It Takes Sacrifice

As a tutor I am able to get a pretty good understanding of the way my students are being treated at school. I can really tell which of my students' teachers care and which ones are just trying to make it through their day with as little effort as possible. The subject that I am hired to tutor the most is math which I know is a very difficult subject for some students to grasp. There are two students that I have in particular that I feel have very different teachers, one being the teacher who just lets the student slip through the cracks and is given useless tasks to work on, and the other being the teacher who cares deeply about their students and wants them to succeed. The first of my students never comes home with any homework, or additional assignments that can be worked on with his tutor. The teacher is well aware that I am at the students house once a week and yet there is nothing from the teacher that I can work on with the student to get him caught up in class with. Most of the time when I ask what the student worked on that day he replies with "Nothing, I just played on Cool Math Games" which if any of you have ever visited has games that do nothing to help a student practice math skills. I feel as if this student is just ignored at school and the only time he gets the help that he needs is when I am there to tutor and he is able to receive that one on one support. The other student that I have has a teacher on the other side of the spectrum. the student always comes home with additional work and comments from the teacher to provide me with the information that I need to better help this student. Another thing about this student's teacher is that she sacrifices her own time in order to help her students succeed. I know that if I am unable to complete an assignment with the student that the teacher stays in her room during her lunch period to help the students that require additional help. She gives up her own time to ensure that the students are able to understand the material and provides a setting where the students can receive that one on one help that they require. She will also stay after school to provide additional help. I believe that this is truly what it means to be a teacher. Someone who is passionate and willing to make sacrifices in order to help their students succeed.

Gently Down the Stream?

What is the purpose of education?  This is a loaded question, and depending on your own personal and professional philosophies, there could any number of different (if not heated) debates over the answer to the question.  I am in no way going to attempt to answer this in this post.  However, I do want to highlight one generalization; that a large portion of education is, in essence, to prepare our students.  To prepare them for what, you might ask?  Well, for many things I suppose.  It's about laying a foundation.  Children often attend daycare, which prepares them for school (think ABC's and 123's).  Elementary school can then be seen as a way to prepare students for the secondary level, which in turn, prepares students for one of many pathways (workforce, college, university, military, etc.).  I say pathways, because that is the terminology that is used.

At the secondary level, we guide students along this path through the process of streaming.  Although, we sometimes don't like to use this term.  When I went to school, there were a few streams, including general and advanced classes.  These same streams exist today, but they have different names to try to reflect the pathway that each student is working toward.  Most students are now placed in either the workplace/essential, applied or academic levels.  The applied changing to college level and the academic changing to university level in grade 11.  In theory, this makes the most sense; have students work at a level that will help them be successful in obtaining the pathway of their choice by the end of high school.  But who decides this pathway?  Well, ultimately, the parents do.  Teachers and principals give recommendations and even the students give their input as to what they would like to do, but the final decision rests with the parents, and rightly so.  However, this can often cause some difficulties.  Parents who have themselves, earned a university degree, often want the same for their children (teachers are often guilty of this).  By no means is there anything wrong with this either.  What can happen though, is despite recommendations from professionals (teachers and administrators), sometimes parents want their child to go into the academic/university stream no matter what, with the expectation that as long as their child 'tries and works hard', everything will work out.  There seems to be a growing fear that if they place their child in the applied stream, they are closing doors.  I often explain to parents that by taking applied level courses, you are not closing any doors.  Students who take applied level courses can still get into university programs, but may need to take a couple of extra steps.  Also, students do not need to set their academic sights on university.  There is nothing wrong with obtaining a college diploma.  In fact, there is a growing trend to earn a diploma over a degree, since the number of university graduates without employment is increasing, while more and more college graduates have jobs (in some cases higher paying than those with degrees). 

As I explain this to parents, sometimes I use an analogy of an actual stream.   Streams have shallow or deeper waters.  In the shallow waters, even if you don't have all of the skills needed to swim, you can still work toward learning these skills and eventually make it to the deeper waters if that's what you want.  However, if you jump straight into those deeper waters without the necessary skills, you will be in over your head so to speak.  Of course, things can be done to help keep you afloat, but will this ever help you tread water all on your own?

