Math Monday Blog Hop #73 (November 5, 2012)

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First Do No (Mathematical) Harm

The principle of "first do no harm" is a familiar one to medical personnel. Wikipedia sums it up in this way:

"given an existing problem, it may be better not to do something, or even to do nothing, than to risk causing more harm than good".

I've been contemplating the phrase in relation to math--specifically the teaching of math. In my job I am privileged to work with a wide variety of ages, abilities, grade levels, and teaching situations. I'm alternately awestruck by some students' mathematical thinking and downhearted to see some students--still quite young--who have already had their little mathematical minds messed up. Some of these kiddos, only a few years into their school careers, have decided that math isn't supposed to make sense. Math is just a confusing, random, jumble of rules that they cannot remember...or rules that they can't apply to situations outside the 25 identical problems given on the daily assignment in their textbook. It's painful to watch a child pull numbers out of the air, as he assumes that a random guess has as much likelihood of being correct as anything else he might figure out. As an esteemed colleague said, "Nothing makes sense after you've had your thinking taken away." I worry about these kiddos. A lot. And they're found everywhere. In every grade. And in every school situation: home, private, and public.

Here we read:

A related section from the Hippocratic Oath has been translated as

I will follow that system of regimen which, according to my ability and judgment, I consider for the benefit of my patients, and abstain from whatever is deleterious and mischievous. I will give no deadly medicine to any one if asked, nor suggest any such counsel...

 What if we applied it to the teaching of math?

I will teach in a way which, according to all that is currently know about learning mathematics, I consider for the benefit of my students, and abstain from whatever will prevent them from becoming the best mathematicians they can be. I will do nothing to mess up any mathematical minds (even if a fellow teacher, homeschooler, administrator, or standardized test points me toward unhealthy teaching practices), nor will I suggest any mathematical teaching strategies that may harm someone else's child.

In the homeschool world we hear a lot of debate about the practice of "unschooling"; I hesitate to even mention it because the concept means such different things to different people. But I will say this. It is far easier to introduce mathematics to a child who has never been taught formal math than it is to try to reintroduce a concept to a child who has had his thinking taken away.

First do no harm.

5 Favorite Fraction Books

It's no secret that I'm addicted to math-related children's books. Yet even within that genre, there are concepts that scream for my attention.

FRACTIONS!

Why fractions? They lend themselves to story. And the stories help to heal a bit of my wounded math self. As a 4th grader, I was one of a small group of kids in the accelerated math group. Our teacher told us to go ahead in the book, as fast as we wanted. I was SO PROUD. I flew. Until I crashed. Into the chapter on fractions. I was too embarrassed to tell her that I had no clue. None. Nada. Zilch. Not even 1/100th of an idea of how to do this new, intimidating stuff that masqueraded as math. So I stressed. Kept silent. And the rest of the class passed me.

Here are some books that help to heal the fraction-anxious 4th grader in me:

The Lion's Share: A Tale of Halving Cake and Eating It, Too

We enjoyed a great little exploration with fractions and doubling with Matthew McElligott's book, The Lion's Share: A Tale of Halving Cake and Eating It, Too (2009.) In the story, an ant is invited to the lion king's dinner party. At the party, the other animals demonstrate horrendous manners. When the king passes the cake, each animal takes half of the cake he is passed. So, the elephant take half of the original cake and passes on a half. The hippo takes half of that piece (a quarter) and passes the remains to the gorilla who takes another half (an eighth of the original), passing the remainder on to each animal until a mere morsel is given to the ant. The tiny creature, embarrassed because he doesn't have enough to share, tells the king that he'll return the next day with a special cake for the king. Each animal, wanting to outdo the next, agrees to bring double the amount of cakes to the king. So the ant will bring one, the beetle two, the frog four, and so on. Click to the entire lesson with visuals.

Little Numbers and Pictures That Show Just How Little They Are!

 

This out-of-print book can often be found inexpensive, used. Little Numbers and Pictures That Show Just How Little They Are! is a nice fraction/decimal book to use with 3rd-5th grade students because:

1. The "unit" is a dinosaur. Specifically, a seismosaurus. Kids need to understand that a "unit" can be flexible. In this book, everything is measured in terms of a dinosaur unit.

2. The book depicts increasingly smaller measurements. If a dinosaur is worth 1, then a dinosaur shrunk to 1/10 will fit in the front yard. It talks about various other tenths, like a dime being a tenth of a dollar. It shows both decimals and the fraction equivalent.

