On Friday and Saturday I’ll be attending my first ever homeschool conference.
And boy am I pumped!
I’m so fresh and new at this – but really, I’ve been doing it forever. My ma sent us to public school (a really good one, Tarkington ISD) but as a single parent, she didn’t have much choice. At least back then.
But she started her own business cleaning houses so she could be an afterschooling mom. She really REALLY wanted us to have the learning and interaction she could provide from 4pm to bedtime.
Almost everything I know about math, I learned from her. She (and you) might be surprised at that because her degree is in English! But she taught me puns, patterns and a way to look at the world in a totally different light. Which is exactly what math is.
I’m an afterschooling graduate and parent.
Husband and I haven’t decided on how we’ll educate Daughter. Right now she’s going to a day school, which is really good for her and us.
And we afterschool like crazy. It takes me forever to get anywhere with her because I let her observe everything. For as long as she wants.
Everything I publish on this site is either used on her or I can’t wait to use it on her.
I need your help!
My mission is to help the first and most important teachers – parents – to be comfortable enough with math to teach it to their children through experiences. Which means I need to know what parents need from me. How can I help?
I’ve got experience with infants and toddlers at this point. I know grownups, too (taught college for 15 years). But school-aged kids? I’m depending on y’all.
So what should I ask when I go to the conference? What should I learn and discover that will help me help you?
Please, please, let me know in the comments!
(Oh, and if you want to meet up, let me know that too – I’d love to connect!)
I noticed Daughter attempting to bejewel Husband with a strand of my faux pearls the other day. I watched, enthralled with the math learning taking place.
She held the necklace in her hands – one on each side. Just about equal. So the space available for Husband’s head was almost non-existent. Like this:
If she were to hold the necklace at two points that were closer together, she would create a “dip” in the necklace where his head could fit. Like this:
There’s an extended learning opportunity here!
This made me think of all the nifty things you can show about the relationship of perimeter to area and how you can have the same perimeter but change the area to all sorts of sizes.
If you aren’t wearing a necklace, find some mardi-gras beads. Daughter has many strands, so I’m guessing your house might be littered with them as well. If not, join the club. Go buy some.
Play with them in the bathtub or right before bed. (Make sure they give them up before going to sleep, though – it’s a strangulation hazard!)
Move the necklace around on a flat surface (or on the bed) and let your child experiment with the ways the area changes. Ask questions like:
How much “stuff” can you fit inside the shape? (If there are blocks or other toys to act as “stuff,” use them.)
How much “stuff” can you fit inside the shape after you move it around?
Is that more or less “stuff” than you could fit inside it before?
Did the distance around the necklace change? (You can introduce the words perimeter and circumference.)
Can you make it into a square? A triangle?
Be careful how much you do.
Don’t forget, activities like this should be fun. For your child as well as you. So don’t get too in depth talking the math talk if it feels weird. Go with the flow.
And let me know how that flow goes, would you? Share your thoughts in the comments.
Most parents aren’t professional mathematicians. But there are a few. This is the third in a series of interviews with mathematician parents with the goal of helping parents integrate math teaching into parenting.
I had the privilege of interviewing John Golden, a university math professor and publisher of Math Hombre, a website with clever and fun math content that’s new every week!
Just a sample: “As a bad beginning teacher, emulating David Letterman of all people, I realized that I loved teaching math.”
MathFour: Thanks for taking the time to answer some questions, John. First, what’s your degree and career? And how long have you been in math?
John: I have a PhD math in 1996, and am working as math ed faculty at GVSU a 25000 student public university in Michigan.
MathFour: Tell us about your children and how they feel about math.
John: Xavier – 11, a bit more positive about math than his sister, Ysabela – 12. Neither loves it.
MathFour: Do you have any worries about your children academically? In particular, do you think they will do better in math than in other subjects because of your influence?
John: They’re both decent problem solvers, but that doesn’t necessarily equip them to do school mathematics. Ysabela, for example, found out this year she wasn’t allowed to use her method to divide and had to use the standard algorithm.
We encourage them to follow their passions. Both are quite artistic, and Ysabela is an amazing reader. I do worry that I’ve emphasized understanding over grades to the point where they have no interest in academic success.
MathFour: How do you play with your kids? Do you play math things?
John: Lots of games: card, board, table. No video games other than some flash games on the computer. I love games for their math like nature, or math for its game-like nature, so I see it as connected.
MathFour: Do you think you speak with your children or behave differently than other parents because you have a math background?
John: Definitely. Distinguish between what they’re asked to do and what math is, talk about cool and interesting math connections, do think alouds when doing homework, etc.
