a guide for teachers on what we should see students doing, sample questions and sample feedback

2nd chart- Indicates key features for Effective Mathematics Instruction
- Encouraging students, ongoing assessment for learning, Building Meaningful success, and utilise many Approaches!! (provides indicators and questions to ask!)

Have a look!
http://www.edugains.ca/resources/LearningMaterials/MathProcesses/MathProcesses_AfL-AaL.pdf

Angela

Time Magazine- The Myth of the Math Gender Gap

I was doing a little research about boys versus girls in Math and I came across an article posted in Time Magazine, that I obtained on-line.

The article was written by Alice Park on July 24th, 2008. The article was based on a report by researchers at University of Wisconsin, University of California,  and Berkeley. The research focused on trying to change the long-held view that girls are not as good in Math as boys. They collected data to help them prove that the gender gap has turned into a myth.

The research looked at the math score and the fact that these score often are the basis for the comparison however in today's world more girls are taking math courses, as in the past girls stopped taking math courses and never learned the skills that were presented to all students on standardized tests.

(Of course in Math today, all students require so many credits in order to graduate!!)

Even though the gap is closing and more girls are taking math courses, doing well in math tests, and are taking on roles in Math based occupations (Engineering, trades...) "the stereotype that boys are better at math is alive and strong" (Janet Hyde- psychologist at University of Wisconsin) "parents still believe it, and teachers still believe it".

Unless we change our views ad help change those of others, we are setting our girls up for failure in Mathematics!!!

Lots to think about, especially how we have to change our views to help our students succeed!

Angela

Park, A. (2008). The Myth of the Math Gender Gap, Time. Retrieved on November 21, 2011 from http://www.time.com/time/printout/0,8816,1826399,00.html

Math-Talk Strategies!

I found an interesting article by Dr. Catherine D. Bruce of Trent University. In the article she speaks about the importance of Math-Talk and how it is a foundation to understanding students knowledge and achievement. In the article she lists 5 strategies that encourage high-quality student interaction:

1- The use of rich math tasks (having multiple answers increasing opportunities to justify answers)
2- Justification of solutions
3- Students questioning each other
4- Use of wait time (students need time to think!)
5- Use of guidelines for math-talk
         * taken from article

As teachers we are constantly being faced with the lack of time and the pressure of curriculum demands, these strategies suggested take time, however; I have used group problem solving with rich math tasks and the amount of math achieved in the activity goes beyond what a lecture or traditional math class can bring to the students.  Something I will do periodically in my class of course it takes time and the curriculum doesn't always allow for the time!

Angela

Bruces, Dr. Catherine D. What works? Research into Practice- Student Interaction in the Math Classroom: Stealing Ideas of Building Understanding. January 2007. The Literacy and Numeracy Secretariant Ontario, Canada.

Classroom Experience on Making Connections!

I have to share my classroom experience that I had in my Math classroom today. I was working on decimals and reviewing rounding decials to the nearest whole number, tenth, and hundredth. I put a number on the board, and the underneath I put a blank number line. The students just sat there and looked at me as if I was loosing my mind. I then took the decimal and said it was a lenth of fabric that I needed to make a article of clothing. I asked them what I should ask for at the counter. The students seemed to be more interested in the task and were able to see the purpose of the question.

I then talked about the importance of rounding and how if we rounded $13.29995 to $13.29 instead of $13.30 and if 1million people did this once there would be a loss of  $10 000. There eyes lit up they were shocked. They wanted me to look at 10 million then 1 billion. I had them hooked! It was because I had made a connection!!!

As my grade 5 curriculum guide states- "Learning mathematics within contexts and making connections relevant to learners can validate past experiences and increase student willingness to participate and be actively engaged."
Angela

Quote taken from:http://www.ed.gov.nl.ca/edu/k12/curriculum/guides/mathematics/gr5_math_guide.pdf pg14

Research on Student's Communicating Math

I have come across and article by Lisa Anne De Garcia titled How to Get Students Talking! Generating Math Talk That Supports Math Learning.

 In this article she speaks about how teaching  can help promote math talk in partners, small groups and whole group to help develop confident problem solvers.

She makes reference to five teaching practices listed below:

Five Teaching Practices for Improving the Quality of Discourse in Mathematics

Classrooms

1) Talk moves that engage students in discourse,

2) The art of questioning,

3) Using student thinking to propel discussions,

4) Setting up a supportive environment, and

5) Orchestrating the discourse.

The article focuses on what a teacher can do to help improve students verbal communication and different strategies that can be used in the classroom to help students improve mathematical communication.

Check it out at http://www.mathsolutions.com/documents/How_to_Get_Students_Talking.pdf

Angela

Little Rant with future Research!

As of right now, this will be a little rant, and I plan on doing some research on retaining math concepts.  Today and yesterday just seemed to be so very frustrating, as I stand in front of the classroom and ask my students a variety of questions that focus on math concepts that we have been looking at for the past 3 weeks or so. The responses that I receive are nil!! I know a few get it, however; they are the quiet timid ones in the classroom. Where do I go from here?? How do I get them involved and interested in sharing their knowledge!! 

Off to the research I go!

Angela

Making the Connection

In any Math Curriculum meeting or in-service we often hear about helping our students make connections. An area that become challenging in trying to help our students understanding the connection between what they know and the problems they are presented with.  We just recently reviewed our schools CRT results and the elementary report revealed to us that the area of Connections and Representations was low compared to the district and province, therefore; we need to increase this number. How do we do this as Math teachers?

