Kids Haven't Changed: Kindergarten Has (must-read article)

Has anyone noticed that new standards seem to move requirements down a grade level? What was once required in 5th grade is now required in 4th. First grade standards are moving into kindergarten. What does this mean?

Are our kids suddenly smarter? More capable? More worldly? More knowledgeable due to all the technology surrounding them each day?  Parents and teachers should read this article...Kids Haven't Changed: Kindergarten Has.

Great food for thought.

NPR: The Way You Learned Math Is So Old School (+Math Blog Carnival)

On NPR, you'll find "The Way You Learned Math Is So Old School" from Weekend Edition Saturday talking about how children learn math today as compared to the way we--their parents, the oldsters--learned math. You can listen to the podcast or read the text. Also check out the visuals showing how the teaching of multiplication has changed.

Just a little personal reflection...  While I never had trouble "doing" the math (as shown in the old way of multiplying) I had no understanding of what it meant. Now, having learned the second way--WITH manipulatives--I can now picture a problem like that (36x24) in my head and do it mentally. No paper. No calculator. That, for me, is a huge step forward.

Also, check out the new Math Teachers at Play Blog Carnival hosted at MathInsider. You're sure to find a lot of new ideas there!

Milk Cap Math: Preschool Activities

I hate throwing things away. I'm less a hoarder than a I-don't-want-my-stuff-to-take-up-space-in-the-landfill kinda gal.

So, whenever possible, I try to recycle. Or, better yet, reuse.

We go through a lot of milk. A. LOT. My youngest came home from China drinking nothing but milk. LOVES milk. And with six people living here, we constantly buy milk.

I either recycle (on the good months that the local recycling center will take most plastics) or throw away 3-4 milk jug caps a week. Ever stop to look at a milk cap? They're actually sorta cool in a "I'm just a lowly milk cap" sorta way.

I decided to make use of 'em.

MILK CAP MATH!!!

I've come up with several games and activities. Here's the first few simple ones, designed for preschoolers.

Preparations:

1. Gather milk caps. Alternately, other caps would work great: juices, water, soda, etc. If they have writing on them, sometimes you can get that off with a little sandpaper. If not, stick to blank ones.
2. Have a variety of colors? Figure out a pattern. (Or, better yet, have the kids figure one out.) The pattern can be part of the math activities.
3. Lay out the caps in the pattern and number them. I first made one set of 1-12. I'm working on two sets for game playing. I put a line under 6 and 9 so as to distinguish between the two.

PreK-Grade 1 Activities:

Numbers/Patterning:

• Put the caps in numerical order.
• Do you see a pattern to the colors?

Sorting:

• Sort the caps by color. 
• Which color has the least caps?
• Which color has the most?
• How many more yellow are there than green? (various color combination questions)

Counting:

• Using tile or another manipulative, have the child place the correct number of tile below each number. If available, use the same color tile as cap.
• What do you notice about the lines of tile?

As soon as I save up a few more milk caps, I'll post another game for bigger kids. In the meantime, save caps. :)

P.S. I did NOT see this idea on any other blog. I thought I had an original idea. (A rare and exciting phenomena.) However, I thought I'd better do a search before I posted. Good thing. I discovered "nothing is new under the sun." Google search gave 120,000 results. Here are some ideas from folks who thought of this before I did:

Milk Cap Numbers and Animal Counting Worksheets--cool templates!

Milk Cap Letters--templates for words/letters

Bottle Caps Math Game--for middle schoolers

This would be a great Work Box activity!


Link up your math ideas at Joyful Learner! ;)

100 Day Countdown to 2011 (#2, more math ideas!)

If you'd like to join us in our 100 Day Countdown to 2011, here are several fun activities designed for different ages:

1. We made 100 paper links and will take one down each day. Every 10th link is black. My 8yo stapled the links after I figured out he could do it independently with a mini stapler. I worked on the chain as well, asking my 4yo to hand me the correct color of paper, following the pattern. (Blue/orange/blue/orange until we'd get to the 10th link.) I used 12" construction paper and cut 1" strips. Had I been more thoughtful, I would have asked my 8yo to figure out how many pieces of each color paper we'd need to get enough links of each color.

As we constructed our paper chain, we counted by tens. After we had the paper piled on the floor, I asked the boys how long they thought our chain would be when we stretched it out. You can see it below, tacked across a wall...

2. Each boy has a hundreds chart. My 8yo is counting down from 100, my 4yo is counting up from one. Each day, they cross off one number.

