Saturday, December 13, 2014

Changing the Culture:

I stumbled upon this article recently and it made me think of how math is thought about within the family unit.
How do we did get a classroom, school, community, entire society to all share the same cultural values in regards to the importance of math? 

The importance to literacy seems to be there.  Parent/teacher conferences will sometimes often have a similar theme if the parent acknowledges during their time in school they were not a strong student.  The parent will realize the importance of their child reading fluently and having comprehension of the text.  No matter what challenges the parent has in providing support to their child they are on board with doing whatever it takes in getting their child to learn to read.

The same cannot be said when it comes to numeracy.  On the topic of math, some parents will throw up their hands.  They will say they never understood math so they are not surprised their child is having difficulty.  The openness to supporting the child does not get the same emphasis as language did a few moments ago.        

I have heard of parents and grandparents going back to high school to complete their diploma’s just to be a role model to their children and end the cycle of illiteracy that kept occurring within the family.  I don’t know many stories where parents went to the same measures to show their commitment to math. 

Why is this?  Why is it that some people are not concerned with being able to make correct change but are embarrassed that they cannot read a menu or put together a proper sentence?
These questions lead me to think of our reliance on math tools and my own family background.  I come from a family of skilled trade workers.  A culture of math is ingrained in the family.  I can remember feeling a tinged of shame if my grandfather asked me an application question related to math and my estimate was no where near the mark.  As a carpenter, I never saw him pull out a calculator when he was designing or completing a project even though he put high standards on the work.  The standard he set for himself resonated throughout the family.

Our “new” methods of teaching math are the same as the methods my grandfather used in the  applications he did many years ago.  Creating an accepting culture to numeracy will lead to student success and continue to build a society that has high standards when it comes to application beyond school.

Wednesday, December 3, 2014

Why Structure is Necessary For Some

In my seemingly recent memory I was a high school student, furiously taking step-by-step notes on math rules from a chalkboard and then completing textbook work quietly in my seat (and finishing the leftovers at home). Now as a teacher of math the methods of teaching have evolved to become more student driven with an emphasis on problem solving (The Ontario
Curriculum: Mathematics Grade 9 and 10).

As I begin to plan for lessons, I’m looking for ways to make connections to my students lives in meaningful ways that will spark their curiosity about math. We take for granted that we are able to infer patterns and connections as well as be reflective, plan and self-regulate our own learning. These skills make up a person’s executive functioning skills and when a student has a learning disability that impairs their executive functioning, the modern methods of teaching Math may not be helping these students out. When executive functioning is impaired students struggle to plan, organize and self-regulate and these are arguably essential skills related to successful math completion.

How then can a teacher support students with executive functioning challenges and still create a classroom that allows for discovery? Roditi and Steinberg’s chapter “The Strategic Math Classroom” provides some sound advice. This advice is outlined below to help teachers enhance the learning for a subset of learners in four key areas:

Support Memory:
Memory strategies help enhance the automatic recall that is essential in math. Remembering the nuances and details required to solve problems can be overwhelming to young learners. Verbal strategies such as acronyms are a great way to help students remember sequences and allow students to attempt problems in a structured way. BEDMAS is one such strategy that can help with algebra. Similarly, the acronym KNOW can be used as an overall strategy (Key Words, Numbers, Operations, Work it out). Visual strategies, are another way to encode information these may include drawing cartoons or concept maps. Last but not least, hands-on strategies are a great way to consolidate information (e.g., manipulating tiles and pipe cleaners).

Organizational strategies:
Students with weak organizational strategies are easily overwhelmed and often approach problems with out a specific strategy. The students benefit from direct instructions which not only include order of operations but how to differentiate between essential and nonessential information. Having students have dedicated pages in their notebooks that outline strategy tools such as vocabulary lists, charts, tables or mnemonics are helpful and essential resources for students with executive functioning difficulty. A strategy new to me would be RAPS: reread and rephrase (promotes understanding), artistic (multiple depictions may help with problem-solving), predict (supports problem-solving) and solve (using procedural knowledge). Alternatively, students could use a Three-Column note taking technique where students use one column for each: important terms, definitions and examples. Check out page 247 in Roditi and Steinberg article for pictorial representation.

Shifting representations and formats:
As teachers we likely do this already but it’s important to note that some students need to different representations that link two concepts they already understand in order to bypass difficulties. It’s just about shifting perspectives, but not expecting students to make the leap on their own. One should be aware that subtle changes in language or format can be very challenging for students with executive function problems. This is where study guides help students practice their test taking abilities.

There are also times that students struggle to select the appropriate strategy to solve a problem. If disorganization reigns as a part of executive function problems it’s easy to see why students would have difficulty solving problems with multiple steps. Teachers can use templates with sequential steps that will help students discern between important information. An example of this is teaching linear equations. Once they’re anchored with their template students can use this to move on to more complex reasoning.

Checking strategies:
Making efficient use of time during tests and the ability to self-monitor and check work can make a huge difference in achievement. How can teachers help support those who do not have the strategies which seem innate to others? Error analysis in which the teacher works with the student to identify individualized common mistakes. They can then come up with “strategy tips” that a student can write at the beginning of the test as a means of reference for checking.
Remember that learning by solving problems without rules, routines or repetition can cause some students to feel lost in the nebulous that is learning. With just a few quick strategies implemented into teaching lessons and paradigms students with executive functioning difficulties can benefit from some of the old styles that many of us grew up with. It is not about making major changes but rather about embracing the past and mixing it with the future.
For more examples consult:

Roditi B. N. & Steinberg, J (2011). The Strategic Math Classroom. In L. Meltzer (Ed.). (2011). Executive function in education: From theory to practice (p 237-257). Guilford Press.