Association of Teachers of Mathematics in Maine

Week 7 (March 2-7) Chapter 5: Pulling It All Together: Glimpses of What We Should See

  • 07 Mar 2013 4:31 PM
    Reply # 1236473 on 1231998
    Gillian Laird Sleeper

     

     

    When reading the samples from the text I found myself smiling and eager to read the end result.  How wonderful for the students to have a problem to solve and to challenge a company on it’s claims! 

    My example of this is very different, but I believe it to be appropriate for the ages of the students I teach.  (I teach Pre-K)  The lesson was to introduce and demonstrate one to one correspondence.  Sometimes, this can be difficult for children to grasp at a young age unless we use samples of “real life”.  When demonstrating this, we discussed getting dressed in the morning and I asked, “How many socks do you put on each foot?” .  They can visualize and understand this example because it relates to them personally getting ready in the morning.  Then, I had 6 pairs of shoes and 6 pairs of socks on the rug for the group to work with.  I asked them to match them up and put the right number of socks into each of the shoes.  They worked together as a group and each one had a turn matching a making sure that one sock went in each shoe.

    Later, to expand the lesson, I asked them to work on setting a table for snack time ensuring that the table was set with each student having a carton of milk, a straw and a napkin.  It was a group effort, but each child had to check to see if its spot had everything that was necessary.  When not, they were asked to get the missing item.  For me, that checked for understanding and allowed the child to problem solve in a real life situation.  (a four/five year old real life situation!)

    Where I fail is producing the arifact to show the students work.  I suppose I should be taking pictures of the students producing the one to one correspondence as evidence of them being able to meet the standard.  I will try to incorporate gathering more artifacts as I continue.

  • 07 Mar 2013 6:14 PM
    Reply # 1236553 on 1231998
    Sally Bennett
    I, too, loved the examples in the book but I wonder if there could be a bank of such examples to assess the same concepts.  I worry that sometimes students unwittingly "borrow" each others' good ideas and then there is a certain "sameness".  I wonder about the value in assessing a fascimile of someone else's work. 

    I have assigned projects from time to time and they have been successful, but I often end up having a real "gut check" every time as evaluating them requires a great deal of thought.  I know that project based learning is valuable and indelible, but there do not seem to be enough hours in the day.
  • 07 Mar 2013 7:26 PM
    Reply # 1236609 on 1231998
    Robyn Graziano
    I've used the NCTM Barbie Bungee project with my Tech Algebra kids. Just imagine these big burly guys playing with Barbies. The project starts off with the question: how many rubber bands will be needed to drop Barbie 'x' number of feet without her head hitting the ground. Yep, you can imagine the comments being made. We had a lot of fun dropping Barbie from many different heights in and outside the school.
  • 07 Mar 2013 7:43 PM
    Reply # 1236620 on 1231998
    Deleted user
    @Nancy: It all came from students being curious about the meteor during science class and my jotting down questions they had.
    @Evelyn: The students have developed a list of questions that they would like to have answered after they have organized their data.

    I love where the students are in these activities, right in the middle of it all. The work they do is the consequence of their curiosity and their questions, features whose emergence is due to the careful guidance of attentive teachers. Steve's examples are not only mathematically rich, they are irresistibly inviting because of the promise they make to connect students to the world beyond the classroom. I think they are notable because they are both, but those are pretty special projects. Not every "driven mathematics" project will necessarily have that compelling, outer-world connection; it may not even be cut from the cloth of the world we walk in, but engagement can still run high as long as students care about what they are doing. “[T]he quality of a task need not be judged by its relation to real life," writes Craig Dwyer, quoting Nicol and Crespo, here, but in relation to how it engages students.” It seems that ways to build that kind of big engagement include 1) keeping our eyes open for math in the wild, for example, being ready to notice that a fiery meteor naturally brings opportunities for curiosity and questions along with it, and 2) helping students map out their own routes through that piece of the wild, thus giving them a safari they can call their own. I think the unnerving part of this kind of practice must be reconciling its responsive posture with other, more formal concerns that might be in place, like pacing guides and textbook commitments, or hindrances to creativity and reasoned risk-taking that some school cultures may unfortunately foster.