3. We posted a hundreds pocket chart so we could add a penny each day, making conversions (to nickels, dimes, quarters, etc) as we go. I'm basically following Joyful Learner's suggestion.

4. My 8yo writes five number sentences each day for the day we're on. He can use any operations, making the sentences as long or as short as he likes as long as the total equals the day. So, for example, for day 100 (counting down), he wrote:

Share your "100 day" ideas in the comments below! ;)

Note: The student math journal page (as shown in #4) is from the Math Learning Center. Undoubtedly, some of these ideas are similar to things I've done with MLC materials, but I cannot give credit because I'm not sure where some of the ideas floating around in my head came from. Anyone else have that problem???

The Children's Mathematics Calendar 2011 (Gift Idea #1)

In anticipation of the upcoming holidays (yes, sigh, I did see Christmas decor displayed at the store already!), I'll be posting gift ideas...math games and activities that feel like way too much fun to contain real learning! (Heh heh...what the kiddos don't know won't hurt 'em...and might just educate 'em!)

I've had my eye on the first one for several months: The Children's Mathematics Calendar 2011. The creator, Theoni Pappas, is also the author of several well-known math books for children, including titles such as The Adventures of Penrose the Mathematical Cat, Fractals, Googols, and Other Mathematical Tales, Math Talk: Mathematical Ideas in Poems for Two Voices...all titles that I own and use in my math/literature class.

The math calendar contains a new problem each day. Although I haven't seen the 2011 calendar, I own an older one and enjoy the format. According to the Amazon product description, "This calendar includes stories that make math ideas come to life, problems with new twists, and ways to share math exercises with parents and friends. Much more than just a reminder of the date (though it does that too), this calendar stimulates curiosity and imagination and helps children develop a positive attitude about mathematics."

If you are looking for more difficult mathematics, check The Mathematics Calendar 2011, also by Pappas. (I read that the children's version is suitable for grades 3-8.)

I will be compiling a list of gift ideas on my Math Gifts and Games page, linked from the menu on the top of the homepage.

What is a "living math" dropout?

To: Jimmie and homeschoolers who are interested in Charlotte Mason "living math,"

I read an interesting blog entry over at Jimmie's Collage entitled "Living Math Dropout." I've thoroughly enjoyed some of Jimmie's past math entries (check out this one on positive and negative numbers) so her revelation surprised me.

But then I started thinking...  What is really meant by "living math?" And what does it mean to teach that way? (BTW, I used to think the Charlotte Mason term was "living math," but I've since learned that Mason never used the term in reference to math...she only used the term "living books." The phrase "living math" has actually been copyrighted by a business owner. I'm using it here only because it was the title on the original blog entry.)

According to Ambleside Online, in a Charlotte Mason math education...

"...the ability to reason is emphasized over "working sums", so emphasis is placed on story problems and working with numbers that are within the child's comprehension, therefore, a manipulative-based instruction is desirable."

Hey!  I do that!!!

But, but...I use a curriculum. In the homeschool "living math" (Charlotte Mason) movement, it seems like good math teaching is often defined by the lack of curriculum. Yes, real books. Yes, real games. Yes, "real life" situtations. But no curriculum. Which, I suppose, makes me a "living math dropout." Or does it?

Most homeschooling parents were taught math with textbooks. Algorithms. Drill and kill. Memorization. It made a lot of us math phobic. (See Math an American Phobia--great read!--by Marilyn Burns. I can certainly relate.)

But here's the thing...while there are many curricula that still teach the "old way" (the way we were taught...I guess that makes us old?? ;) ) there are some that teach completely different, doing just as Mason advocated, emphasizing reasoning, problem solving and manipulative based instruction.

I first learned that there was an alternative when I landed a teaching job in a third grade classroom. As a new third grade teacher I was "tutored" through the math curriculum with a district math specialist who came into my room each week and walked me through the upcoming week's math lessons. We used manipulatives, exploring multiple ways to solve problems. I can't begin to tell you how many times she said, "Can you show me another way to solve that problem??"  This was TERRIFYING for me in the beginning! There is more than ONE way to solve a problem???

You've got to be KIDDING ME?!?!?!!!!!

The emphasis was no longer on memorizing algorithms or drill and kill, but on mathematical thinking and problem solving (and not the problem solving that sounds like "when a train leaves Chicago at 55 mph" either!) I learned to use math strategies, read real math books, and use real activities to explore mathematical concepts.  Real, "living" math...in the context of a published curriculum!

