Mathematical Musings

I just read a great article in last month's NCTM journal, Mathematics Teaching in the Middle School. It describes how algebra teachers can use the properties of slope to clarify student understanding of fraction operations. If you are an NCTM member, you can access the article here.

The article got me to thinking about several different ideas. First of all, the ability to work with fractions is critical for student success in upper levels of math. High school teachers are constantly providing remediation to students who are having trouble with fractions. I would dare say that fractions are to pre-algebra and above as basic facts are to arithmetic. I hear 5th-8th grade teachers saying, "My students struggle with what I am trying to teach because they don't know their basic facts. " I hear 7th-high school teachers saying, "My students struggle with what I am trying to teach because they don't know how to work with fractions." Each year in math builds on the previous years' work. If students are missing crucial pieces of their mathematical foundation, they cannot build upon that foundation and acquire the new knowledge they need. The longer this is allowed to continue without repair, the more unstable the structure becomes.

I am not saying that we should neglect the required content for a grade and just reteach skills from earlier years. The second thing I want to share from this article is that we should be constantly looking for connections in the content we teach. There are many ways to embed skill practice in grade-level contexts. In fact, the new context may be what certain students need to see in order to master content that has been troubling them. As the author of the article says, making a connection between two math concepts may help "students develop a richer understanding of both (Cheng, 2010)." Where are other places that we can embed fraction understanding?

Reference

Cheng, Ivan. "Fractions: A New Slant on Slope." Mathematics Teaching in the Middle School 16 (August 2010): 34-41.

Labels: basic skills, fractions, slope

This is a test of the mobile blogging network. I'm sending this post from my mobile phone. Isn't that cool!!!

I just sent the previous sentence to my blog from my phone. Now I am editing the post from the computer. I can see possibilities for this! I get lots of stray ideas that I would like to blog about when I am away from the computer. Now I can send those ideas to my blog, start the conversation, and edit it later if necessary! Blogging has changed a lot since the old days! (ha!) I am really excited about the possibilities and hopeful that this will encourage me to blog more often!

Labels: blogging

I love going into classrooms and seeing teachers excited about what they are doing that is working well! Last week I visited a 6th grade math and science teacher who is thrilled with the way her new cooperative learning strategies are working in her classroom. She learned these strategies at AMSTI training this summer from a math specialist who refuses to take credit for the ideas. :-) However, they both gave me permission to share, so here goes...

Rules for Super Teams

• Works together for common goals
  
• Makes sure that everyone in the group understands the concept
  
• Allows for different opinions in working toward a solution
  
• Is patient with all members
  
• Encourages each member to do their best work
  
• Stays on task
  
• Is eager to share after exploring together
  
• Is careful with manipulatives and tools of math
  
• Leaves team area neat and clean
  
• Brings our math notebook each day
  
• Collects papers when a team member is out
  
• Increases scores on tests and daily work

She groups students randomly and changes the groups regularly. Students are seated in groups of four, and each student has a role in the group. Cards outlining the duties of each role and "sound bites" that might be overheard from someone performing that role properly are at each desk.

Roles for Team Members

Coach/Leader

• Makes sure every voice is heard
  
• Focuses team on learning task
  
• Collects handouts for members who are absent
  
• Manages time so that the group gets the task completed
  

Sound Bites

• “Let’s hear from Ben next.”
  
• “That’s interesting, but let’s get back to our task.”
  
• “Let’s settle this by voting or paper/rock/scissors.”
  
• “If we can’t agree, we will have to ask Mrs. Smith to intervene.”
  
• “Here are the handouts you missed and I will ask Mrs. Smith to give you a copy of our Venn diagram from yesterday.”
  
• “We only have 5 minutes left. Let’s see if we can state this in a sentence or two.”
  
• “I think it is time to ask the teacher for help since I am not getting cooperation.”

Gopher

• Follow directions regarding materials for the day
  
• Picks up materials when instructed
  
• Makes sure everything is in good shape
  
• Reports to Coach if anything material is broken or not working
  
• Turns in all materials in good condition
• Collects all papers to be turned in
  

Sound Bites

• “Coach, this ruler is broken. I will get another for us if you will let Mrs. Smith know.”
• “Please hand me your papers with your names on them so that I can turn them in.”
  
• “I see you are still using the calculator, but my instructions are to return them now.”

Reporter

• Reports to class what the group has discovered
  
• Makes sure that he/she understands what the group wants to say about a topic
  
• May not always agree with the groups response
  
• Speaks clearly so that everyone in the room can hear
  
• Uses graphic representations when appropriate to help audience understand
  

Sound Bites

• “My group thinks that…”
  
• “We found that….”
  