3. The numbers creatively get smaller, each time decreasing by powers of ten. For example... 1/10,000 is an ant. 1/1,000,000 is an amoeba. Some kids will be very intrigued by the exponents, which are also included.

4. The book is big (13 x 8") and good with crowds.

Picture Pie

The boys and I found a book that we absolutely love. Ed Emberley's Picture Pie is a circle drawing book. He shows you how to divide circles into fractional pie pieces to create designs, flowers, birds, animals, fish, clowns and a whole host of fun pictures. Click to the entire lesson with visuals. And a follow up lesson with creative writing. With the same lessons we also use Picture Pie Two.

The Wishing Club; a Story About Fractions

My opinion about The Wishing Club; a Story About Fractions by Donna Jo Napoli, totally changed. When I read it alone, I wasn't terribly excited. When I read it to my student, his enthusiasm was catching. In the book, siblings, ages 8, 8, (twins), 4, and 2, wish on a star. Over several nights they discover that their wishes are granted in fractions, determined by their ages: 8yos get 1/8, 4yo gets 1/4, 2yo gets 1/2. My student quickly understood the concept of fractions, exclaiming after the second page (which shows four 1/4ths make 1), "then one penny is 1/5th of a nickel!" In the story, the siblings put their wishes together to make one whole wish and get the wish that all of them want.

Disclosure: If you purchase books through my Amazon links, all commissions go toward foster care through Grace and Hope at no additional cost to you. I do not keep any money myself; I am hoping to be able to sponsor an additional child in foster care through commissions on this site. Thank you!

Math Monday Blog Hop #72 (Oct. 29, 2012)

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10 Ways to Mess Up a Child's Mathematical Mind

I don't know many people who went into elementary education or homeschooling because of their love for math. (I know a few of you are out there. You're weird. Outliers. Accept it with pride.) Teaching math can be challenging, particularly if we have our own math demons lurking in the closet. The following post is designed expressly for those who would like to ruin the mathematicians of the next generation. If that's not you, you can skip it...or read it with the humor intended.

10 Ways to Mess Up a Child's Mathematical Mind:

1. Teach her that there is only one way to solve a problem. Reinforce that by giving her assignments in which she learns a set of predetermined steps to solve a particular type of problem and then practices that sequence over and over and over. And over. Don't ask her if there are other ways to solve problems.

2. Teach him that math is a solitary process. Reinforce it by placing him alone in front of a computer or textbook without talking about a variety of math strategies that might be used to solve similar problems. (See #1!)

3. Teach her that math only exists between the pages of textbooks. Don't point out the math you use as you grocery shop, balance your checkbook, calculate miles/gallon, prepare dinner, or figure how long it is until her bedtime so you can watch Jersey Shore in peace.

4. Teach him to be fearful of math. This is easy. It helps to do #1-3 above. But it also helps to model your own fearful behavior. Say things like, "Math is hard for me." Or "I never liked math." Or "I was born without the math gene." According to Marilyn Burns (Math: Facing An American Phobia), you're in good company with 2/3rds of American adults being math phobic. You're already on the bandwagon. It's a popular place to be. Don't jump ship now!

5. Teach her that math is primarily a world of pencil and paper. Don't ask her to estimate or use mental math.

6. Teach him to avoid visual cues. Forget using manipulatives, sketches, or drawings.

7. Don't read any math-related children's literature. Don't play any math games.

8. Always emphasize the importance of fact memorization. Drill, drill, drill. And if she can't get it, drill some more.

9. Never look at what wrong answers have to teach us. That would just be wrong!

10. Teach her that math is boring. And scary. Reinforce with #1-9 above.

Want to add to my list? Comment with your own ways to mess with children's mathematical minds!

Math Monday Blog Hop #71 (Oct. 22, 2012)

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Math Monday Blog Hop # 70 (Oct. 15, 2012)

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New Math Monday Blog Button!!!

Here's a HUGE SHOUT OUT to Heather of Teaching My 3 who created this gorgeous button for the Math Monday Blog Hop. Thank you so much, Heather!!

Ironically, and without Heather's knowledge, I've been doing a lot of finger math this fall. The new picture couldn't be more perfect!

While you're blog hopping, check out Heather's big fall blog hop!!

Explore Units of Math -OR- What is One?

Nice video from TED-Ed. Description:

One bag of apples, one apple, one slice of apple -- which of these is one unit? Explore the basic unit of math (explained by a trip to the grocery store!) and discover the many meanings of one.