  • 08 Mar 2013 6:10 PM
    Reply # 1238148 on 1231998
    Kate St.Denis
    Last fall, my algebra class worked on the classic cube factory problem. I took a photo of their solution, but have failed to figure out how to insert a photo into wild apricot so I'll summarize:

    "The MDES algebra class has started a cube factory. We build different sized cubes out of unit cubes and we painted the outside. Then we had to figure out how many sides each unit cube would have painted so that we could plan how much paint to buy."

    (notice the investment in the context)

    They built and built with plain wooden blocks and then found some painted blocks that better demonstrated the pattern that they were discovering. Because they didn't have enough blocks, they kept track with a series of photos. Then they made tables, talked, made more tables, graphed, changed the graphs, talked more and finally made generalizations about the number of sides that they needed to paint and drew conclusions about the variety of growth that they were noticing. 

    (notice the verbal models, communication, perseverance, structure, repeated reasoning....)

    Now it's March and we're using the quadratic formula. My students use the exponential growth modeled in the cube project as a common reference point. They get it.
  • 09 Mar 2013 8:26 AM
    Reply # 1238401 on 1232667
    Anonymous
    Katrina Hall wrote:However, a recent webinar brought the idea of a RAFT to a higher level for me. Dr. Robert Dillon, Principal of Maplewood Richmond Heights Middle School in Missouri, shared ideas and resources for adding student engagement to the CCSS.  Project-based learning, experiential learning, and technology-infused learning all discussed as being best practices. However, his main point was going beyond the RAFT and made the important statement that it is the role of the educations for set the stage for innovation. It is the role of teachers and leaders to support students in using mathematics to change our schools, communities, states and world.  


    Katrina, thank you for referring to Dr. Dillon's talk.  I found it at:

    http://www.instantpresenter.com/WebConference/RecordingDefault.aspx?c_psrid=EA53D9838346 

    and viewed it, myself.  He shared some great resources and left me feeling even more inspired to do something "different."  Truth is, the glimpses in chapter 5 do not resemble the 25 minute sessions I facilitate with some of our most struggling learners.  I recognize that all and especially my students would benefit from engaging, concept-oriented tasks described in chapter 5 and by many of you (loved your Bungee Barbie investigation, Robyn G.).  I am thinking about how my days could be scheduled differently so that I could spend my time engaging strugglers in mathematics.
  • 09 Mar 2013 8:29 AM
    Reply # 1238404 on 1238401
    Tracey Hartnett
    Anonymous wrote:
    Katrina Hall wrote:However, a recent webinar brought the idea of a RAFT to a higher level for me. Dr. Robert Dillon, Principal of Maplewood Richmond Heights Middle School in Missouri, shared ideas and resources for adding student engagement to the CCSS.  Project-based learning, experiential learning, and technology-infused learning all discussed as being best practices. However, his main point was going beyond the RAFT and made the important statement that it is the role of the educations for set the stage for innovation. It is the role of teachers and leaders to support students in using mathematics to change our schools, communities, states and world.  


    Katrina, thank you for referring to Dr. Dillon's talk.  I found it at:

    http://www.instantpresenter.com/WebConference/RecordingDefault.aspx?c_psrid=EA53D9838346 

    and viewed it, myself.  He shared some great resources and left me feeling even more inspired to do something "different."  Truth is, the glimpses in chapter 5 do not resemble the 25 minute sessions I facilitate with some of our most struggling learners.  I recognize that all and especially my students would benefit from engaging, concept-oriented tasks described in chapter 5 and by many of you (loved your Bungee Barbie investigation, Robyn G.).  I am thinking about how my days could be scheduled differently so that I could spend my time engaging strugglers in mathematics.
    I noticed I accidentally posted anonymously.  I don't mind admitting that I am the one that recognizes I need to change the way I do things...
  • 09 Mar 2013 11:25 AM
    Reply # 1238490 on 1231998
    Tom Light
    It was fascinating to read the book and everyone's thoughts and examples.  I especially appreciated the example of the young students using socks, shoes, and place settings to learn about one-to-one correspondence (and perhaps addition) as Steven's examples were all for older students, as is my experience.

