WHERE IN HEAVENS NAME DID THE TERM
COME FROM? And who linked it to the math curriculum? MISCONCEPTION ALERT !!!
YOU WILL NOT FIND IT IN THE ALBERTA MATHEMATICS CURRICULUM…
I am a teacher, a learner, a researcher… I meet the criteria for expertise having devoted more than 10 000 hours studying how students learn… I have listened to students in classrooms across 4 provinces, across all 12 grades, within over 2 000 classrooms. I count among my colleagues and friends; teachers, mathematicians, education researchers, scientists and computer scientists from around the world… I speak from a body of experience and knowledge that I have gained over more than 30 years in classrooms and in study with real kids and real teachers.
Mathematics is not a set of arithmetic rules and we are not living in the 1950’s. The space race and the cold war are over. It is the BRAVE NEW WORLD. We are not preparing students to balance cheque books, run cash registers or sit on an assembly line… We are preparing students for a world of information that is raining down at an incredible rate… we are preparing students for a world of MISINFORMATION that is pounding down on them in real time. When John Paulos wrote INNUMERACY so many years ago, when Clifford Stoll wrote SILICON SNAKEOIL so many years ago, their warnings were clear: BE CAREFUL what you wish for. We are now constantly and consistently being manipulated by the influences of mathematics used poorly.
Our students must learn to think about facts and how they are related. To prove why they are “FACTS” and under what conditions they may not be.
Where is it that parallel lines do meet? In what number systems is it not true to write 9 + 4 = 12? In what number systems is 4 + 1 equal to 10. I am talking about understanding how to interpret the symbol system, rather than believing the symbols are the math. I particularly like this statement written by John Holt:
Since we can’t know what knowledge will be most needed in the future, it is senseless to try to teach it in advance. Instead, we should try to turn out people who love learning so much and learn so well that they will be able to learn whatever needs to be learned.
As a teacher, my number one priority for every student is to love to learn and that is not accomplished by drill and chanting and mindless repetition.
Learning is not being told what to do, in how many steps, then repeating those steps mindlessly until you can do them without thinking….
Learning is not sitting alone at a desk for 45 minutes filling in blanks and counting on your fingers…..
Learning is created by you in your mind as you experience objects, situations, sets of information and data… As you construct your understanding, you compare it to others, to what is known in the field or discipline or body of knowledge you are learning about or within.
Learning is active, engaging, pushes you to talk, build, debate, re-consider, compare. Learning makes you wiser, more flexible, more creative, more innovative and gives you power to control your own destiny. Learning FREES YOU TO THINK…. Thinking teaches you to take responsibility for, and be highly critical of, your understanding and current level of knowledge and ability, your responses to others, the work you do, the way you respond to others and react to the world around you. LEARNING teaches you responsibility and stewardship. What you choose to learn must be separated from how you come to know how to learn. Once you are proficient at learning, you can learn anything with accuracy and fluency. Now go ahead and drill all day. But no one will choose to because they already know enough to engage in far more interesting pursuits.
I teach for thinking and understanding so that every student has a chance to learn how to learn. The current Alberta Math Curriculum is focused on teaching students to communicate, make connections and learn to understand and take charge of their thinking. Problem solving is at its centre, unfortunately most of us have no experience with either teaching or learning through problem solving processes and so we have decided that toiling over the stilted and contrived “word problems” at the end of the chapter in the textbook is problem solving in math.
I teach so that every student can experience the power of thinking of learning to construct ideas, compare ideas and verify and justify ideas. MISCONCEPTION ALERT: Students are not continually constructing “new Math”. They are learning by engaging with and constructing personal understandings of the mathematics we all think we know and love. Problem solving is not reading words, picking out numbers and doing calculations…. Problem solving is trying to figure things out for yourself… Here are ten blocks, how many ways can you arrange them in twos… How about 20 blocks, 30 blocks, 40 blocks… is there a pattern? What did you find? Do we agree? Will it always appear?
I have 24 cookies. If I want to share them with 5 friends and give everyone a fair share, what will I have to do with the cookies. What if I had 6 friends. What about 7 friends? Why do I sometimes have to break left over cookies into fractions?