• “As the graph shows…”
  
• “Although we all did not agree, the majority thinks…”
  
• “The last group was correct, but we also found…”
  
• “We got the same answer, but we did it this way…”

Recorder/Checker

• Records what the reporter will say
  
• Completes any written assignment that the team is required to turn in
  
• Reads instructions on any handout to the team
  
• Rechecks figures on answers
  

Sound Bites

• “Here are the instructions for this sheet we are to do and hand in at the end of the exploration.”
  
• “This is what we have decided the reporter should mention.”
  
• “Will you help me because I need to write a summary statement and draw this polygon.”
• “Now, let me read this to you and see anyone has anything to add.”
  
• “Well, we can do it that way, but it has to be done this way to hand in.”
  
• “Let’s all write our names on this since it is being turned in.”
  

The teacher encourages teamwork by giving points for working together, completing homework, improving test scores, etc. She has a collection of green and red craft sticks: green sticks are for positive behaviors that are rewarded with points, and red sticks subtract points for inappropriate behavior and work ethic. Each team turns in a record of points earned at the end of each class period, and the team with the most points is rewarded with a treat at regular intervals. The students are working together to help each other learn, and their teacher is very happy with the results!

So, how is cooperative learning working in your classroom? What strategies are working well for you? What challenges do you face? Let's start a conversation and learn from each other!

Labels: cooperative learning

Lots of new projects to ponder....coaching...formative assessment...differentiated instruction....interactive student notebooks...5E lessons...distance learning...new hire training...sustainability...

Trying to decide where to focus my energy for the moment, but knowing that some mundane details must be taken care of...More to come later...back to work for now!

How many times am I going to start then stop blogging before I finally stick with it? I really, really, really want to make blogging part of the way that I communicate with the teachers that I serve. I used to find the time to do this, and I know I can do it again! Of course, that was in the days before Facebook...surely I would find blogging just as rewarding (probably more so) than the mindless minutes (hours?) that I spend there. Of course, blogging is not mindless, so maybe that is why I have avoided it for so long?

I considered starting fresh with a new blog, but I kinda like this old friend. I spent a long time making it look a certain way, and I just don't want to do that again for now. I want to encourage conversation among the teachers I serve through AMSTI, and I invite anyone else who is interested to join in with us. I may end up talking to myself, but I guess that's okay, too.

So...what are we going to talk about? Teaching and learning math, science, and technology. What should students know? How should we teach it to them? How do we know if they have learned it? What should we do when they haven't learned yet? We are going to start off by talking about differentiating instruction, but I will save that conversation for another day. Have a great weekend!

It is that crazy time of year, and I would guess that many of you are dealing with math placement decisions for your students. The following link has an interesting article about the effect that math placement has on certain students.

“More challenging middle-school math classes and increased access to advanced courses in predominantly black urban high schools may be the key to closing the racial academic achievement gap, according to a University of Illinois study. "

http://www.sciencedaily.com/releases/2009/04/090420121423.htm

Here are a couple of quotes from the article that really made me think.

Students who take more advanced math courses in middle school lengthen their lead over time, and the positive school-related behaviors developed in those advanced courses lead to even higher achievement.

Being in a classroom where the expectations are higher, the course work is more rigorous, and the climate is more academic has huge effects on student effort.

These finding don’t surprise me because I have seen this happen with my students, but it is great to see research that backs up my instincts. So my questions are, “so what?” and “what now?”

• What implications does this have for our students?
  
• How can we use this information to help students?
  
• How can we duplicate the positive effect of advanced classes for students who are not advanced?
• If we put everyone into "advanced" classes, would they still be "advanced?"
• Should we pick promising students to "place" into advanced classes even if they don't "qualify?"

I would also like to see the researchers' definition of "academic climate. " Obviously, this includes more than high expectations and rigorous coursework. I would think the climate would be the most challenging to change. I also think that we might have many different pictures of what a room with an academic climate looks like and sounds like.

What are your thoughts?

I created a new blog for a class I am taking. I will be posting there for the next few weeks, so feel free to come on over and join the conversation!

After a prolonged absence from the blogging world, I am back.....at least for 8 weeks! I am taking my FINAL master's degree class, and one of this week's assignments is to set up a blog. I will be required to post to it during the course, and I hope that I will be back in the habit by the end of the course. I have so many new ideas that need to be processed...I have some job responsibilities that could be met by blogging...I enjoy it! There is no reason not to jump back into blogging, so here I go!

My children are now 15, 11, and 5. They are eagerly anticipating a driver's license, middle school, and kindergarten!. My husband is STILL on active duty with the Army. He was recently promoted to Lt. Colonel. We are very proud of him. I am in my second year as AMSTI math specialist, and I am loving it. More on that later. Good night for now...I am looking forward to some great conversations on here!