This idea was inspired by something Tom with Leaving Work Behind wrote in an article about success months ago. He wrote:
Principles are timeless – techniques are not. Would you rather I give you a fish, or teach you to catch your own?
Here’s a week in the lives of Tom and me… “fishing”…
Monday
Bon: Hey, whatcha doing?
Tom: I’m fishing.
Why?
Because I’m hungry. You can eat fish.
Bon: I’m hungry too. Will you share your fish?
Tom: Sure!
Tuesday
Bon: I wonder where Tom is. I’m hungry.
Wednesday
Bon: Hey Tom!
Tom: Hi Bon!
Bon: I’m hungry. I haven’t eaten in two days. You weren’t here yesterday.
Tom: Well, I’m fishing now. Watch how I do it and if you ever need to, you can do it yourself.
Bon: Swell!
Thursday
Bon: I wonder where Tom is. I’m hungry. Good thing I watched him yesterday. Now I can catch my own fish.
<pause> Bon: What’s going on. I’m not catching any fish. And I’m doing it exactly as Tom did! I’m so hungry!
Friday
Bon: What’s up, Tom!
Tom: Hey Bon. How are you?
Bon: I’m SO hungry. I tried to fish yesterday but I couldn’t catch anything. And I was doing it exactly like you did.
Tom: That’s strange. How about this. I’ll let you do the fishing today. Together we’ll see what you’re doing and adjust it so it works for you.
Bon: That sounds great!
Saturday
Bon: Bummer. Tom’s not here. But I was successful catching fish yesterday so I’ll have no problem catching fish now!
Sunday
Bon: Hey Tom!
Tom: How’s it going Bon?
Bon: Excellent! Hey – wanna join me for lunch? I’ve caught enough fish for both of us!
Do you really want to teach someone to fish?
There’s a difference between teaching someone to fish and helping them learn to fish. In the case of Tom’s teaching medium – his website – he can only teach. Likewise, here at MathFour.com, my writings can merely teach.
But when you’re face to face with a student, teaching isn’t nearly as valuable as helping them discover.
Indeed, if you’re going to teach a child who really needs help learning, you might as well just give them the fish.
Do you teach your kids to fish – or help them learn?
Inquiry-based math instruction is the opposite of performance-based math instruction. And the research shows that inquiry-based math instruction is more effective than performance-based.
But performance is required if you’re teaching anywhere other than a homeschool. So what do you do?
You have to balance the requirement of performance with the need for discovery and inquiry-based learning. Which means you have to integrate discovery and inquiry-based elements into your math teaching.
You can do this formally or informally. You can say it out loud, or just do it. And which method you choose will depend on how much you are supported.
Set aside time for inquiry-based instruction.
Bring inquiry-based math instruction into your lessons by breaking up class time into “performance-for-tests learning time” and “discovery/inquiry-based learning time.”
You can have specific topics for the discovery learning time or even a “free math time” where there is no specific topic.
Make sure you keep the discovery topics independent from test based/performance-based topics. As much as you’re tempted, don’t connect the two. If the students connect them, acknowledge it briefly and keep moving.
Keeping them separate keeps the “must get the right answer” attitude out of the discovery time. This is very important.
For example, if you’re teaching multiplication this week in class, set aside the discovery time as patterns or geometry. This can be 5-10 minutes at the beginning of each class period or one day of the week devoted to it.
Create a safe discovery/inquiry zone.
If you want to include discovery in the regular curriculum, you have a little bit more of a challenge. Children learn early that performance is required in math classes. So they avoid being creative and asking questions. (See the research paper on that here.)
Which means you have to undo years of creativity-destruction to get them to participate in inquiry based activities. Depending on the students’ ages, you might have to start with introducing really goofy stuff to break them out of their comfort zone.
Let them wear fuzzy red hats and crazy glasses and tell tall math tales for the first few times. They’ll get warmed up to dig into some creative math inquiry. Anything’s easy when you’re wearing fuzzy red hats!
After a while they’ll be used to the safe environment and the inquiry-based math learning will start to flow from them.
Do both.
Ideally, you can have a “fun” time – where the math you have to do is set aside and you let the students dream about crazy math stuff. In addition, all your lessons involve the safe zone.
If you can make it work – do it. You’ll grow confident, adventurous, smart kids – the research supports it!
* Inquiry based math instruction is really the wrong term. Instruction means giving of something – in this case knowledge. It really should be inquiry based math learning. Teachers and parents are inquiry-based facilitators.
Feature image by philcampbell | Flickr.com | CC BY
I was reading a research paper about math teacher shortages by D.R. Sterling. Turns out that less than 12% of math teachers leave the profession through retirement.
So 88% of the time math teachers quit, get fired or die!
Have you avoided the profession because it doesn’t pay anything near what you make now?
Could you use a 9 month vacation to do something totally different, worthwhile and exciting?
Can you afford a 70% cut in pay for 9 months to really make a difference?
If you want to change things in math education, you can!
You can give 9 months to make a difference in the lives of 100 kids!
Is that do-able?
In Texas, and I’m guessing lots of other places, there is an emergency teaching certification some schools are allowed to offer when they can’t find any certified teachers. You go through an interview process and if the school decides you’re qualified – then you get to teach.
It expires after three years, but hey – you’ll probably be gone by then anyway!
Find one of these schools – it shouldn’t be hard. Go to work making a difference for a lot of kids – and making a difference in the system!
Why would you do this?