Math Monday Blog Hop #69 (Oct. 8, 2012)

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Math Monday Blog Hop #68 (Oct. 1, 2012)

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Homeschool Chicks Have Hatched!

The Homeschool Chicks website has hatched! Several of the bloggers from www.TeachingBlogAddict.com have come together in a brand spankin' new website for home educators. Each of the five of us will focus on a specialty area. We have a Fun Chick, Organized Chick (that's NOT me!), a How-To Chick and a Reading Chick. I'm the "Math Chick." (Never in my wildest dreams...) On the site you'll find a homeschool blogroll (we'd love to add yours!), pinboards, linky parties, and lots of freebies. Spread the news! And click the button below to come check us out.

Poison! Race to 100

Poison! Race to 100

In the upper grade Math Club we played Poison! Race to 100. Here are instructions to continue play at home:

Materials Needed:

• Base 10 manipulatives: 1 mat per child and a bunch of strips (10s) and units (1s) - those pictured can be purchased from The Math Learning Center.
• 2 Dice labeled 0-5 and 1-6

Directions
Each player gets a mat (red 100s grid shown above) as a playing board. Player #1 rolls the two dice, adds the numbers, and collects that many base ten pieces. The player can choose to keep those pieces, adding them to the playing board (the red mat), or roll again and collect additional pieces. BUT, if the dice rolls a 0 (POISON!) he loses everything in that turn.  (Once pieces are on the mat, they are safe.) Each time the player rolls, she must exchange base ten pieces from that turn so that she has the least number of pieces in her possession. So, for example, if in one roll she gets 8 and then in a second roll she gets 4, she must trade in 10 units for 1 strip (ten) with a total of 1 strip and 2 units. The same is true of the board. As pieces go into the safe zone/red board, they are exchanged for the smallest number of pieces.

As students play, they might consider:

• How much do you have?
• How many do you still need to reach 100?
• How many more/less do you have than the other players?
• Challenge: What is the probability of getting poisoned (a zero)?

Ruptured Eardrum

I'm out this week with a ruptured eardrum. Hope to be back soon. Carry on with math!

Math Monday Blog Hop #67 (Sept. 17, 2012)

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Subitizing - Try it Online!

Familiar with subitizing? Try some online subitizing exercises for yourself. Can you see how many dots there are...in a flash??

Math Monday Blog Hop #66 (Sept. 10, 2012)

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Students Who've Suffered Early Trauma - Dealing with Behavioral Issues

Over the last several years, I've worked with students who suffered early trauma, usually as infants. Contrary to what I used to think, trauma can involve many things other than abuse. Neglect, separation from birth mother, extended hospital stays, inadequate daycare...and many, many more things can contribute to a traumatic start, which can eventually lead to rather unappealing behaviors as students reach school age.

If you teach (or parent) a child with behavioral issues, take a moment to read "An Open Letter to Educators Who Work with Students Who Have Been Diagnosed with Reactive Attachment Disorder or Have Suffered Early Trauma." It's an excellent primer for those who are struggling with disruptive student behaviors.

Sometimes I shake my head. At myself. I thought I knew so much as a 22-year-old beginning teacher. And later as a beginning parent. Now, over twenty years later, I'm amazed and humbled as I consider all that I still have to learn.

Taking the Outside Temperature

I love this idea for learning about temperature, found on the Math Learning Center Blog. It could be done at home or at school. Students read the outdoor temperature each week, thinking about a range as they consider this poem:

Fahrenheit Weather

90 degrees is pretty hot.
70 degrees is pleasing.
50 degrees is getting cold,
and 32 degrees is freezing!

Look at the original post for detailed lesson instructions. You'll find a blackline classroom wall thermometer here if you'd like to add one to your room. I printed one on cardstock, slit the very bottom of the thermometer and added a thin strip of red tagboard to slide up and down for the temperature gauge. 

Math Monday Blog Hop #65 (Sept. 3, 2012)

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TBA Open House Week ~ Monday: Meet the Teacher!

Over at Teaching Blog Addict (TBA) they are having all kinds of link-ups to introduce some changes to the website. Bloggers (teachers and homeschoolers!) can link up to share:

Monday: Meet the Teacher- tell us all about you and your teaching style!
Tuesday: Classroom Photos
Wednesday: Handouts for Parents
Thursday: Bulletin Board Photos
Friday: FREEBIES!

Meet Me...