If students are placed in the wrong stream, it can have a significant impact on their academic performance, their self-esteem, and in the end, their life goals (even if they don't know what these goals are yet).  This is a huge issue, especially when it comes to mathematics.  I have found in my position this year (student success) that many of these students are not in the proper math stream.  We educate students on math pathways, but many continue to perform poorly on tests and assignments, and it isn’t for a lack of trying.  Math is one of those subjects that can be very difficult to grasp for some students.  Sometimes we can catch this early, and try to make changes to their timetables.  However, the final decision still rests with the parents and the fear of limiting their child’s academic opportunities often wins out.  To try and prevent this, I have worked on a collaborative inquiry team to try and come up with a way of recommending streams with some facts and data to back this up.  Diagnostic assessments of what is expected at the academic or applied math levels could be given to grade 8 students, and recommendations could be made based on these outcomes.  Information booklets containing examples of math questions from each stream, as well as careers linked to each stream, could be given to parents to ensure that they are properly informed.  If students are in the wrong stream in mathematics, it can cause them to fall behind…quickly.

I am not sure if there is really a solution, but this is something that deserves some exploration.  If we are to prepare our students properly, they need to be able to meet with success in the math courses they are taking. Most of all, they need to know that it’s okay if they are not taking academic/university level math courses in high school.  Sometimes you simply need to go with the flow, rather than fight the current.

Redefining The Subject of Math Through Focus Classes

Picture this.  20 athletes walk into a math class, excited and bursting with enthusiasm asking the teacher, “Sir, what are we going to learn today?”  Discussions are going on in the background about last night’s homework that involved watching a professional sporting event.  You’re probably thinking this scenario belongs in a fairy tale, yet I pose the question, why does it have to be?  I’m sure many of you have heard the term “differentiated instruction” being tossed around the education world in the past decade.  This theme is becoming more and more important as our student’s needs are changing and we are realizing that the old model of teaching just isn’t cutting it.  We as educators are constantly trying to find new ways to engage our student’s interest and bring life to our lessons in a fun and interactive environment.  Web sites, blogs, and articles are filling up with research on the effects of differentiated instruction and how we should be implementing it into our classrooms on a regular basis.  This topic is especially turning heads in mathematics courses where there has been a huge push to linking abstract concepts to real world application.  It’s never been a secret that the students in math classes are consistently asking themselves, “when are we ever going to use this in the real world?”  Educators nowadays are realizing more and more that success in the math class relies heavily on the interest and motivation of the students.  If there is none, the students do not pay attention and important concepts are missed creating progressively larger gaps in their knowledge in the subject.  On the flip side, if students are genuinely interested or curious even, their attentiveness increases causing a ripple affect resulting in a positive and successful learning experience. 

I’m not sure about other schools, but in the one I am currently teaching at, over the past 5 years we have introduced focus classes in the physical education stream.  A focus class as it pertains to physed is an entire course tailored specifically to one sport discipline.  This was done in an effort to cater to our students who were passionate about the pursuit of excellence in their specific sporting interest as well as bolster the level of development in our athletic programs.  The concept of the focus class spread like wild fire and students loved it.  This form of differentiated instruction that tailored to the specific interest of the individual created a positive atmosphere for the student athletes to thrive in without the distraction of being disengaged in activities they had to participate in that they weren’t particularly thrilled about.  As a math/physed qualified teacher the notion of the focus class and its success had me thinking.  What would it be like to have this concept applied to a mathematics setting?  How awesome would it be to offer math courses that carried a theme over the entire semester and integrated it into various lessons to engage and bring life to those teachings?  Why can’t math have focus classes too?  Imagine signing up for classes in grade 9 and seeing in addition to the regular math class the option of, mathematics in sports, and mathematics in media.  This would definitely create a stir in the school.  Students would be asking one in other what stream they were going into, what they think they would learn, curious as to what this is all about.  You would have students taking that specific focus class because they were interested in the subject (ie, sports and media).  This would also make the life of the teacher easier in the sense that they would not have to worry about bridging multiple real world topics into the math that some pockets of students would disconnect with because they didn’t care about how many comic books Sammy bought at the store.  Now I realize that in theory this sounds like it could be a great idea, but in reality many hurdles would need to be overcame before it could reach the schools.  Hurdles that would include; how to adapt all the content of that topic to the curriculum in a logical progressive manner.  Which focus topics do you introduce?  What grades do you offer it in? 