When I first began homeschooling ten years ago, one of my first concerns was math. As I mentioned, I've certainly experienced moments of math phobia in my past, so I didn't want to make the wrong choice in picking a curriculum. We tried several. But nothing reached the level of engagement that I'd had with my third graders. So I searched. And found a very worthy curriculum. I do intersperse other games and living books just because I love to find and use them, but not because a great, non-textbook, "living" curriculum isn't available.

I'm not sure I know what homeschoolers mean when they say they exclusively do "living math." (And, again, I'm talking about the Charlotte Mason concept in reference to Jimmie's blog post, not the trademarked term.) I think it would be very hard to ONLY use real books, games, and experiences...making everything up yourself. Very hard. I admire those who appear to do it well.

Truly yours,

Perhaps another "living math" dropout. Who uses "living" curriculum!

I may be kidding myself. But I really think Charlotte Mason would approve! :)

"Math to Inspire" in Home Education Magazine!

Please check out the Sept/Oct issue of Home Education Magazine. Look for an article entitled "Math to Inspire." :)

Math Transition from Homeschool to Public School

Frankly, the idea freaked me out. Why?

1. I didn't want my child(ren) to suffer unnecessarily.

2. I didn't want to look like a lame teacher.

Those are two of the big concerns that went through my head as I prepared to transition my children from homeschool to public school MATH.

In our case, one child went to public school kindergarten and then was homeschooled from 1st grade until the last couple months of 7th grade. Another child was entirely homeschooled--from kindergarten through the last couple months of 6th grade. So both were entering "middle school"-ish math classes, not having been in public school math for basically all of elementary school.

I didn't doubt that there would be holes in their learning. I think holes are pretty much inevitable when children only have one teacher...even when the teacher is a math genius...which I am not.

Someone recently posted a question on a math forum asking what to do to ensure that a child is at grade level and ready to transition from homeschool to public school. Here's a couple things to consider...

Check Out the Current Curriculum
One of the first things I did was ask to see what curriculum the school was using in my child's grade. However, it was important to also ask "how far have you gotten in the book this year?" It's not unusual for a class to not make it through an entire curriculum (or textbook) in a year. In one of my children's cases, I think the class had only made it a little over halfway through the book. If I would have assumed that the child had to know everything in the book, I might have panicked. (More than I was already!)

It's not a bad idea to ask to borrow a book for the summer prior to the child entering school. Although some schools may be reluctant, I think that most administrators would be happy to see that parents are interested in ensuring that a child is entering at grade level.

Look at NCTM's Focal Points/State Standards/Common Core Standards
National Council of Teacher's of Mathematics published "Focal Points" which specify what math content is to be covered at each grade level. Most states are aligning their standards with these Focal Points. Unfortunately, states aren't all interpreting the Focal Points the same way. So it's worthwhile to check your state standards to see what is expected for students in your state at each grade level. In June 2010, the National "Common Core State Standards" were released. This changes the playing field slightly, as each state considers how to implement. But if you look at the three--Focal Points, State Standards, Common Core Standards--you get a pretty good picture of what a child in a given grade level is expected to know.

The only other advice I have? Relax. I did not and I should have.

Yes, my children had a few holes. But for every hole, they were ahead in another area of math; they've spent more time waiting for the class to learn things that they already know than trying to catch up in things they were never taught. It all worked out.

The kids didn't suffer.

I didn't look too lame.

This time.

Skills Practice Vs. Concept Development

Balance.

It's where so many things go wrong.

In trying to do one thing well, we overlook something else.

It frequently happens in math education. Whether in homeschool or in public school, math education is often imbalanced.

It seems that we may wish to ask ourselves this question...

"Does my child's math education present a balance between concept development and skills practice?" 

• Am I so focused on "skills" (math drills, flashcards, pages & pages of traditional story problems or algorithms) that I'm missing the "big picture," not allowing my student the time and opportunity to development mathematical thinking?
• Am I so worried about NOT doing the "traditional" stuff that I've thrown out the proverbial baby with the bath water...never allowing my student time to practice math skills?

I sampled an on-line math curriculum with one of my children a couple years ago. Sadly, the program over-emphasized skills practice and just assumed that students would develop concepts through very brief tutorials. I'm afraid that my child soaked in the concepts long enough to practice the prescribed drills, but failed to further develop mathematical thinking skills.

Yet there is a place for skill practice. Even electronic.

Saturday, on a weekly basis, I'm starting a series of posts on using math apps. While I would never want this to become the staple of a math education, I do see value in allowing kids time to practice skills already learned through fun, unique apps.

What do you think? How do you balance concept development and skills practice for your student(s)?