Policy (In)Consistencies

Policies.  Guidelines.  Rules.  One may think that school boards in Ontario all have to follow the same requirements in regards to technology use; however, this is not the case.  Policies and guidelines differ from board to board, school to school, and even from class to class.  What are the implications of these inconsistencies?  I have briefly outlined my thoughts below.

Benefits of diverse policies:

• Allows for teacher freedom
• Customizable to the board/school/class
• Addresses the individual differences in the community
• Plays to teacher-strengths

Barriers of diverse policies:

• Inconsistent regulations
• Can be frustrating for families who move 
• What is deemed acceptable in one place may not be in another
• Some may feel disadvantaged if they are not able to use the same tools as others

What do you think?  Should there be consistency?  Weigh in on the poll on the side of my blog!

Math - Mistakes and Communication

What are the purposes of mistakes/problems when learning math?

• Teachers can determine where students need support
• Learning is a messy process and so if no mistakes are occurring, then learning is often not happening at an effective rate
• Students learn from each other by explaining their thinking and then being challenged and encouraged by the teacher/peers through feedback
• Ultimately mistakes allow for a deeper level of understanding
• “I haven’t failed; I have just found 10,000 ways that didn’t work” - Thomas Edison

How do I develop math communication skills in the classroom?

• Teach students how to talk about math (questioning, explaining)
• Creating a math word wall of key language 
• Use stories to help teach concepts - primary students love being read to
• Use oral and writing prompts such as "Show me how you..."
• Model math speech through think-alouds
• Create math tasks that are worth talking about/discussing (rich tasks)
• Provide wait-time after asking questions
• Teach cues "thumbs up/middle/down"

Teaching Modern Math

"One of the biggest challenges for teachers is trying to teach mathematics in ways they did not experience as students" (Literacy and Numeracy Secretariat, 2010b)

Boy is this quote accurate!  As someone who did well in math because she was a great memorizer/robot, I really struggle with the new problem solving/inquiry approach to teaching and learning math.  However, here are a couple things that have helped me along my math journey:

1.  Finding an outstanding math mentor
I am very fortunate to be working alongside a grade partner who is exceptional when it comes to teaching math.  He has been extremely helpful in encouraging me to try new approaches and not revert back to my old ways without being pushy.  Reflecting on my year, I'm sure there were times that I taught math in ways which would have driven him nuts, but having his support and guidance was instrumental in my own learning.

2.  Using new resources
It's hard to revert back to old practice when you are using resources that don't let you!  For example, I found that using strings and Fosnot lessons really set me on the right track for teaching math in new ways.  While I admit that there were days when I taught using old methods, the majority of my math periods were done in a way I can feel proud.  Another new resource that I dabbled with this year was MinecraftEdu.  My only regret is that I hadn't gotten on board with it sooner!  What an incredible way to let students engage with math and explore in a context and world that they connect with.

3.  Ongoing Professional Development
I still have a lot to learn.  While I have made some good leaps with my math program, I am aware that I still have a lot of questions and unknowns when it comes to teaching with new approaches.  I am looking to connect myself to more math communities where I can participate as someone who is willing and open to trying new things in order to learn from the best.

Reflex Math

Reflex Math is a website geared towards obtaining math fluency through fact recall.  While it does have several benefits, it is certainly not in line with the new shift in how we are to teach math.  Here is some more information:

Positives about Reflex:

• Engaging - students can create their own avatar and enjoy using online games to learn
• Adapts to the student (if they consistently struggle with 2 x 5, it will show this fact more so that the student memorizes it)
• Effective in developing and reinforcing fluency (students are able to recall their math facts quickly)
• Parents can create accounts to monitor their son/daughter's progress

Negatives about Reflex:

• Does not teach concepts!  Strictly focused on fact recall and speed
• Follows US curriculum standards so grade levels are not perfectly aligned
• Lab time is required for students to use the site (can be an issue in larger schools or schools without an abundance of technology)
• Very independent - no collaboration or discussion since students need to be focused on their own screen to ensure speed and accuracy
• No problem solving or explaining of concepts if they are not understood (students may know 3 x 5 = 15 but they do not know what that means)

As a result, this is not a website that I would have my students use to learn math.  However, I may allow them time on the site to reinforce concepts that are already clear to them as I do value fact automaticity.  For these reasons, I would give this website 3/10 stars.

The Classroom Environment and Math Instruction

A quick Google search reveals hundreds of articles discussing the importance of creating a positive classroom environment to optimize learning - some with an emphasis on math and some of which were more general.  Here are a couple articles that I found to be particularly interesting coupled with my own thoughts below:

Edugains
-establish positive attitudes and beliefs about math
-support risk-taking by ensuring a positive classroom community
-provide physical spaces for collaboration, manipulatives, technology etc
-collaboratively construct class norms (especially important if math is taught on rotary)

Learn Alberta
-address students' preconceptions and discover what they think and know to be true
-organize knowledge around big ideas and important concepts
-focus on why math is important and provide lots of opportunities for students to engage in deep thinking
-encourage a class culture of respect


Education - Alberta 
-teachers should model think-alouds, precise language, and written records
-teachers need to have high, but realistic, expectations of the students
-differentiation of tasks and multiple entry points is key
-implement rich, meaningful tasks (open-ended problems, questions with multiple solutions etc) to make real-world connections
-use probing questions to engage student thinking
-represent math in a variety of ways
-teacher needs to be available to work one-on-one and in small groups
-intentional use of technology to facilitate learning

So why is this important?  Students need to know that:

• they are valued as learners and can work collaboratively with their peers
• they are supported if they make a mistake and are encouraged to take risks
• they have choices in their learning and need to take responsibility for their actions
• everyone in the classroom is important and need to be valued and respected
• sometimes they will struggle, and that's okay
• they can learn math

Once this climate of learning has been established, students will be in an environment that fosters learning and gives them the confidence they need to achieve success.  Without this positive environment, learning is stifled and becomes stressful and pessimistic.  Consequently, the role of the teacher is of utmost importance in ensuring that all students will be able to learn and develop as mathematicians. 

Creative Commons Use

Here is a handout with some reminders for both students and teachers about using the Creative Commons.  It also has information about adding your own work to the CC and some helpful links if you need more information.

*Click image to enlarge

The Evolution of Math

From an emphasis on the '3Rs' to a way in which we can view the world around us in a logical manner, math has greatly evolved over the years.  As a result, our instruction of math has had to make significant changes to address the ever-changing nature of the "math beast."

Here are a couple of noteworthy changes:

"Then"	"Now"
Focus on basic computation	Emphasis on critical thinking/problem solving
“Drill and Kill method”	Use of manipulatives
Memorizing rules and succinct way of solving problems	Experiential learning
Being successful meant that you were a good robot	Focus on thinking and understanding concepts
Predominantly individual tasks (little to no discussion/group work)	Specialized math courses (economics, engineering, physics)
Math taught in isolation	Math is interwoven into all subjects

What new understandings have emerged?

• Everyone can learn and be successful math
• Students may have different strategies to solve the same problem
• There are many ways of teaching math.  Here are a few used in the DSBN:
• Fosnot
• Strings
• Gallery Walks
• Group Work
• Teachers need to keep learning and attending workshops/PD events to remain effective math teachers and keep up with latest pedagogy