Any errors are my own. In particular, sometimes a remark can be interpreted in multiple ways, so you’re seeing my viewpoint below.
Marian began by acknowledging how teachers can be “caught in the middle” (between policy and the public). The media may or may not end up offering factual arguments about curriculum/implementation, yet that’s what most people see. So, when speaking with others, a teacher must be honest, informative, and professional, yet divorce themselves from professional language - don’t sound like the ministry, sound like a “regular person”. And don’t talk about ‘buts’ (eg. “I do this, but sometimes...") since once an already insecure parent sees a possible weakness, it’s over.
With respect to mathematics education, the same big questions tend to come up.
“Do students have to know their times tables?” YES. There isn’t a debate here, the real issue is whether there is only one way to learn them, and whether that way is best for everybody.
“Is knowing the facts the key to success in math?” While it is extremely important, it is not a KEY to success. (An excellent K-5 resource from Alberta clarifying ‘basic facts’ for parents is at this link. It’s a result of a reporter in Edmonton who published numerous articles.)
“Are students still learning the ‘right ways’ to do mathematics?” Let’s look deeper at that one.
IS THERE a “right way” to learn mathematics? After all, in different countries, different ways are right, who’s to say our convention is any more or less right? One could argue there are “more efficient” ways - but our whole lives are inefficient, why should math be so different? “How many 9 year olds do you know who are efficient?” Besides, is the “standard algorithm” always the most efficient? (NO: Consider 300 - 2. Or using quadratic formula to solve x^2 = 9.)
Does that mean we should force kids to use multiple strategies, or merely expose them to multiple strategies? Consider, if you look at a curriculum document (in Ontario) there are many mentions of “multiple strategies” - it doesn’t mean we always require 3 ways to solve a problem. We can, for instance, differentiate assessment OF learning from assessment FOR learning (show many in an instructional situation, then the student uses one for an evaluation).
|Aside: I hate those BEDMAS Qs on Facebook.|
Homework! “Don’t they have to practise?” What does ‘practice’ look like? It could be 30 questions that are very similar, or one question like: “You multiply two numbers and the answer is about 65 less than if you add them. What might the numbers be?” This can engage a student for an extremely long time. (Leading to: How do we get a LESSER product? A fraction, a negative?) Practice is not always obvious. Unfortunately, there is also no way to be RIGHT when a teacher is answering a question about homework - some parents will always love you or hate you, and different places have different rules. One rule of thumb is ‘multiply your Grade number by 10 to get number of homework minutes’.
A key point: If homework is confusing, it might do more harm than good (it should not make things worse, and reinforce errors). Should it be about rote skills? Sometimes, but there can be more conceptual things that aren’t difficult to try. (For instance, “You have two fractions. If you add, subtract, multiply and divide them, what is usually the order from least to greatest?” Exploring that can be lots of practice.) What if you offer homework but don’t require it or mark it? Pro: Homework for marks is a problem anyway, you don’t know who did it, plus no marks makes it low risk, a chance to make (and fix) mistakes. Con: A lot of students/teenagers may not make the right choice in doing it.
“Why are textbooks so wordy and unclear?” In real life, nobody says “Subtract now!” (with the exception of Revenue Canada). People won’t tell you what to do, applying math in life is a different skill than performing calculations. (Besides, how do you describe a problem without words?) While new digital tools can make math more oral (hear instead of read), in books things have to be written down. That said, perhaps oral responses can be an additional option, if it gives a better sense of whether the student understands.
“Why do we have to learn things in a different way?” Lots of people today may know their times tables, but are still anxious about math. Change is needed. Yet “discovery” is not a good word - how can you discover if you don’t know the basics? Well, think about how we learn to do new things. Do we read the manual first? Or explore first, and check later? Some basics do come first, but lots can be learned through investigating and inquiring.
|It's not all about that bass.|
“Why is my child always working in a group?” These days, it’s less likely that we work in isolation; even in university/college lots of work is done in groups. Teaching problems can also be talked about with colleagues. More to the point, we need to focus on getting students cognitively ready, not merely structurally, since later structures will be different anyway. (Now, evaluating in groups is a whole OTHER question. We need to find strategies to deal with that.)
“What do you think of [Kumon/Khan/flipped classes/etc]” Nothing is right/wrong or good/bad, it’s more complicated than that. Be respectful. The issue is whether such things are effective as the main event. If you think drill will garner success or cause enjoyment, likely no, but if the student needs skills, then yes. Of note: The goal of math is not solving a problem. Math is learning how to think in mathematical situations.
We used to believe that the best way to learn facts was to sit down and repeat them over and over. We now realize that you are ahead of the game if you have more strategies to fall back on. Even though some kids memorize well, for kids who are anxious about math, having to be quick and use the old strategies dooms them to failure. Moreover, research tells us that effort and persistence account for more variability in scores than native intelligence. “Hard work and good study habits are effective. Bad attitudes are a killer.” Telling a student you believe s/he can do it works - but no guarantee! Similarly, a parent saying they’re bad at math is an invitation for kids to tune out.
|Temporal paradox? Seems legit.|
What can I do (at home)? Number play. Avoid saying “That’s hard” just say “Let’s do it”. Marian’s theme is that math classes should be about thinking and not doing. Estimation is important, and there is learning through problem solving. eg. “I bought something for $10. She gave me back one bill and 4 coins. How much might the item have cost?” Counting dots on a piece of paper is hardly exciting, but counting all the spoons that exist in your house, that’s kind of interesting. Or sections in an orange (do they always have the same number?). Consider rolling two dice - you can double one result then add the other, the first player to 100 wins. Consider a strategy. Support involves not showing, but probing.
What is success? Not just a mark. In the last round of EQAO (the Ontario Grade 9 equivalency test), 93% of Grade 9 kids said they hated math. (Aside: Ontario is the only province that makes you report on five strands in elementary, no other province does that.) Enjoying the math is success!!! So you, the teacher, need to show that you enjoy math too. Show confidence, believe that the student can do something if you give them the time. Meet your audience where they ARE and take them somewhere better, rather than starting above them - they may not want to listen/climb.
In the end, you’re the manager of a classroom the way there are managers in a workplace. “Make stuff happen.” Don’t simply stand there.
Marian’s website: www.onetwoinfinity.ca