Wondering about teaching math, timed tests and why?

"Many parents have asked me:

What is the point of my child explaining their work if they can get the answer wright?

My answer is always the same.

Explaining your work is what, in mathematics, we call reasoning, and reasoning is central to the discipline of mathematics." 

- Jo Boaler  - https://www.youcubed.org/

Dr. Jo Boaler is considered to be one of the premier voices in mathematics teaching and learning and wrote one of the most interesting books I've read in a long time called "Mathematical Mindsets" - among others that I have also enjoyed.  I encourage parents and teachers to go to her website and take a look - there is so much there to challenge thinking about what teaching mathematics is about and how to engage kids in really learning about math rather than just 'doing' math!

This week there was a firestorm of opinion slaking through Alberta over the 'terrible' performance of grade 9 students on the Provincial Achievement Test.  I followed this story with great interest - I have never taught grade 9 Math but, as a grade 5/6 teacher for 20 years, I am very familiar with the concept of 'timed' math tests since they used to be a part of the Grade 6 PAT for several years too. As I listened to the outrage and upset and finger pointing at elementary teachers who apparently 'avoid' teaching children how to count and form numbers - among other things, I have some wonders after listening to a week's worth of upset...

I wonder why a timed test?

In the days when I was a student, and when I was a young teacher, we used to give timed math facts tests to students in elementary school -  for awhile, we called them Mad Minutes after a program that was popular at the time, and we pretty much gave the tests every day to kids.  Each test would be focused on one or two concepts - adding, subtracting, multiplication, division - or a combination of adding/subtracting or multiplication/division - at least, towards the last couple of months of the school year.  Tests would offer fewer questions in the beginning, and would gradually increase in complexity as the year progressed with the idea that students would get faster at answering questions over the course of nine or ten months. Including the at-minimum 5 minutes it would take for kids to set up for the tests (distribute the photocopies and have kids find pencils and erasers), and the 5 - 10 minutes per day we took to check and correct the answers, we would spend approximately 60 - 75 hours each school year trying to get our kids faster at filling in the same facts over and over. 

One thing I noticed over the years was that kids really didn't get much faster if they wanted to be accurate; if they sacrificed accuracy then they were faster but not successful. Once they knew their facts, they knew them - they didn't get faster at recording the answers on paper, probably because recording the answers on paper took the same amount of time regardless of how quickly you knew the answer. And your answers had to be legible so they could be marked. I used to wonder about those timed tests - and how much time was devoted to practicing for one PAT. Was that the most important thing to assess in learning mathematics - how fast they could fill in the blanks? I wondered where the kids would use their quick regurgitation of math facts when they became adults? 

Having learned all my math facts did not make me any less of a mediocre (at best) algebra and trigonometry student in high school and, e other than trying to figure out how much six pairs of socks will cost when shopping, I haven't used my instant recall of math facts too much at all as an adult either. I do use a calculator to add multiple, large numbers - although I am sure I could eventually get the right answer if I tried to add them mentally - it's just that the calculator makes my work faster and more accurate. 

So I wonder about the concept of timed testing - are we finding out what we really want to know about what students understand about math? 

I also wonder about the nature of the timed test - 1.5 minutes per question to complete multiple step/multiple operations questions that include reading - not basic recall of facts at all but applying concepts and strategies in a timed situation - I wonder about that too. 

Kids learn to apply multiple strategies to questions from Kindergarten (first we sort blocks into appropriate groups, then we add them, for example) but we don't give them a time limit because we want to know what they can do, how they reason and make sense of the world through a mathematical lens, not how fast they can think. Adding, subtracting, multiplying, dividing, finding square roots and converting to fractions from decimals are all mathematical strategies students learn to do and use - trying to do them all as quickly as possible within one question in a 15 minute time span just may not be a quality indicator of student achievement... 