Teaching is not for cowards….. It is not for the faint of heart and it is certainly not 9 to 5 with major holidays and summer off. Teaching is constant and continual learning and growing… I have invested my life in coming to better understand how children think, learn, play and grow… I still do not know enough. I doubt I ever will. The child I taught 25 years ago is not the child I teach today… just as the world I was or thought I was preparing those children for is not the world today…
I teach for understanding to stop the cycle of failure and despair that so many students experience… I am so tired of the stories Johnny can’t read, Johnny can’t spell, Johnny can’t add, Johnny can’t multiply….. When the biggest disgrace of all is that after sitting in classrooms for 9 years the only problem Johnny is really good at solving is how to get the heck out of this classroom….
There is no “fuzzy” curriculum or “fuzzy math” but there sure are some “fuzzy” excuses for why we choose not to teach our students to understand what they are learning. The “fuzzy” thinking that concerns me is about what it means to learn. Learning cannot take place if students are not engaged socially and emotionally. Learning cannot take place if students are not allowed to talk, explain, observe, reflect, question and compare…TEXTBOOKS CANNOT TEACH, and the current set of textbooks available to teachers are not helping…. this is a confidence problem and it involves our coming to understand that textbooks never did and never will TEACH. They provide examples and exercises which may or may not further your learning.
The teachers I work with seek rigour, clarity and understanding… they exhaust themselves everyday in trying to reach EVERY STUDENT. NOT JUST YOUR CHILD but every child. They invest hours in studying their students, the curriculums and adapt their instruction to better reach more students. They do not expect the textbook or worksheets to teach…. They do not hand out 40 questions and a timing device… they work tirelessly and often thanklessly to listen to students, to engage them in investigating number, space and shape, prompt, guide and question their thinking and encourage them to believe in themselves and the power of their brain to learn. They see students build understanding and then challenge them to practice, practice, practice by actively and deliberating engaging in explaining and representing their learning…
I teach for understanding. I teach parents, children, teenagers, administrators, teachers, University professors, businessmen and women, professionals from all walks of life… I ALSO TEACH FUTURE TEACHERS… The stories I am told can be heart breaking….
“I always felt I was stupid because I couldn’t shout out the answer to 8 x 7 as fast as the kid across the table. The teacher called it a game but it was not a game for me, it made me sick to my stomach.”
I always would ask why does it work, why do you have to do it like that but the teacher would just say because that is how you do it… I wanted to understand why. I needed to know.”
“If I had been taught like this all through school I know I would have enjoyed the math. I had no idea I was actually very good at thinking. I always thought I was dumb because I couldn’t remember the steps or I did them out of order or worst of all I couldn’t shout out the answer fast enough”.
“I had no idea multiplication and division actually could make sense. I can do most of this in my head”
Wanting to understand why things work is the key to an engineering or science career but not when you are told it doesn’t have to make sense it is “just the way you do it”.
I am tired of the buck passing, blaming the kids, blaming the curriculum, blaming the textbook, blaming the teachers…..Our students need to know how to learn before we start “telling them” what they Have to Learn. They need to know that learning involves making meaning and finding sense and logic. They need to know that being able to communicate, connect and reflect on what they are doing as they are learning makes them stronger and more confident learners.
This curriculum is not “FUZZY”. It is built around a set of understandings that place teaching students to make sense and think ahead of telling them to just memorize this because for some reason some day you need it…
This curriculum is set up to focus on building understandings of KEY RELATIONSHIPS between numbers as students learn numbers, not after they have memorized a set of facts.
- Equality is introduced in Grade one and contrasted with inequality in Grade 2
- The commutative property appears as early as Grade 2
- expressions to describe quantities are called for as early as Grade 2
- Understanding and applying inverse operations begins in Grade one and carries through from addition and subtraction to multiplication and division.
- The Distributive Property is introduced in Grade 4 and repeated in Grade 5.
The BASIC SKILLS for mathematical thinking are not the addition and multiplication facts and they certainly are not counting by ones. They are the skills of sorting, matching, classifying, comparing, organizing data, searching and describing pattern, generalizing and testing and justifying.
We know too much to settle for our kids only getting what we got for learning… I am not arguing there are not things that may be worth learning, I am arguing unless our students know how to learn we will continue the cycle of memorize, regurgitate, forget that “got” many of us through but left us “hating math” or seeing no real purpose in math other than making change.
In the weeks to come I will add to this message to include further discussion of why the THINKING BASICS must be taught before there is attention to MEMORIZING FACTS.
I will also include the reflections and responses of students who are achieving incredible personal success with learning… Students who have come to recognize that learning is hard work and requires them to actually learn to start thinking in class….. stay tuned…