Good morning! There is nothing like a sitting down with a morning cup of coffee and a good math book while the sunshine streaming through the windows. There is an appreciation for moments like these where professional growth can be absorbed instead of served up like fast food. We can take our time and think about the information. At least we can until the kids wake up. Then it's anybody's game!
So let's take a look at what we have for this week.
"Although children have an impression of division as more advanced than, say, addition, it is just as much a part of their day-to-day experiences as addition, subtraction and multiplication. Think of kindergartners passing out birthday treats or first graders sharing a bag of pretzels or a pizza." (Hazekamp, pg. 76)
So why is this such a difficult idea for kids to master? Hazekamp suggests it is because we are tied to the algorithms and not the concepts. In her division chapter, she suggests a sequence of 6 steps for teaching division.
1. Number Bonds
2. Place Value charts and disks
3. The distributive property
4. Partial quotient division
5. Traditional long division
6. Short division
I have spent the last month discussing number bonds but what intrigues me in this division chapter is using the distributive property. I actually spent some time online researching it further, looking for videos of teachers using it in their classes or even showing lesson plans for how they would introduce this concept in division. I have a few links below for your perusal but what I realized is that to use this strategy, kids have to have a VERY strong sense of numbers. They need to be completely comfortable with place value concepts and multiples of numbers, at least within basic fact families. Hazekamp mentioned that is is a strategy used with "friendly numbers". Kids would have to learn what a friendly number looks like and what an unfriendly number would look like.
Resources
https://m.youtube.com/watch?v=9PqQCCcP0u0
https://www.teachingchannel.org/videos/common-core-teaching-division
http://www.cpalms.org/Public/PreviewResource/Preview/72779
Reflection Questions
What strategy intrigued you?
Name your biggest challenge when teaching division and how you plan on addressing it this year.
What underlying knowledge and skills do you think are the most crucial to teaching division?
I always think it is important to connect anything and everything with real life. Again the sequence of steps to teach division follows the others, which is great!
ReplyDeleteI have to say something that threw me at first was when I got to the second part of place value disks(when they are drawing them), they didn't have the numbers anymore on the disks. I personally think you should still label the disks as you are drawing them before you just draw the disks. I found it a little confusing at first myself.
I liked the strategy of working with place value disks personally. I am a visual person and I love the way it is broken into the steps. That is why the labeling the disks would help someone like me. haha.
I don't teach division, as I teach first grade, but if I did I would follow the same process (number bonds, place value disks, etc). I do plan to use those processes with addition and subtraction.
Place value and number bonds are the most crucial to teaching division. I hope to lay the groundwork for both so each year they can continue to build upon those skills.
Thank you Carrie for doing this book study. It has been fun and interesting! When's the next one? LOL
I really like the “friendly numbers”. With Pearson we refer to this as compatible numbers, and the lesson was only given one lesson in the textbook, but I used the strategy throughout, because I think it is so powerful. Kids who can look at these numbers and make them “get a long” are able to solve long division problems in heads. Again, they have to have a strong place value understanding in order to see the answer.
ReplyDeleteNumber one challenge, kids not knowing their multiplication facts fluently!!! The students who did not know their facts floundered, and took waaaaayy too long to work out the most basic division problems. Without the fluency they could not visualize the inverse operation clearly. The fact families should jump out at the student by the time they embark upon division.
The other big obstacle was, working through long division correctly. Even my students with fact fluency had difficulty remembering all the steps. They made many mistakes within the process. Long division is very cumbersome and labor intensive!!
Here are some examples
Setting up equations correctly by mixing up dividend and divisors
Not using place value correctly on top of the division symbol
Working sloppily and loosing place value while subtracting
Forgetting to “bring down”
Knowing when to place a zero on top of the division symbol
Going back and forth between multiplication and division (loosing track of what process they were working on)
The most important thing they need to understand is that they will be breaking the dividend into smaller parts. While this seems like a no brainer, sometimes kids get so involved in the process of long division they lose sight of the actual problem.
What is crucial is that they understand PLACE VALUE!! Especially once they begin dividing using decimals and whole numbers.
BTW, just reading/thinking/writing about all this gets me so pumped for teaching math!!! Thank goodness I have you guys as an outlet. My family glazes over when I go on these kinds of rants.