With all this in mind idea of implementing math focus class’s sounds like it could offer something to the students that they haven’t had before.  Choice.  The choice to take control of their education and adapt it in a way that fits their lifestyle and personality.  If we can offer a differentiated approach to teaching a subject that has carried a stigma with it for generations, it might be a way for society to embrace it in a new light, and reconstructing its image starting with our children.

Dispelling the notion that "I'm just not good at Math"

I think often we hear from students who struggle in Math that it is because they are "Just not good at Math". They say things like, "My parents, sisters, brothers are all bad at Math and so am I".  But is this true, is there a Math gene which makes a student good or bad at Math? I don't think so. Obviously, there are people who Math comes easy to, but I believe that every student can be successful at Math at the high school level.  Researchers have looked into this issue and have found, "For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence." (http://www.theatlantic.com/education/archive/2013/10/the-myth-of-im-bad-at-math/280914/).  I think self confidence especially plays a huge role in a students success in Math (and for all academics for that matter).  It is our job as teachers to instill that confidence in our students, dispel this notion that they are not good at Math, and create an environment for all of our students to be successful.  How do we do this? By doing all of those pedagogical strategies which make our learning environment fun, inclusive safe and memorable.  We do this by creating fun interactive lessons which provide our students with the opportunity to gain a passion for the Math we are teaching.  We use differentiated instruction to allow our students to be successful in their own way, have them gain in confidence in their Math abilities and  build upon their skills.  With some hard work and preparation, our students can be successful and we need to get away from the idea that to be successful in Math, you either have it genetically or you don't.  

Financial Literacy...Why are we not teaching more about this in Ontario schools?

A theme that seems to keep arising in this course is the concept of making the Math tools we teach applicable and meaningful to real life.  After thinking about it, I was wondering why we do not teach more about personal finance management to our students?  Why do we not teach our students (or at least give them the option to take a course) about personal finance, learning about spending, saving, borrowing, budgeting, debt, interest, investing and things of this nature?  These are very important life skills that people should have or at least know a little bit about when getting started out in the world (whether that is in post secondary education or the workforce).  Especially in times where it our society has been on the brink of financial crises, and students are carrying more debt than ever before, these skills seem like highly necessary ones, to help prevent our youth from putting themselves in tough situations, or even financial ruin.
      In Ontario, there is no separate course which teaches about financial literacy. In 2011, a financial literacy program was introduced to integrate these types of financial skills into the curriculum from grade 4 onward (http://www.edu.gov.on.ca/eng/surveyliteracy.html).  But some teachers, such as Genevieve Tran (licensed teacher in Ontario, Masters of Education, and has taught financial literacy abroad) believe that the lack of knowledge, accountability and assessment component for this program means that students are not getting a good understanding of these issues (https://ca.finance.yahoo.com/blogs/insight/why-isn-t-financial-literacy-taught-school-180027714.html).  I know from my own personal experience, I was not very well versed in areas when I was younger, such as getting a student loan from the bank, purchasing cars, the different types of financing there are, utilizing OSAP, interest rates on different debts and what should be paid off first etc.  If not for guidance from my parents and some knowledge I had learned in school I would have been lost.  A lot of students do not have the luxury to lean on their parents for this knowledge, because many of them may not know a lot about these topics.  Having more background information on these topics, and gaining a better understanding of them could have huge benefits for our students and their financial stability in their future.  Many of these skills, even ones as simple as planning a budget based on a fixed income, should be essential skills that our students learn and become familiar with to help them with real life practical applications.  What do you think, should we invest more time in teaching our students to be more financially literate?
  

More on Math stories

One of the things that teachers are noticing is that students are afraid to fail.  If they don’t get the answer right away they often will stop trying and wait for the right answer to be given by the teacher. 

According to Dr. Margaret Taplin of  the Institute of Sathya Sai Education, Hong Kong a growing problem is “that more and more students are becoming afraid to try new things in case they fail, and/or become depressed and question their own self-worth if they do make mistakes. Mathematics, with its emphasis on 'right' or 'wrong' answers can potentially reinforce these fears.”

So how can we make it okay for students to “fail”?  Well there are the obvious things we can do in our classrooms, like make them welcoming, building relationships, making the classroom safe for mistakes (no put-downs, listening with respect, responsible talk) and introducing stories of famous mathematicians and what they did when they couldn’t find the “right answer”.

