“Mathematicians do not study objects, but relations between objects.” Henri Poincare
I was chatting with a few of our staff this week about the ways we help our students develop their ability to work with numbers, specifically when they are adding and subtracting in the early years. An important point that I often stress when talking with parents and teachers about mathematics is that the area that many of us believe to be the critical focus of mathematics (the operations of adding, subtracting, multiplying and dividing) is actually of secondary importance.
Simply put- we spend way to much time trying to force children to memorize or learn the operations and not nearly enough time helping them understand the numbers they are using. Put another way- think of the numbers as nouns and the operations as verbs; in math, as in life, there are way more nouns than verbs and they are much more interesting!
This media clip on Using Open Number Lines from Dr. Alex Lawson does a great job explaining how using a model like a number line can support children to think about the quantity value and relationships that exist between numbers in a mathematical situation. It also shows how using models as a precursor to what we call the standard algorithm is important at all stages of mathematical development. For most of us, this type of instruction was just not used when we were learning math in school and it is too bad, because it would have save many of us from a life of math phobia.
A lot of students and adults think that using the algorithms is the math- it’s part of it, but not nearly the most important part. In fact, the algorithm can most simply be described as a way of showing (or modelling) what has been done with the numbers. A student who uses an algorithm to solve a problem without understanding the relationships between the numbers is no better off than a student that uses a calculator- they both don’t really know what they have done.That’s why we are using models like the open number line- they allow the student to see the connections and relationships between the numbers and build a model of how they can solve a problem.
There are only a few mathematical operations but the numbers are (literally) infinite- the numbers are much more interesting than the operations- tools like the open number line help our students discover and harness this idea.
“We all want straightforward information about what’s working and what needs improvement. We also know there is more to education than scores in reading, writing and math.” ~People For Education~
Here is a question for parents- what do you really want from our schools and school systems? It’s a challenging question for challenging times. One reason for this is that the expectations parents have of our school system are often based upon their own experiences and their own unique contexts and priorities. We want schools to be safe, we want our children to be successful, happy and equipped with both knowledge and skills and we want our children to have friends. Let’s face it; when it comes to school, parents want it all (not to worry- it is okay for a parent to want it all for their child).
The challenge lies in how we decide to define the real success of a school and the ways that we may choose to measure this success. As a school and district we use surveys, focus groups, standardized assessments and and a wide range of demographic data to define and measure; and we respond through our school and board improvement plans.
As a principal, I count the smiles on the faces of the students and adults in the building; a simple but surprisingly useful metric.
The Ontario-based advocacy organization People for Education is exploring this topic because they believe that; “…it is both necessary and possible to create an easy-to-understand Canadian-made set of indicators that will be useful to educators, publicly accepted, and that reflect a complete education.” I encourage parents, educators, interested community members and students to click on this link and join the conversation.
“In the end it is better to see the world for what it is becoming, instead of what it is. Better to fight for the future, instead of the past.” Joe Keohane
I spent the past few days at the annual provincial conference for the Educational Computing Organization of Ontario (ECOO). The conference is an important part of my principal learning; it exposes me to the emerging ideas and concepts in my field and provides me with the opportunity to connect (and re-connect) with the many creative and passionate colleagues that make up my online professional learning network. As an added bonus, this year I was able to attend the conference and learn along with two of our Park Ave PS teachers, Andrew Bernier and Erin Stanojev- a genuine treat!
I’ve embedded an earlier version of the talk given by one of the keynote speakers, Jamie Casap, that really did a nice job of synthesizing the key theme of the 3 day conference: Bring IT Together. In a clever piece of wordplay, the ‘it’ is actually the IT, or Information Technology, that we take for granted, and often make limited use of, in our schools. Those who know me also know that I am a keen advocate for ‘better’ not ‘different’ – for me, they are not the same thing. Better speaks to the impact our work has on student’s lives and learning, where as different is often nothing more than a change in tools- like how we now use data projectors the same ways we used to use overhead projectors and VCR’s.
For me, the real learning begins after I have returned from an workshop session or conference;and I have just a few reflections from my time away (infused with a Beatles motif) that I wanted to put out there- both from a personal and system stance:
- Get Back- I am at my best as a school principal when I get back to where I started from; the classroom. I have to admit, I’ve been a bit of an office cat since the start of the school year and that needs to change. As I spent the last few days immersed in learning alongside classroom teachers (I’ll get to that point next) it reminded me of how my leadership needs to be situated at the intersection of students and teachers- in the classrooms and halls. Not only when I am co-teaching, but even just sitting somewhere other than my office when I have work to do on my laptop- our school-wide wifi enables anyone to connect and create anywhere- myself included.
- Come Together- The best part about the ECOO conference for me is that it is almost entirely made up of attendee’s who are classroom teachers. There are a smattering of district IT folks and a tiny number of school and system administrators. The ideas, passions and frustrations of these most innovative and gritty educators fuel my head and my heart and make a direct impact on my thinking as a school principal. I don’t doubt the importance of the large, prestigious, mega-conferences that administrators typically attend; I just doubt the impact these events have. They are often so disconnected from classroom practice, and lacking in teacher voice, that the transference is limited. I know that time away from the school is a challenge for principals but I would love to see more of my colleagues attending teacher-focussed events like ECOO.
- The Long and Winding Road- The keynote speakers at this event were thought-provoking, edgy and authentic. @ambermac, @jcasap and @kevinhoneycut each talked about how the changes that the we have seen in the past 5 years will require adaptive, creative and deep evolutions to classroom and school practice and they alluded to the importance that our public schools lead this process. The teacher-led sessions offered ideas that were cutting-edge, creative and impactful. We are in a context where we have to fight against the inertia of traditional school cultural norms; with school and system leaders, with parents, with policy makers, and, in many schools; with ourselves! Too many in our profession are not looking ahead to the place where our students have already arrived-and are still moving, and if we are not with them we cannot have an impact on them- and they need us now more than ever.