Several years ago - back in the early 2000's - I had an opportunity to join a very brilliant group of teachers of mathematics to become part of a team that wrote elementary grade level mathematics text books for the "Math Makes Sense" series, an approved Alberta curricular resource. I learned much more than I could ever have contributed to the process for the Grades 3/4/5 text resources, about teaching mathematics but also about understanding what mathematics was all about. What I know is that we have to have a balance in teaching math, just like we have to have a balance between reading and writing when we are teaching literacy. Students need to figure out numbers and then understand they are reliable - 6 is always 6, 6 x 2 is always 12. They also need to know how to use that information in a practical sense and apply it to any and all situations - filling in pages of questions on copied sheets will not make them faster once they know a math fact is always a math fact, and adding up long columns of numbers when you can't really relate to how many 11,654 is, let alone 11,654 + 12,123 will not solve the problem of how many tiles to purchase for a bathroom renovation when you are 35 years old. 

Because, to my way of thinking, this is the crux of the math dilemma - we need to teach kids math so they can carry it with them into real life and make sense of mathematical things - like area and perimeter, interest on mortgages, doubling or halving a recipe, how to order shingles for the roof or calculate your rate of pay for a summer job that needs to cover your university tuition. Some of our kids will definitely become engineers, computer programmers and commodities brokers. Regardless, they will all need to know a number is a number, concrete and useful and easily manipulated to make life more simple and sensible. 

Timed tests? I wonder if they tell us much more than it might be hard to read a bunch of multi-step questions, calculate and record the answers in a very short time frame. I am not convinced they make us faster at recording answers we already know - it takes us the same amount of time to record the answers, even with much practice. 

I understand why the public is upset - on the surface at least, the results don't look so good. But I wonder if it just might be possible the results aren't really showing what we want to know - which is how successfully students can manipulate numbers and ideas to demonstrate understanding of their relationships to each other and other mathematical concepts. 

I also wonder about all the kids who have learned to dislike mathematics and opted out of amazing careers to avoid math altogether...as a mother, I learned the hard way that this is sometimes the way kids feel about math - and I am determined to offer a different way of seeing and thinking about math at EHS. No timed tests but lots of opportunity to cement knowledge of numbers, recall what we know and make sense of how numbers connect to shape and space, known and unknown, parts and wholes. That's the real challenge of mathematics - learning to see numbers as real and useful and fun rather than blanks to fill in on a page.  At least, in my opinion :)

Lorraine Kinsman

Principal

Is School About Students?

"I don’t want our school to simply be a reflection of society... I want our school to shape society."

- Danny Steele

One of the most significant challenges for teachers of any grade level is to help school make sense for kids. This may just be one of society's greatest ironies - that a place designed to teach children really is not about them at all! 

A structured day with specific tasks is not a natural way of being for children - especially young children - and the content is not necessarily meaningful for every child either. Although our repertoire of teaching skills and strategies has expanded greatly over the decades, we still tend to teach as though children are small adults waiting impatiently to grow into full adulthood. In reality, children are more inclined to resist - consciously or subconsciously - what they don't know until they see a reason for learning something new. Especially when they are not yet developmentally ready for learning a particular skill, concept or strategy that we, as adults, believe they must!

Historically, children were taught the accumulated knowledge, traditions, skills, values and beliefs of their cultures at home until such time as society knit itself into tighter units where large clusters of children with common age ranges offered additional challenges. These new challenges included child care with the onset of the industrial age, as well as demands for learned people to assume governance and leadership roles in the sparse population bases establishing citizenship through colonization. With an eye to bringing youngsters together for learning - thus making it less expensive both in terms of costs and time - schools began to form in multiple ways throughout Europe and both North and South America. And with the development of schools came the need for management - schedules, timetables, groupings, instructors, what to teach. Few of these decisions were made from the perspective of the child - most were made to ensure effective school operation by the adults.

As time passed and research became a key component of education, many changes to organization, teaching strategies, scheduling and development of curricula took place.  Infinitesimally slowly sometimes, and not necessarily in keeping with societal changes but there have definitely been developments that have been positive for children - as well as some that have not been so positive.  And today, we are still struggling to balance between an archaic system designed for adults and a child-centered one that meets the needs of children. 

