Student Thinking #5

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I’ve found it interesting how much difficulty some of my students have with multiplying and dividing by 1.  I think they do know, at some level, that one times any number is just that number.  But it seems like when it is applied in someway, they have a hard time seeing it.

For example, there was one problem that we did on the daily warm up.  We were creating an estimate and had rounded our divisor to 1, and the dividend to 0.25.  When I asked what my quotient would be I got a lot of confused looks and shrugs.  With enough prompting, they could see that the quotient was 0.25, but I’m not 100% certain that all of them really saw it.

I’m not sure if this is because they feel overwhelmed by the fact there was a decimal in the answer, or if they really don’t have a solid grasp of that particular math fact.

Student Thinking #4

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One thing I’ve found interesting in student thinking is how students decide what operation a story problem calls for.  When I was asking one student why he had decided one problem was a multiplication problem, it was because one of the items in the problem had units of something per something.  Despite having worked to not connect specific words to specific operations, and stressing that you need to think about what the problem is asking, he still saw the word “per” and automatically assumed the problem was asking for multiplication (it was really a division problem).  This was even with a specific set of notes, with a very similar problem, where we went step by step and solved it as a division problem.

It makes me wonder if there is a way to teach students how to look at story problems that allows them to move away from latching onto specific words and helps them to be more successful solving the problems.  We’ve attempted having them write their own stories, in the hope that if they are writing a story using that operation, it would make it easier to identify that operation in a problem they are given.  It seems to help some students, but other students still have difficulty in identifying the correct operation.  I know it was something that even I had problems with up until college, when engineering courses present you with only story problems.  I feel like there has to be a more efficient way, rather than hoping that constant exposure will make all the pieces click into place.

Student Thinking #3

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We’ve spent this last week covering decimal multiplication.  The biggest issue my students have had is trying to line up the decimal points to do the multiplication.  Students (and even I) find it confusing that, in addition and subtraction, you line up the decimal points to perform the operation, but multiplication and division are more based in whole number operations.

After we had covered solving decimal multiplication with both the standard algorithm and by using fractions, I provided students with 6 practice problems and allowed them to choose the method that worked best for them.  The majority chose the standard algorithm, but many were still having problems with the multiplication because of the decimal point.  One student called me over for help and said “I just don’t know what to do, I don’t know how to multiply these.”  I rewrote the problem without the decimal points, he looked at me and told me “oh I can do this!”

I’m hoping that giving students a skills sheet that has multiple problems to practice with will help them.  It’ll be interesting to see how many will still try and line up the decimal points to solve the problem.

Student Thinking #2

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At the beginning of the decimal unit, we included a variety of addition and subtraction problems on the warm-up for practice.

One day we had an addition problem, one that we were using to ensure that students knew how to “carry” when the sum in one column was a double digit number.  The standard way to solve decimal addition is to line up the decimals, then to add from right to left.  “Riley” chose to solve the addition problem a different way.  He split each number into it’s whole number and fraction parts.  He added up the fraction parts first, then added up the whole parts.  Then he added the two results together to get his final answer.

If the problem was 12.37+4.86, he first added together 0.37 and 0.86 to get 1.23.  Then he added together 12+4 to get 16.  Finally he added 16+1.23 to get his final answer of 17.23.

It was a unique way to solve the problem.  It isn’t the most efficient way to solve the problem and it opens up more opportunities for error, but it was fascinating to see how he view the problem and how to solve it.

Student Thinking #1

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During the ratio and rates unit, we provided a variety of warm-up problems that allowed students to practice the math.  One of the unit rate problems was to find the price for one apple if 5 apples cost $8.35.

At the beginning of class during the warm-up, we paused the time and had students line up in the hallway.  As we were walking out, “Michael” asked me what the problem was.  I told him the problem, he thanked me, and we went out in the hall.  After a few minutes, we returned to the classroom and everyone resumed working.

As I went around to check on students’ progress, “Michael” stopped me.  He asked me to check his answer to the apple unit rate problem.  As I looked over it, he told me that he did all the math in his head as we were standing out in the hallway.

It was impressive to me that he could do that kind of mental math.  Most of my 6th grade students need to write out all of their division problems and that he could do the division without needing to see it in front of him was really interesting to me.

Common Core State Standards – 6th Grade Math

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According to Common Core, instructional time should be spilt between four areas:

  1. Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems;
  2. Completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers;
  3. Writing, interpreting, and using expressions and equations; and
  4. Developing understanding of statistical thinking.

In 6th grade, students will learn to:

  • describe and summarize numerical data sets
  • identify clusters, peaks, gaps, and symmetry
  • consider the context of collected data

They will also be building on their work with area in elementary school, teaching them the basic information to prepare them for 7th grade math, where they will work with scale drawings and constructions.

Chapters 7 & 9 – Images and Social Media

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Images are an extremely powerful way to convey a message.  I think it’s why the adage “A picture is worth a thousand words” is so enduring.

There are now a multitude of sites that now incorporate easy to find, high quality images.  The best known of these is Flickr.  Flickr is an online photo-sharing community that contains millions of photographs that cover a broad range of topics and interests.  Within Flickr, users can group, tag, share, and create presentations that can have incredible potential in the classroom.

The use of Flickr, and other sites like it, can extend across so many different subjects.  Having a strong visual can make conveying a new concept clearer and more meaningful for students.  Some students need that visual to really have a grasp of the material.  Using a photo-sharing website within my lessons could help a student understand the material.

With the option to tag and describe photos, it allows you can connect to a larger group of similar photos, allowing for a wider breadth of options.  Students can find and share photos that are meaningful to them, as well as find discussion points to share in class.  It also allows teachers to find classroom display ideas that can help them to create bulletin boards that help their students.  The ideas available to students and teachers are almost endless.

 
One of the most powerful things that can be done through Flickr is the idea of a virtual field trip. Due to geographical and economical constraints field trips are often unrealistic. While students are studying the Lewis and Clark expedition, they can be shown photos to enhance their understanding and help draw a better picture in the students mind.
 
Just as with all things connected, there are some risks.  The most obvious concern is appropriate content.  Because anyone with an internet connection and an email address can create a Flickr account, there are a great deal of inappropriate images on the site.  If you decide to use Flickr in the classroom, you need to be aware and set boundaries for your students.
 
Another powerful classroom tool is social media.  The textbook discusses the classroom potential of Ning and Facebook.  While I think that using social media in the classroom can be a unique way to build community and facilitate learning, sites like Facebook should be used with caution, if at all.  Because so many students are familiar with Facebook, it would seem to be a great option to use in the classroom, but it is too easy for students to get off track.  I think, for all the good that Facebook could provide, there are too many distractions for it to be a really viable tool.
 
Ning is a site that allows you to create your own social network, allowing you to easily upload videos, presentations, and articles.  This ability makes it a great resource for students.  Having a forum allows students to communicate with each other and with you as the teacher, allowing for greater collaboration.  It opens up a new way for students to have discussions, as well as providing a place for students to help each other with homework, as well as allow the teacher to chime in and make any necessary corrections.  Since the teacher can create the network, it limits the number of distractions, making it more beneficial tool in the classroom.