Jamie Casap started his talk with the statement that public schools are integral because,”Education disrupts poverty.” Whether we are talking about a poverty of resources, ideas or opportunities; this is true. If public schools are going to remain a place where they have an impact on children’s lives we need to be both different and better, it’s getting too late to Let it Be.
“Statements without evidence are just opinions – there are too many of those in education and that’s what’s got us into trouble.” ~John Hattie~
There are a lot of opinions about what our schools should do to fix the problem of of gaps in student achievement. We don’t really have the luxury of entertaining popular theories or opinions- our professionalism requires that we look to the valid research on what represents effective classroom practice. The chart above is an attempt to represent the complexities of effective teaching into a manageable graphic. It is a representation of the massive inquiry that John Hattie, a researcher from New Zealand, conducted to answer the question- when we consider learning for children what influences or factors actually have an impact on academic learning?
If you click on the link it will enlarge and allow you to read it more closely. The inquiry focused on six areas that contribute to learning: the student, the home, the school, the curricula, the teacher, and teaching and learning approaches. A key understanding in reading the graphic is the idea that the longer the slice, the greater the impact on academic learning. Another understanding in decoding the chart is that the average of all the influences is .40, so any influence above .40 in the study was deemed to have an above average impact, and any lower a below average impact. There are a few items, like summer vacation and retention of students, that were deemed to have a negative impact on academic learning.
I’ve read the study and took away a few key points:
- The factors with the greatest impact on student learning are classroom and school-based and involve the interaction between teachers and students
- Teachers need to reflect upon, on a daily basis, the impact of their actions on student learning and adjust accordingly
- The giving of feedback to students on their performance only matters if the student understands and acts on the feedback
- Teachers need to work together to build their understanding of how to design, teach and assess classroom learning; this learning needs to be situated in classrooms and focused on what the students are doing and saying
As you can see from the graphic, some factors have a greater impact than others. As a school community we need to focus our resources and attention on making changes that will have the greatest impact for all our students, but especially those students who need it most urgently.
The problem we really have in math education is not that computers might dumb it down but that we have dumbed down problems right now. Conrad Wolfram
Staff, parents and students are having many conversations about math at Park Avenue these days…given some of the recent trends in our mathematics performance on the EQAO assessment; these conversations are both timely and important.
We are all entitled to have an opinion about this topic and I’m glad people are sharing their opinions. I came across this TED talk from mathematician/researcher Conrad Wolfram that poses some dramatic and interesting challenges to our traditional views on how mathematics should be taught. I am hoping that those who wish to continue this dialogue will look beyond what they know and believe and open up to the ideas of others; from within our school community and from beyond – including those who are engaged in research like Wolfram.
It turns out that Barbie was right- math is hard. Learning to think mathematically is a difficult as is teaching others to think mathematically. I am hoping that we can extend the conversations we have started into this forum; to capture some of our ideas and perspectives, the build some understandings on how we can work together as students, families and educators and to push all of our thinking forward.
Our school improvement work isn’t easy, it not always quick, but it is both urgent and important.
On behalf of our staff I wish all of our students and families a restful and happy Thanksgiving Day. Please click on the link to read this week’s edition of the Park Avenue Post:
“Do not worry about your difficulties in mathematics, I assure you that mine are greater.” Albert Einstein
The chart pictured above is a simplified representation of our school’s most recent results from the provincial EQAO assessments our grade 3 and 6 students wrote late last school year. To view the detailed report for Park Avenue PS just click on our 2013 EQAO Report.
The information conveyed from these assessments is used for a myriad of purposes, depending upon the stake and stance of the user. Parents use the school and individual student reports to get a sense of how their child is performing against the established curriculum benchmarks. School and district staff use these results to provide information on student strengths and needs in the areas of reading, writing and math to inform program and professional learning needs. The Ministry of Education uses the results to gather information on the performance of students across the province- to determine program needs and priorities- but also to demonstrate accountability of the system to parents and taxpayers. And members of the media and other pundits use the results to support and advance opinions and theories on our public education system as a whole.
For us, as a school community of parents, educators and students, these results have given us some things to think about and talk about. It’s not my place, at this time, to spin the numbers. I invite those of you who are interested to read through the report, reflect upon what this information means to you and join us in the conversation about our next steps. The other reason I won’t spin the numbers is because the charts don’t represent numbers, to me they are real kids- the students who spend their days with us at Park Avenue Public School. At the core, I look to these assessments as one way that our kids can tell us how they are doing; what they are doing well and where they may be struggling.
So, in looking at our assessment results, this year and over time, the trend that we have seen in the area of mathematics is a concern. In spite of what media reports or popular sentiment may be, mathematics is more than just ‘memorizing stuff’ and ‘drilling the basics’. Math is a complex and specific language that is used to describe our both our physical and abstract realities, realities that are based upon patterns and relationships using numbers. However, like any language it can be learned, with direct instruction from adults who know the language and know how to teach it.
There is only one way for our students to receive classroom instruction like this; professional learning for our teachers. No packaged program, no quick fix, no short cuts. Richard Elmore reminds us that ‘real accountability’ is not found on standardized assessments or tests. Real accountability is the relationship that exists between students, teachers and the classroom tasks that students do each day. Our staff are committed to work together and learn together about how to design and teach tasks that will enable them to provide our students with this instruction in mathematics; from Kindergarten to grade 8.
And it is my responsibility to lead this learning.