It is an epic struggle and as an early elementary school it is our fundamental work - trying to help children make sense of a 'school' not necessarily designed to meet their learning needs but rather the organizational needs of the adults.  Essentially, school are still designed in alignment with these early concepts of school - although our curricula have become saturated with much more than the early reading, writing and basic math students were expected to become proficient with in school.

“The world is more connected than ever, but the nature of its connections has changed in a fundamental way. Individuals are using global, digital platforms to learn, find work, showcase talent, build personal networks.  -McKinsey & Co. 

In a changing world, schools are beginning to seek ways to make greater sense for their students, to offer them reasons to attend rather than learn online, to create learning opportunities that will lead to future careers and options for living successfully, to generate interest and wonder and pique curiosities for living in a world that has increasingly become encased in multiple boxes - our homes, our schools, our places of work, our communities, and now our digital platforms. 

How can schools offer students a different way of understanding and making sense of an increasingly complex yet highly fragmented world? It is time, it seems, to re-think the bells, groupings, schedules, content-heavy curricula and confinement that has been the mainstay of school since formalized schools began to emerge almost two centuries ago.

"While we have this tendency to focus design on the classroom…it is so important that leaders are also looking intentionally at the design of the organization and its processes and systems for future learners."  - David Culberhouse

Educators know kids need to move so we are re-thinking the design of classrooms where students have flexible seating, options for standing or sitting or even lying down to work, think, create, innovate. Children need to be both outside and inside to make connections, ask questions, learn first hand of the integrated nature of the world. In a world where children need to be contained for safety reasons rather than allowed to run free in their neighbourhoods, we must find ways to bring physical literacy to them through play, music, action that is also contained - and because of this, we explore the world together in intentional ways through community walks, coulee visits, field trip experiences. Learning to create and make things using tools originally designed by ancient ancestors and consistently improved and perfected through generations is honoured in our Studio with Maker Space and Design Thinking opportunities - and choice is championed through our weekly Wonder Times. We bring music, drama and art together to perform and share our thoughts, beliefs and ideas. We group and re-group for literacy and math to problem solve and challenge each other's thinking as we learn and process and figure out reading, writing and mathematical thinking together. 

We are not at the end of the journey of evolving educational approaches - we are at the beginning of recognizing learning is not about how children mimic and act like adults but rather about how adults understand the complexities and subtleties of learning from a child's perspective.  It is only in this way that we invite, encourage and support each child to maximize multiple aspects of their learning capabilities.

A new entry point for students coming to school each day at EHS has been the introduction of our IGNITE time every morning for 30 minutes. IGNITE time starts as soon as children arrive for teaching and learning - it is a brief focusing time at the very beginning of their learning days where they get to choose how they are going to kick start their attitudes and mindsets towards learning. 

Students might choose reading, games, math, drawing, building, designing, music, active play to start their days - some make different choices every day while others are drawn to the same IGNITE activity daily. Teachers monitor but also engage students during this time - some are in SPARK or CALM while others are doing yoga in classes, pedaling on stationary bikes, writing or constructing in the hallways or the Hub, reading in the Learning Commons, hallways or a classroom cubby spot. Teachers might also be involved working 1-1 with a child on any particular day to strengthen a learning concept or strategy taught previously.  Each child's brain seeks different ways to engage in learning and thinking at all times, and IGNITE has proven to be a highly popular, engaging beginning for students.

The two most significant benefits we can see after almost two months in school is a decrease in late starts - children want to be here for the whole IGNITE time - and very smooth, quick transitions to learning tasks when IGNITE time ends - there is no complaining or whining or 'just a minute' - they know the activity will be there tomorrow should they still want to choose to stick with the same focus. IGNITE is reliable, engaging and effective to promote student thinking and learning.

So, is school about students? I do think we know it's time to shape the institution to reflect the children in the building and to get to know our learners as well as we know the curricula and the expectations from adults at the district and provincial levels. Huge work for sure! But also work we believe will benefit all students as school becomes more about who they are as learners rather than who the adults are that designed the building, the curricula or the classroom-based experiences.

Lorraine Kinsman

Principal