I just finished Seth Godin’s book Tribes. The premise is that a tribe (a group of people with common thinking) needs a leader – and you are that leader. So get up off your tooshie and lead, already! (That’s not a quote – it’s just what I got from the book. But it should be a quote.)
If you can afford it, and you’re passionate about helping kids learn math, then you have an obligation to help. Teachers in the system won’t risk getting fired to make change. You can!
But really, WHY would you do this?
Tons of people – teachers and parents – know beautiful and encouraging ways to teach math.
But there’s a group of people who have put together these nutty rules of what performance in math should look like each step of the way (the Common Core Standards and NCLB). Those rules prevent teachers from doing what they do best – teaching. Instead they fear for their jobs and teach the tests. All the while struggling to fit in a little learning here and there.
If you jumped in there, with no intent on following the rules, think of what would happen:
You’d teach. Not some crazy set of rules, but you’d teach math the way only you know how. And that’s probably a beautiful, experiential, exciting way.
You’d change the lives of the kids. They would see what real math might look like. They would see someone not paralyzed by fear of having your students fail the latest standardized test.
You’d inspire the teachers. Sure, some of them would call you a heretic. And so what – you would be! The ones who really want kids to learn math would follow your lead.
You’d be giving of yourself in the most valuable way there is. Talk about donation – you’re likely to need an extra $40K to make your bills. Is it tax deductible? If you consider that it puts you in a seriously lower tax bracket – yes!
You’d get fired. Yup – and isn’t that the point? Then you could go back to your high paying job, hire an attorney to sue the state and make big news. Show the public what it means to teach math!
Are you in?
I’ve put in notice at my day-job. I’m fixing to hit the pavement as full time Math Education Advocate at MathFour.com. Last year I made $16 in Amazon.com affiliate sales from this website, so I’m not falling back on any income here. I’ve also picked up teaching two community college developmental math classes. Which means I’m going to be gaining 32 hours a week to work on math ed advocacy – and taking a 90% pay cut.
I’m scared out of my mind.
But Daughter is 2 years old. I can’t afford to not go at this full time.
Will you join me?
Feature and post images by ewen and donabel | Flickr.com | CC BY
This is a feature article by William Devine, MA, LPC, CART. Wil is the Research Guy at MathFour.com.
The “old guard” of academics focused on rote memorization, correct answers, and academic performance – performance based, measurable objectives. To a large degree some of these focuses continue to prevail.
But a different way of teaching is emerging. Based on the research, this new way is more helpful, sustainable, and effective.
They were studied in an attempt to understand the affects of teaching styles on the students. And they were observed during regular, non-testing times.
It was noticed that their teaching styles tended to fall into roughly two categories: performance based and understanding based.
Performance-based teaching was found lacking.
When the teachers focused only on math performance, students were more likely to disconnect and feel intimidated.
In these cases, if a student gave an incorrect answer, they were told as much. Then another student was called on and so on until the correct answer was given. The problem with this search for the right answer was the lack of instruction that followed. It became all about doing it right instead of teaching the kid how to do it.
The instructor would then approach the next math problem with little or no discussion on how the correct answer was determined. Where was the teaching?
As we all know, if we feel uncomfortable with something, have anxiety, we tend to disengage or avoid the situation. This was observed to be the case in the classrooms of performance-focused teachers .
Students disengaged and were concerned about not only doing something the wrong way but feeling unable.
Understanding-based teaching was effective, helpful and encouraging.
Other teachers focused on helping students understand where he or she may have come up with the incorrect answer. The observed results were very different.
Teachers would help students arrive at the correct method. They would work to help them understand how to do the problem. Ultimately, students would arrive at the correct answer.
Furthermore, they would engage on each of the next questions – and get those right too!
So what can we do right now to move toward this idea of supportive academic encouragement?
Be careful with the words “wrong”, “incorrect”, and “bad”.
Kids are sensitive to these terms because they imply doing something they aren’t supposed to do and that lead to things they don’t want. And then we wonder why they don’t want to try!
We want them to continue engaging and putting forth effort because this is how learning happens. A “wrong” answer is so much better than no answer at all.
We’re not proposing that you stop using these terms altogether. Just do so sparingly.
Encourage improvement, not performance.
Focus: How much time do we focus on the incorrect answers? Instead, acknowledge what was correct and build on this. Recognition and praise for what they are doing well will encourage them to continue to stay engaged in the exercise.
Before: “I graded your paper and you missed 4. Let’s try those again until you get them right.”
After: “Good job! You got 6 right. Let’s try a few more.”
Help them discover how they got to where they got.
How: Understanding how they arrived at a particular answer can help determine what needs to be corrected in how they are doing something. It becomes a truly instructing experience rather than a performance (you got this one wrong and this one right). We want them to learn how to do something. If they feel pressure to get the right answer the first time, they will hesitate to offer any answer at all. This stifles trial and error learning and instills an aversive experience (fear) into the learning process.
Before: “5 is the wrong answer. Try this next one and really concentrate.”
After: “I see that your answer is 5 here. Walk me through how you got there.”
A note of concern: I have found in the research literature an indication that some teachers think if a child is having fun while learning, they aren’t really learning. Wow.
William Devine is a Licensed Professional Counselor in private practice. He has joined the MathFour.com team as the “Research Guy”. Connect with him in the comments, on the contact page or via twitter @MathPsych.
Feature and post images by ukanda | Flickr.com | CC BY