MathFour: Have you ever had any of your children express negative thoughts about math and how did you handle it?
John: More than occasionally. I take it with a grain of salt because I hated math at this age, too – for being boring and repetitive. I talk about the importance or confirm the irrelevance of what they’re doing, and try to emphasize making sense, and help them make sense.
MathFour: Have you ever disagreed with one of your children’s math teachers?
John: I always volunteer in their classrooms and bring games and such into it. This year, my daughter’s middle school classroom didn’t have me until the end of the year to do algebra tiles, but that was a positive experience. I strongly respect teachers, whether I agree or disagree, and never feel like they’re doing anything other than what they think is best.
MathFour: Now to change direction a little to a more worldview of math. What do you see as the biggest challenge in math education today?
John: Irrelevance of school mathematics, anti-math culture, misunderstanding of what math is, professional/governmental insistence on teaching junk, high stakes tests that preserve bad pedagogy…
MathFour: Wow, that’s a lot. So what do you see great happening in the world of math education?
John: Internet networking, slow but growing awareness among new math teachers about better ways, leveraging of new technologies and opportunities for change because of bad test results.
MathFour: What advice can you give to non-mathematician parents that might help them raise their kids to like and appreciate math.
John: Give it a go themselves. If it didn’t the first time, try to make sense of it along with your kids if they learn it. Value thinking and communication over the right answer. Play games!
MathFour: Thanks so much, John! Great tips and insight.
How about you? What are some questions you have for a mathematician parent? Share them in the comments – I’ll try to get John in here to answer them.
Cuisenaire Rods are brightly colored wooden sticks. Technically, they’re “proportionally sized rectangular parallelepipeds.” (But only say that if you want to hear your 3 year old repeat something really cute!)
The “proportional” thing is important. The white ones are 1cm square, the red ones are twice as long and each color is 1cm more than the next color.
I’m anticipating many articles and videos on how to teach with these (since the possibilities with these things are virtually unlimited), so I thought I would start a running series. Here are the ideas and the links to the articles/videos that are ready:
Cuisenaire Rods – (this one) graphing and practicing coordinate pairs (see video below)
Learning math isn’t just about being taught math. It’s about fun, discovery and experimentation. In the Count 10, Read 10! program, parents get to spend 10 minutes a night playing math with their children.
Like many games you’ll find here, this is a version of Calvinball (from Bill Watterson’s Calving & Hobbes cartoon). You and your children make up the rules as you go along or as you see fit.
The next player says “plus” and another number. Then adds them and says the result.
The next player says “plus” and another number. She adds that to the previous result and says the new result.
Play continues until a winner is determined.
Example
Leader: Five!
Player 2: Plus three is eight!
Leader: Plus one is nine!
Player 2: Plus two is eleven!
Leader: WINNER!
End game, and how to choose a winner.
The round ends when the youngest child reaches their limit of counting or adding. The winner is determined by a rule or random choosing. The older the children, the more “real rules” you’ll need to follow.
Possible winning rules:
The first person to add up to 10 – or a number designated by the leader at the beginning of the game.
The person who noticies that another player is wrong in their calculations (this is perfect for the parent to “test” the kid).
At the whim of child or parent.
Variations
The point is to have fun with counting and math. As your children grow, you’ll have to adjust the rules to give them more challenge and to fit the “real game” model. Here are some options for variations:
Each player can only add a multiple of their age (grownups use one of the digits from their age).
Each player can only add a multiple of a roll of a die (get foam dice for bedtime).
Subtraction – instead of adding up, start with a higher number and add down.
Multiplication – instead of adding, multiply each new number. This one could get “fun” really quick!
Will it work?
All games created at MathFour.com are tested or will be tested on Daughter. The rub is that Daughter is almost 2 – we’ll have to wait a while to do this one. So your input is important.
Will it work? Did it work? Try it and let me know how it goes in the comments, please. Also share your own variations.
When looking at the IXL sample page, I started having some concerns. Here are some screenshots that I’m running into, as well as my thoughts:
Kindergarten Skills
Some people say “dinner” for “lunch.” They reserve the word “supper” for the evening meal. Instead of using terms that might be cultural, perhaps they could have used breakfast.
I was so confused by this one. I’ve never seen a graph made of two objects. Nor have I seen graphs made with giant Xs. I think a graph with lines or bars instead of Xs would be clearer. As well as having a few of the objects, not just one of each.
These suitcases appear to be the same but zoomed in. A reference object would certainly help this.
I didn’t know what plane geometry was until college. I’m pretty sure that five-year-olds and their parents will figure out what the answer is, but the question stem is written at a really high level.
