Focus on Math

Helping children become mathematicians!

Math Camp 2013 Reflections… August 28, 2013

Screen shot 2013-08-27 at 7.13.49 PMWow! Math Camp 2013 was a resounding success! The focus each day was on how we can structure routine activities for our students that will allow them to build number sense. We also talked about Carol Dweck’s research about mindsets and looked at how we could help our students build a ‘growth mindse’t in mathematics and not be stuck in a ‘fixed mindset’. (If you have not read Dweck’s book Mindset, I encourage you to get a copy asap!)

We looked at visual routines, counting routines, and routines involving number quantity, and discussed how each of these can be utilized for learning.

Our visual routines involved using 10 frames, dot cards, dot plates, 100 dot arrays, fraction pocket charts, percent circles, base-10 grid paper, and number lines (I always have students draw these rather than use ones that are pre-drawn and pre-marked). See end of post to download the various tools.

Our counting routines involved choral counting, counting around the circle, and stop and start counting, and counting up and back.

Our routines for number quantity involved mental math, number strings, “hanging balances”, and decomposing numbers.

It would take too long to write here in one post about how best to use/do each of these ideas, but over time I will get to them. Are you interested in something in particular? Email me and let me know and I’ll get to that one right away!

All of the “math campers” went away with lots of ideas that can be implemented in the classroom right away. I’ll be excited to hear from them how it goes it their classrooms.

I’ll leave you with my favourite definition of number sense: “Number sense can be described as a good intuition about numbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms.” (Hilde Howden, Arithmetic Teacher, Feb., 1989, p.11).

There is much food for thought in that quote alone!

Mathematically yours,

Carollee

Click to download: student 10 frames , teacher 10 frames; student dot cardslarge 100 dot array, 12 small 100 dot arrays, 6 small 100 dot arrays, 4 small 100 dot arrays, teacher dot cards set 1, set 2, set 3; template for making dot platesbase-10 grid paper, percent circles; directions for making fraction pocket charts;

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What NOT to Say to Your Children/Students August 21, 2013

We all know that praising a child can be a boost for their self-esteem, but do you know what kind of praise can actually do more damage in the long run?

Carol Dweck of Stanford University has been looking into achievement and success for some time, and in her best-selling book Mindset she discusses praise and its effects. (I am only able to give you a scanty thumbnail version here, but hopefully it will whet your appetite to read her book.) What Dweck found is this: if you praise someone for being smart or clever, eventually that person tends to quit taking risks or engaging in challenges. They develop what she called a “fixed mindset” believing that the amount of intelligence they have is fixed. They will, when give a choice of tasks, choose something easy in which they are sure to succeed rather than risk choosing a more difficult task that they might not accomplish so successfully, for doing so would make them look dumb and they want to maintain their “smart” image at all costs. They tend to give up easily on difficult tasks and see hard work as useless since, after all, if one is smart, there should be little or no effort involved.

However, Dweck also found that if someone receives praise for working hard, for persevering in a task, for making a mistake and then learning from it, then this person will develop what she termed a “growth mindset” and believe that intelligence is not fixed, but can be added to. Instead of shrinking from challenges, these folks will embrace them. They believe hard work pays off, and that effort is, in fact, the path to mastery. They will persist in the face of difficulty or setbacks and know that mistakes are an important part of learning.

I am adding a link to a short interview that Dweck did in which she discusses fixed and growth mindsets.

Considering the two mindsets, which do you want for yourself, for your children, for your students? The wonderful thing that Dweck’s research reveals is that even if someone has a “fixed” mindset, it can be changed to a growth mindset.

For now what I hope you will ponder is this: what is it that you are praising in your children? Are you praising them for being smart, or for working hard and persevering in a task? Do you want them to develop a “fixed” mindset or a “growth” mindset? It seems such a small change, but it makes a world of difference!

What you say matters!
Mathematically yours,
Carollee

 

Mrs. Norris’ “String Theory” August 20, 2013

Screen shot 2013-09-11 at 9.00.15 AMI was having a conversation with my brother just the other day about measurement. Warren is a finish carpenter and deals with measurements that have to be very exact. For instance in creating a wood inlay of almost any size, being off by even 1mm is noticeable — there is almost no margin of error. Our conversation went on to be about the idea of estimating linear measurements and what is “acceptable” when doing so. I went on to tell him one of the ways I give elementary students experience with estimating using string. It was Warren who suggested that I had my own “string theory”.

I give each student in the classroom a randomly cut piece of string, usually in lengths from about 8 cm long up to about 120 cm long. I then ask the students to take their individual pieces of string around the classroom and find some things that are about the same length as their string.

Once they have done this I give them a chance to share their various discoveries, and something interesting always happens: the students notice that the longer the string is, the greater the amount of leeway in the estimation. For instance, someone with a string nearly 120cm long may have as their item something about 110 cm long, a difference of 10 cm. But that difference is greater than the total length of string for the student who has only a piece of string 8 cm long. For a short string, the margin for saying “about as long” must be much smaller. Eventually the students notice that “about” is relative to the initial measurement.

Of course this principle of is true for measuring any attribute, whether mass, time, area, volume, etc., and it is important for students to have experiences with various units of measure to develop this understanding for themselves. It is easy to vary this activity by giving students either weights or particular items and asking them to try to find something in the room that has the same mass. It is interesting to watch them comparing with their hands as if using a balance scale. For sharing, make sure you have a scale available that will weigh both the original item (if it is a random item) and the “found” item.

I hope you will give “string theory” a try in your classroom!
Mathematically yours,
Carollee