I'm Cindy. I first entered the classroom a little over 20 years ago as a high school English teacher. I looked too young for that setting (got asked for my hall pass!), so I found a job teaching middle school language arts, social studies, Spanish, drama, and more. That experience made me interested in learning more about self-contained classrooms, and I went back to get my Master's in Elementary Education. As an elementary teacher, I loved teaching literacy, became addicted to children's books, and then...wait...fell in love with teaching MATH. Over the years I've taught almost every grade level, preschool to graduate school. I do a lot of consulting, work with both classroom teachers and homeschool parents, and teach kids of all ages in a wide variety of both public and private settings. Oh...and I have 5 kids.

My style? LOL. Based on the description above, I'd say ECLECTIC. :) One of my hobbies? Collecting math-related children's books.

Who are YOU? Introduce yourself and join the blog hop! :)

My Life in Numbers

Here's an idea for getting your math year off to a great start...

When I posted about Math Journals & Notebooks, I mentioned that I loved the idea of having children make covers relating math to themselves as Courtney shares at A Middle School Survival Guide. Ideally, I'd begin the lesson by reading aloud a book that relates math to everyday life. (I mention several suggestions here.)

When I first considered what might go on a cover, I didn't have a lot of ideas. I just thought about # of siblings or children, year of birth or age, height or weight, etc. But the more I considered, the more ideas multiplied! I'd definitely want to do this as a brainstorming activity with students rather than giving them a list. See what your collective brain energy can come up with! How is math related to our daily life? Here are some of the things we thought of:

• time you wake up/go to sleep
• # of favorite ____________ (sports, colors, hobbies)
• # of years _____________ (teaching, being a student, playing an instrument or sport)
• time each day that you ___________ (exercise, go to school, watch tv, read, play video games)
• # of _____________ that you own (pets, video games, books)
• # of years until you (finish school, turn 21, want to get married or have kids)
• cost of your favorite (restaurant meal, soda, candy bar)
• amount you spent per week on (lunch, snacks, coffee)

The possibilities are endless!

A follow-up post will show you how to turn this into a problem solving activity!!

Math Calendar Notebook Pages - free & awesome!

Don't miss these free Calendar Notebook Binder Printables from Homeschool Creations! They are gorgeous, kid-friendly, and packed with great mathematical explorations. They could be used in a home or school setting. Jolanthe includes both a textual and a video description of how they can be used.

Thank you for offering this, Jolanthe!!

Math Monday Blog Hop #64 (Aug. 21, 2012)

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Free Math Strategy Posters

If you're looking for some math strategy posters to use in your classroom (home or school!) check out these Math Learning Center freebies:

Addition/Subtraction Strategy Posters
Multiplication/Division Strategy Posters
Multi-Digit Multiplication Strategy Posters

Math Monday Blog Hop #63 (August 6, 2012)

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Online Math Dictionary for Kids

Need some online references for math terminology? These may be of use at school and at home:

A Maths Dictionary for Kids-- "animated, interactive online math dictionary for students which explains over 600 common mathematical terms and math words in simple language." Kid-friendly.

iCoach Math Dictionary --comprehensive list of terms with definitions and visual representations.

Math Glossary of Terms --one page list of terms and definitions.

Harcourt Math Glossary--definitions with visual representations organized by the grade level in which the term is likely to appear. Includes sound option.

Math Monday Blog Hop #62 (July 23, 2012)

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Elapsed Time with Scaredy Squirrel

Have you read about poor Scaredy Squirrel? He never leaves his nut tree. He's too scared of the unknown. So his daily schedule consists of:

"Wake up. Eat a nut. Look at view. Eat a nut. Look at view. Eat a nut. Look at view. Go to sleep."

Not a whole lot of excitement for that furry critter.

Then one day, in the most hilarious way, Scaredy Squirrel is forced into the unknown. He makes some changes in his life:

"Wake up. Eat a nut. Look at view. Jump into the unknown. Play dead. Return home. Eat a nut. Look at view. Eat a nut. Look at view. Go to sleep."

My 6 & 9yo kids have read this book with me over and over and over. We all LOVE IT. It's one of those books that tickles the adult funny bone just as much (or more) than it tickles the kids'.

I've always thought this book would make a great tool for considering elapsed time. Today I asked my 9yo to figure out how much time Scaredy Squirrel used for each daily activity on the old and new schedule. He then did a little comparison of how time was spent in each chart. We noticed that some of the time Scaredy Squirrel spent observing the world in schedule #1 was now spent experiencing the world in schedule #2.

I wouldn't hesitate to use this with any age, but it's especially valuable for 3rd & 4th graders who are exploring the Common Core State Standards involving time:

3.MD.1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.
4.MD.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Calculating elapsed time isn't scary. Try it!