Dr.Margaret Taplin feels that telling our students about famous mathematicians and what struggles they went through to become successful is one way.

Another way is to read our students stories which one might think are only for young children.  As a high school teacher I often read children’s story books to introduce novels or topics.  (For anything to do with civil rights, children’s rights, oppression, or government, I always read Freedom Summer by Deborah Wiles: read it, you’ll be glad you did.)  But when teaching math, I always start with Math Curse by Jon Scieszka and Lane Smith.  It’s all about a girl who is the victim of a “math curse” and a great way to introduce how much math is a part of everyday life.

Little anecdotal stories about mathematicians can be found at

http://www.mathgoodies.com/articles/stories.html

Math Curse is available on line and most likely at a bookstore near you.

North American Math Reform: Where should we be headed next?

What direction are we heading in regards to Math with our students in North America?  Trends at the high school and university level tend to show that the Math reform which happened in the North American education system about 25 years ago, which focused more on large concepts rather than mathematical techniques, has improved our students grasp of concepts, but has in turn there has been a decline in numeracy and mathematical techniques. As Robert Mann, a professor of physics and applied mathematics at the University of Waterloo, put it, “Now, they know what to do but they don’t know how to do it,”.  In an age of computers and calculators, this concern has grown even more.  Sherry Mantyka, a professor of mathematics and statistics at Memorial University, has also found that this is a problem with students working memory was not sufficient and they make constant mistakes.  She states over the last few years, hundreds of their undergraduate students were in need of remedial math to get their basic math skills to where they should be. 

                This is not strictly an issue that is being faced in North America.  In Canada we have placed in the top five for math scores on PISA tests (Program for International Student Assessment), but are seeing these issues with our students.  The country which has placed number one on these tests in recent past has been Finland, but they have also been seeking help with their students having issues with numeracy and computational skills.  The PISA tests seem to focus mostly on applying Math to the real world (Math Literacy) and not as much on Math fluency.   We have recently debated the Pros and Cons of standardized testing (specifically EQAO), and there are valid points on both sides of the argument. The debate on this issue is contentious, with people stating that Math fluency, and compensating for this with calculators and technology, is not an issue as long as they understand the broader concepts.  Others, such as Dr. Mantyka, believe these issues may have even attributed somewhat to mortgage crises because of individuals lack of basic Math knowledge and computation skills (Although I think this may be somewhat of a stretch to relate).

                I am a firm believer and advocate of using technology and implementing its use with our students to create a better learning environment.  But, I also do believe the need for the basic understanding and application of math techniques should be had by students before they start to use devices, such as calculators, to aid them.  I think we need to find a balance in our teaching between Math Literacy and Math Fluency, so our students are not only able to ‘know what to do’ but also know ‘how to do it’.  I do think we need to promote and have our students learn the ‘Big Ideas’, and concepts of Math in our curriculum, but I do think we must not neglect the basic Math skills and techniques for which those big ideas and concepts are built upon.  As teachers we also need to dispel ‘Math Anxiety’ as Jo Boaler (Professor of Math Education at Stanford University) has said this to be one of the major reasons for decline in the math proficiency of our youth in North America.  I read a book years ago called ‘Outliers’ by Malcolm Gladwell, where in one chapter he discussed English speaking’s non-sensical (or at least more difficult) way of counting compared to other languages, and why that affects young students counting and computational development compared to other ethnic groups.  It creates some ‘disenchantment’ or anxiety with students at a young age when learning math.  So why can’t we attempt to make this more efficient or better for our students? (I understand that would be a massive undertaking but may be something to look at).   As teachers, we ourselves are constantly changing, learning new things, and trying to adapt to our ever-changing teaching environment.  We should strive for reform on more constant basis to do our best to give our students the best education possible.  What do you think? Where should we head next in our math development as North Americans? Is Math Literacy more important than Math Fluency, or should we strive for a better balance between the two?

Resources:

 http://www.universityaffairs.ca/news/news-article/big-drop-in-math-skills-of-entering-students/

http://joboaler.com/timed-tests-and-the-development-of-math-anxiety/

http://gladwell.com/outliers/rice-paddies-and-math-tests/