Grade 2 Skills
The right answer (the pens) are very very hard to see here. And the various colors and objects are confusing. Better would be the same objects, or bigger or with more space between the lines.
These pies really look the same to me. If I look and count really, or look at the fractions, I can see they’re different. This might be more effective without the pictures. For a seven year old (and for me), if you had 2/10 of that pie and he (or I) had 2/11 of that pie and it looked like these pictures, they could easily be perceived as the same.
Stopping Now
Of course I haven’t really gotten into the curriculum. These are merely samples. I don’t know how they teach this in the IXL Math Practice program. I worry, though, that these examples might be representative of the way it is taught.
I welcome a view into the curriculum, if they’re interested in more thoughts on their offering.
Update March 29, 2012: IXL has communicated to me that they’ve been making changes – including some based on this article. They’ve also hired me to take a deeper look at their product and give them feedback. I look forward to seeing what they’ve got.
The comparison of numeracy to literacy is curious.
Learning math is the opposite of learning to read. When you read, usually simultaneous to learning a language, you sound out words and then put meaning to them. When you learn to count and do math, you know the meaning inherently and then put a language to it.
At some point we learn to recognize words without sounding them out. And at some point we learn to recognize quantities without counting them out. This is called subitizing.
The Your Baby Can Read program uses the concept of subitizing to teach reading – you show your baby the word alongside the object. So the shape of the word car is as recognizable as a car itself.
The children using Your Baby Can Read don’t learn to sound out words. They don’t understand the concept of letters any more than babies not using the program. But they instantly recognize the shapes of the words – giving them an (assumed) advantage.
Aside: We didn’t use the “Your Baby Can Read” program, not because it was gimmicky (I love anything that looks gimmicky), but because there is a huge DVD element to it. We decided not to put Daughter in front of the TV for her first 2 years. A decision we stuck with, but sometimes was a struggle!
This article contains a “your baby can count” type program. (And it’s a free download!)
How did we learn subitizing?
I don’t recall having been taught it directly. Although I could be wrong. The research on it has been happening since the early 1900s, so it might have been taught without being labeled “subitzing.”
I wonder how many of us do that. Are grownups so adept at subitizing that they forget that’s how we assess quantity? Maybe we’re taught to chant-count because that’s the way we think counting is.
But it isn’t!
How do you teach subitizing?
Images are accompanied by the written numeral as well as the number spoken aloud. The images would be printed on cards, done via video or “live” with 3D objects.
I’m still working on the numbers 5-10 and up, but for the numbers 1-4, the following 8 styles of image sets would be done twice. Once using the same objects for each image set, and once using different objects for each image set.
Organized in a row vertically.
Organized in a row horizontally.
Organized in a row diagonally.
Organized in a row other way diagonally.
Organized in a regular shape (triangle, square).
Organized in a differently oriented regular shape.
Organized in an irregular shape.
Organized in a different irregular shape. (There will be more of these for 4 than 3, etc.)
The objects could be blocks, cars, little dolls, just about anything. I created the set below from blocks I found left in Daughter’s block set.
Each zip file contains a few .jpg files with 4″ x 6″ pictures. You can print them at home or ship them to Walmart, Target, CVS, etc. for printing. I left off the MathFour.com logo so the kiddos wouldn’t get distracted. Please share them along with links back here.
Most parents aren’t professional mathematicians. But there are a few. This is the second in a series of interviews with mathematician parents with the goal of helping parents integrate math teaching into parenting.
I had the privilege of interviewing Caroline Mukisa, a math teacher and math blogger.
MathFour: Thanks for taking the time to chat, Caroline. First, what’s your degree and career? And how long have you been in math?
I’ve a Bachelors in Civil Engineering from Imperial College, University of London and a Post Graduate Certificate in Maths Education from Cambridge University. I taught maths to high school students in the UK, and I also ran a Kumon tuition centre before moving to the Middle East as an expat. I now run the Maths Insider website. My husband has a Bachelors in Maths also from Imperial and a Masters in Mathematical Modeling from Oxford University.
MathFour: Tell me about your family – how many kids do you have and how old are they? Are any of them more or less interested in math than the others?
Caroline: I’ve got four kids aged 11, 10, 4 and 2. My 10 year old son is very much the maths boffin, he’s memorized the first 300 digits of pi just for fun. His 11 year old sister is more of a problem solver. The younger two like counting and sorting but it’s too early to say if they’ve caught the maths bug yet!
MathFour: Do you have any worries about your children academically? In particular, do you think they will do better in math than in other subjects because of your influence?