    These real-life examples (or even unreal problems) engage students, involve students in true mathematical practices, and check student understanding.  One concern that I read and have often heard was from Heather and Kim:
    We learned a ton about who really knew how to compare fractions with unlike denominators, who could demonstrate it with a diagram/drawing, and the numerous misconceptions that abounded! But, we can’t help but wonder how to help those students who simply don’t get it.
    I would say that, as they found, this type of problem really asses if students understand the math as opposed to memorizing a procedure.  In addition, students who think the mathematics are more likely to be able to solve the problem in the future, something that is very important for the CC in which each years math builds upon previous understandings.  Lastly, in my experience (and I'm an "old man") some of the students who we think "get it" because they can solve the traditional problem are least able to apply the math in different types of problems.  They are so good at memorizing and applying algorithms that they don't develop understanding.

    I was disappointed to not see samples of student work, and have none myself, but I have been inspired to save examples so I can share them on future prompts (if I can figure out how - maybe copy and paste or link to a site such as photobucket.

    Now, my own examples/thoughts.  I try to give problems related to real life regularly, but they are seldom connected to the world as artfully as the burger king or car speed examples. I think I need to do a better job of keeping my eyes open (and using my students' eyes once they have seen some of these problems.  Any problems that connect to real life are excellent formative assessments - they show a lot about student thinking.  I have had much support for this, especially from our math interventionist, Tracey Harnett.

    I believe it is difficult to ensure that all content targets are included using Problem Based Learning.  We have an alternative, hands-on program at our middle school.  The program integrates literacy, science and engineering, and math into learning projects such as building a racing car with support of a local racing team, developing and maintaining a community garden, and learning about ecology.  Despite this, the one class the kids must participate in separately from this program is math.

    I have done Service Learning with my classes the last several years and have not done a particularly good job at integrating math.  This year, my class will be divided into groups and take on three projects at Robert's Farm, a local community garden and natural area.  One will involve building a chicken coop.  Proportions and fractions can fit nicely into this.  Another group will work on a nature trail, a bit more difficult to incorporate math unless we do some statistical analysis of what grows where or mapping.  Our third project will be growing in a hydroponic system.  I'm not sure yet how math can work into this; the nutrients are supplied by a "pill" put into each plant container.  Perhaps some geometry looking at volume, measurements, and planting density.

    I hope I have success incorporating math into these projects!

  • 09 Mar 2013 4:06 PM
    Reply # 1238602 on 1231998
    Gail Stetson
    Like Tom, my class has been involved in experience based learning at Roberts Farm.  Last week, we tapped maple trees.  In addition to the general learning about this traditional Maine farm activity, my students are using math in many ways.  Once we had identified a maple tree, we used estimation to determine the age of the tree by finding its circumference.  We estimated a 20 foot area around each tree and estimated the tree population within that area by each student sampling part of the area and combining their results.  We will be measuring sap production.  In checking buckets place by other classes ahead of ours, we used fractions to describe levels .We will be graphing.  We are working with the ratio of gallons of sap to syrup.  Some of our data will be reported to foresters with the purpose of helping to make decisions about managing the forest property and making decisions about which trees to harvest.  It was interesting to see the mathematical questions that arose naturally from this real world activity.  Back in the classroom, these activities bring life to our daily math work. There is no question that my students are more engaged in their math work when it is connected to their life outside of the classroom.  
  • 10 Mar 2013 11:09 AM
    Reply # 1238909 on 1231998
    Amy Hediger
    The tasks served as a guiding light on how to engage students in SENSIBLE, real-life work filled with mathematical concepts and communication.  It is also overwhelming as you take stock against what you are currently doing in your classroom.  The speed and pace of the school year is fast and furious, so I always try to remind myself that replacing one of my "boring" passive, lessons with one that students assume greater responsibility is the way to work.  I know we all want it all, and want it now, but Leinwand reminds us to work collaboratively with our teammates to make these gains. 
       I also try to focus on what is relevant to students and what is going on in the news.  For instant, there was a leaky hydrant in the news a few weeks back, so I asked kids to watch a news segment and do the calculations on how much water is lost per hour, and per month.  Or for our ratio/proportions unit asking students to find the better deal with prices from the grocery store, or DirecTV vs. Dish.   
      We know that kids love to come to math class, and tend to do this type of work outside of the classroom, so it is imperative that we work collaboratively not just with our own team members, but virtually with all of our colleagues to give students opportunities to engage in real math.

Powered by Wild Apricot Membership Software