The NL Mathematics Curriculum guide describes one of the main goals of Mathematics education as: “make connections between Mathematics and its applications” and “When mathematical ideas are connected to each other or to real-world phenomena, students begin to view mathematics as useful, relevant and integrated. Learning mathematics within contexts and making connections relevant to learners can validate past experiences and increase student willingness to participate and be actively engaged”. (Mathematics Grade 5 Curriculum Guide, Dept of Ed, 2009)  This area is also one of the items that are to be given a grade level 1- 5 in the K-6 report cards. Indicating to teachers of Mathematics that there should be a level of importance placed on this area.

In Schoenfeld’s article Good Teaching, Bad Results, there were many areas that he spoke about that struck a chord with me, my schooling, and my teaching. I look at his example about the “key word procedure” in problem solving. I as a student and as a teacher have used this method in helping students look for words that help them figure out what they have to so in the problem. I even went as far in my first few years of teaching to post on the wall key words for adding, subtracting, multiplying and dividing.  These keys words helped students focus on what they had to do to get the correct answer. I also saw responses like the articles referred to like “the number of buses needed is ’31 remainder 12’.”  These type problems have to presented to students making them understand that ‘math’ is just part of the problem, the algorithm is a way to help you solve the problem, but always ask yourself ‘Does my answer make sense? Is my answer possible?’

I’m going to leave you with a quote to think about as you take a little more time to think about making connections in your Mathematics lesson Planning.

Angela

“Because the learner is constantly searching for connections on many levels, educators need to orchestrate the experiences from which learners extract understanding.… Brain research establishes and confirms that multiple complex and concrete experiences are essential for meaningful learning and teaching” (Caine and Caine, 1991, p.5).

Physical verses Virtual Manipulatives

I have recently agreed to take part in a pilot of incorporating technology into my Math teaching. I have several students who have personal laptops in the classroom for written output difficulties and I felt like this was a great year to take on a project involving technology.  

I was doing a little research on technology and mathematics and came across an interesting article  entitled : Technology’s Impact on Fraction Learning: An experimental comparison of virtual and physical manipulatives. This article compares physical and virtual manipulatives on the topic of fractions. The study was conducted over a 10 day session with evaluations at pre-unit, 5 days and 10 days. The research was conducted by  Maria Mendiburo and Ted Hasselbring

The study revealed the many benefits of using technology as a way for students to use manipluatives:

-          Students using virtual manipulative were able to do more practice than physical manipulatives.

-          Virtual manipulatives were more time-efficient than physical manipulatives

I thought this was interesting to share, as the NCTM are really promoting the use of manipulatives, and the amount of manipulative provided and available are just sufficient for a full class. This causes trouble in implementing physical manipulatives in a lesson.

Angela

What is Math and Why do we teach it?

I bet if I asked most teachers on my staff these questions they would defiantly ponder the thought about what is math and why do we teach it?  We often have philosophies in areas of language arts and our approach to teaching and setting up a language art program. What about the set up of our mathematics program? We often feel driven by the abundance of outcomes and curriculum provided to us to teach in the school year/grade.  As I read the three assigned articles, I found myself thinking back to my approach to teaching math. I do truly enjoy math, and I wish my students shared the same enthusiasm that I do about the subject but there are many times I feel like the robot in front of the classroom.

I often feel that I am taking on the Formalism philosophical attitude that Hersh speaks of. I feel that there are times, too often for my liking, that I resort to rote calculations and finding the right answer by following the rules. I do think there is some need for this, but I also believe that personal connections foster understanding and ownership to a student’s individual learning. I hope to focus on my approach to teaching and look for different approaches and/or philosophies that could work in my current math setting, as we all know the approach each year changes as we work with different groups of students and individuals.

 I also feel that our provinces approach or philosophical attitude is leaning toward the humanistic philosophy, creating a mathematics curriculum that hopes to increase the likelihood that a student can learn math.  I guess I could ask the question now WHAT DOES IT MEAN TO LEARN MATH?

Math Autobiography

What has been my path to Math???

It all started as a student, in Grade 7, when I had to make a very vital decision in my schooling. Would I choose the advanced Math route or French Immersion, because I could not do both!  I choose the Math, despite all my closer friends choosing the French. I had a goal for myself to do university Math in high school.  Well that plan kinda crumbled when in Grade 8 the French Immersion students were allowed to join the advanced math group and skip grade 8 Math. So I was still in Math however, didn't get the opportunity to join the French a year later, it was too late.

Math wasn't a subject that came easy to me. I had to work at it A LOT! The one thing I did like about the subject is that I knew there was always an answer at the end. There was none of this gray matter like English, if I kept trying I knew that I could get to the end and get it right. (Of course today my viewpoints have a changed a little as I challenge my students with problems.)  I stuck with the advanced program, and forced myself to keep pushing though despite the not so good exam marks at times, they just made me work harder.

I've always liked working with numbers, figuring out the cost of things, how much of a discount would I be getting, playing with the calculator...

Today I teach Grade 5 Mathematics and have been for the past 5 years. I've worked with the Dept of ED with the new math program and have enjoyed the experience.

I love the classes when I have to try new strategies for learners and they work!!! What an awesome feeling when you see the light bulb go off and they are able to do it!

Angela

My First Attempt at a posting!

This is my first time creating a blog. I guess there is where I'm supposed to rant about something however I'm not at that level yet, just creating a message to see if it works and if I can see it!

Angela