Caroline: With maths, being a former maths teacher, I have a feel of how they’re each doing with that subject, whereas with the other subjects, it’s difficult to judge. For example, “Is that poem they wrote good for their age level?”
MathFour: How do you play with your kids? In particular, what kind of math play do you do compared with non-math play?
Caroline: We talk a lot about maths, we like showing them You Tube videos or Ted Talks related to maths or science, but we also try to expose them to different things like poetry, anthropology, and business.
MathFour: Do you think you speak with your children or behave differently than other parents because you have a math background?
Caroline: I’m not sure about that. I don’t talk about maths with my kids in front of other parents – I don’t want to appear to be “showing off” although my 10 yr old likes to “perform maths.”
MathFour: Have you ever had any of your children express negative thoughts about math and how did you handle it?
Caroline: Of course! There’s always days when maths homework is not appreciated, and although my 11 year old finds maths easy, I wouldn’t say she loves it – she likes that maths can help her do the things she likes, like Design and Technology and Science. It’s not a problem – kids shouldn’t be carbon copies of their parents.
MathFour: How is the interaction with your children’s math teachers?
Caroline: I usually let my kids teachers know early on about my and my husband’s maths background. We try to work with the kids teachers to help extend their maths but in the end we can supplement and support their maths ourselves at home.
MathFour: Now to change direction a little to a more worldview of math. What do you see as the biggest challenge in math education today?
Caroline: With the move away from rote learning towards practical maths, kids mental maths skills are declining. Parents need to make sure that they’re reinforcing those skills at home, since there’s not enough time allocated to fully learning them within the curriculum.
MathFour: What do you see great happening in the world of math education?
Caroline: I love that kids get to explore different practical applications of maths, with many teachers, using technology to present real-life math problems.
MathFour: What advice can you give to non-mathematician parents that might help them raise their kids to like and appreciate math.
Caroline: I think the key things are to stay positive about maths even if you hate it, try to spot something related to maths as often as you can. If your child is having problems with maths, act early and make sure their basic skills are solid. And of course, read MathFour and Maths Insider!
MathFour: Thanks so much for taking the time to answer our questions, Caroline!
How about you? Do you have any questions for a mathematician parent? Share them in the comments – I’ll bet Caroline will be around to answer them!
I started this series over a month ago. In that time, I’ve gotten pretty deep in thinking, learning and reading about the order of operations. I’ve seen a variety of ways people view, use and teach it.
Before I go too far into some conclusions, though, let’s look at addition and subtraction.
Consider the problem . Moving from left to right, and doing both subtraction and addition as we come to them, we get 4. If we found a book, or person, that meant the full-on PEMDAS and wanted addition done strictly before subtraction, then we would end up with 0. The latter is because we would do the addition of 3 and 2 before we did the subtraction.
Which is right?
It depends on what you really mean. If you don’t know if you should go left to right or strictly addition before subtraction, either look in the textbook you’re using or demand parenthesis.
The text will clearly outline the order of operations it’s following. Be careful, too because there isn’t always agreement among textbooks. I have seen some texts that instruct the learner to do multiplication first and then go back and do all the division signs. While others (and this is more common, today) have us do multiplication and division from left to right, simultaneously.
If you compare contemporary texts to each other, you’re likely to find them all the same. But grab a math text from the 80s at Half Priced Books. I’ll bet you’ll find at least 50% of the time they put division strictly after multiplication. (I’ll verify this the next time I’m there.)
The order of operations needs context.
I have $5 in my bank account. Then I bought a coffee for $3 and a bagel for $2. I might accidentally write down . I still mean, “I need to add up the stuff I spent and subtract it from my balance.” I wrote it in error, though. What’s “mathematically” correct is .
But you knew what I meant.
This was a typo that was helped along by using the context.
Until there’s a reason to do arithmetic, the order in which we do things is arbitrary. If we all agreed to do addition first, then multiplication, we would calculate and come up with 35 (instead of 23).
As long as we all come up with the same thing, we’re fine.
“We” have agreed to do multiplication things before we do addition things. So “we” would come up with 23 in the example.
Coach G noted it correctly: the order of operations is a convention. In other words, we’ve decided on it. We invented it.
How can you use this to teach your children?
The coolest thing is that you can let them play. Get dirty. Break it.
Remember opposite day? Have that. Let your little one make new rules. Let them see what happens if you all decide one day to do multiplication before addition. If your child is older and doing some algebra, this will mean reversing the order in which you UNDO the operations too!
This is a real brain stretcher. But it’s just math. You’re not building a bridge or balancing your checkbook. Let them break it. Let them see what happens if you make your own rules.
And then they’ll really learn!
Let me know how it goes – share your stories in the comments.
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