Disclosure: If you purchase books through my Amazon links, all commissions go toward foster care through Grace and Hope at no additional cost to you. I do not keep any money myself; I am hoping to be able to sponsor an additional child in foster care through commissions on this site. Thank you!

Review: Marie's Words (picture vocabulary cards)

One might ask why I'm deviating from the usual math postings in order to do a review of vocabulary cards. So here it is in a nutshell:

1. Before my math education days, I was an English Education major. Yes, I used to assign vocabulary lists to hapless* youth.
2. Despite my youthful vigor, I am the proud parent of two assiduous* children who have taken the SAT test...and three more who will take it in the future. (How can I be that old?) I've heard a lot of talk about the importance of vocabulary.
3. As a high school student and future English major, I bemoaned* the fact that I personally did better on the math portion of the SAT than on the reading portion.
4. I saw Marie's Words in the Timberdoodle Catalog and was intrigued. They sent me a free review copy. I am not paid for this review and I can say whatever I please. (Scary, but true.) If you're interested in learning more about the company that trusts me to say whatever crazy thing pops into my head anything, you can learn more about Timberdoodle on Facebook.

Marie's Words consist of 550 vocabulary word cards depicted by a drawing on one side and the definition, a sentence, synonyms and antonyms on the other side. 

Although we are on summer hiatus*, I'm very aware of the importance of keeping my 9-year-old son busy. So as not to become indolent.* (Anyone else have a 9-year-old who needs to be busy?) Each week, I put ten words on a ring and challenge him to learn them by Friday. He usually memorizes them on Monday. Although I don't know if they'll continue to stick in his brain, so far, so good; he seems to be recalling words from past weeks with ease.

What I like:

• Portability - the cards come with a pre-punched hole, so I can easily add and subtract them from my own ring. 
• Time - quick, easy, can do it anywhere.
• Illustrations - the pictures make even difficult words accessible to many ages and abilities.
• Bang for the Buck - at 550 words, it's going to take us more than a year to get through the box. And ten cards a week is nothing to sniff at. 
• Another Tool - while I wouldn't want to limit vocabulary learning to cards, this is certainly one tool to add to the toolbox. 

Things That Made Me Pause:

• Some Illustrations - while we have not gotten through the entire box, I have run across a few cards in which I had a hard time connecting the illustration to the vocabulary word. This has been less an issue for my son than it has for me. Perhaps I'm old and set in my vocabularific ways.
• A Few Words - sometimes the word on the illustration is altered for the purpose of making it easier to remember and understand. For example, the card for "abhor" includes a small letter "c" and "e" on the word on the illustrated side of the card:

ab c hor e

The sentence on the back reads, "Josh abhors his chores so much that he taught his dog to do them."

That makes me a tad nervous. I'm afraid that a few kids could decide that the word is actually "abchore." Hopefully, I'm wrong. Irregardless, this only affects a handful of the cards in the box.

In summary:

I have an affinity* for the cards. And will use them with my children. While I think that the best way to enrich vocabulary is to read widely and often, I did that as a teen and didn't ace the SAT. This is another tool to add to the learning toolbox.

Please Note: no vocabulary cards were harmed in the writing of this post. But if you see an (*) next to a word, it means I borrowed the word from Marie in an effort to show my grandiloquence*.


As a member of Timberdoodle's Blogger Review Team I received a free copy of Marie's Words in exchange for a frank and unbiased review.

Math Monday Blog Hop #61 (July 9, 2012)

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Math Monday Blog Hop #60 (June 25, 2012)

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Organizing Your Children's Math Library

After reading The Book Whisperer by Donalyn Miller I felt inspired to update the organization of my math library. When I had a fewer books, this technique worked, but in this past year I've been using books less--only because I couldn't find them--and knew something had to change.

In her classroom Miller uses small tubs to hold books on the bookshelves. As the number of books grow, it's simple to add more labeled tubs. With the labels, it's easy  to put your hands on the topic you need. I used the concept headings on my Math in Children's Literature list to label bins. Since my bins taper a bit, I lose a little shelf space, a sacrifice that's worth it when I can locate the book I need. When I bring a new book home, the book first goes on a spreadsheet, and then straight into the appropriate concept bin, where books are then alphabetized by title.

This is a great summer project! If you're looking for some summer reading, check out the current or past Math Monday Blog Hop(s). During the summer, hops will remain open for 2 weeks. Happy Summer!

Math Monday Blog Hop #59 (June 11, 2012)

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