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

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  • 03 Mar 2013 7:58 AM
    Message # 1231998
    Anonymous member (Administrator)
    Reading:  pp 63-75

    Prompt:   On page 64, Steve sets the stage for the "glimpses" he shares in Chapter 5.  He offers us examples that he describes as engaging, concept-oriented, problem solving, problem driven mathematics.

    What is your example?  Have you seen it?  Have you done it?  Trying to do it?  Got student work to show it?

  • 03 Mar 2013 12:40 PM
    Reply # 1232189 on 1231998
    Nancy Sirois
    I enjoyed reading the examples in the book about how teachers have had students work on engaging problem-solving that directly connects to the world outside of school.  We see these types of claims in advertising all the time and knowing how to read and assess the information in those ads is lifelong  skill.

    Working with 4th graders, I try to incorporate things like this as often as possible.  Recently, when the meteor hit in Russia, we discussed the information in the news and did some activities to answer questions the students had.  First question: how does a rock explode? This baffled them.  When we watched the videos and you could hear an explosion in the background, we talked about how/why it would make that sound and blast a hole into the ground.  It didn't hurt that we were studying the solar system at the time.

    We scoured the news for information and I found a great interview with a physicist on NPR that described the meteor and gave great information about how fast it was going, etc.  We tested the theories by making snowballs outside and making them as hard as possible using water so they became iceballs.  Students then threw these iceballs as hard and fast as they could at a brick wall and we watched the iceballs "explode".  We figured out how fast the ice was thrown and compared that with the speed of the meteor (7 miles per second).  

    They loved getting the information about how many feet in a mile and how fast was their iceball going in m.p.h.? How long did it take to throw an iceball 10 feet and how does this relate to the meteor?  If it was traveling at 7 miles per second, how many miles per hour was it traveling? 

    It all came from students being curious about the meteor during science class and my jotting down questions they had.  We talked about how we could answer those questions and went about designing an experiement that answered those questions.  I'm sure there were flaws in our design and implementation but for a bunch of 4th graders, it was a very fun, hands-on way to answer questions they had about an event in the real world.
  • 03 Mar 2013 7:13 PM
    Reply # 1232667 on 1231998
    Katrina Hall
    I loved every glimpse inside a classroom which Leinwand presented here.  I could only wish that they were examples from my classroom.  What I see is not just mathematics but the engagement of the learner.

    Engaging students in their learning is an over arching task for learning professionals. As school, it is important for us to look for a variety of ways to provide individualized learning opportunities which are based on our students’ interests and passions; if we want them to truly learn.  Students are looking for opportunities where they have a voice and a choice in how they can showcase their talents and learning.

    I think back to the some of the first professional development opportunities where I was exposed to the RAFT; engaging students by giving them a role, audience, focus and topic.  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.  If a RAFT is a teacher’s tool to engage the learner then providing an authentic audience and a genuine opportunity to make a change in our school, community, or beyond is truly a way of maximizing engagement, especially in mathematics.

  • 04 Mar 2013 8:55 AM
    Reply # 1233061 on 1231998
    Mary Belisle
    I Loved reading about the RAFT. Great ideas in this response.The role of homework is hotly debated. I was interested that he thought homework assignments should not be pages of mindless exercises. That is the worst. Worksheets without end. The cure to understanding is to do more of the same in endless fashion in hopes of seseeing a change.  Or is that the definition of insanity. Although constructing the summative assignments here is labor intensive, a good place to start is to improve the quality of homework. It can be more real world and student oriented. 
    Tests and quizzes provide some information but doing more problem solving and project oriented work is also good. It is a place to start. Many release items from common core point the way but need more work. 
  • 04 Mar 2013 10:05 AM
    Reply # 1233144 on 1231998
    Deleted user
    Steve's examples are very interesting and clearly engaging for students. I have posed questions similar to the ice cream problem but have not had students take that next step and actually send letters to people making a claim like the other problems. Students do get more involved when there is a context. They are willing to do a little research or investigate how to solve a particular problem when there is a context. When I was teaching, I always enjoyed the classes when I was facilitating versus lecturing. I observed more students being involved in their learning of mathematics just as Steve suggested.
  • 04 Mar 2013 10:51 AM
    Reply # 1233174 on 1231998
    Maggie Griswold
    Check out the following that mirrors the classroom examples in the readings.
    • Article from NCTM News Brief. Classrooms in W.VA    http://wvgazette.com/News/201302270313
    • Also, Title IIB: Mathematics & Science Partnerships Projects have linked Middle Schools, High School math classes with Technical School faculty for hands-on projects. Meghan Southworth is the contact for the Title IIB Projects at the Maine Dept. of Ed.
    • STEM is also a great sources for math in context.
  • 04 Mar 2013 6:46 PM
    Reply # 1233654 on 1231998
    Evelyn Krahn
    I really enjoyed reading the glimpses presented in Chapter 5. The classroom activities provided examples of how mathematics fosters students ability to be a major part of their learning. I do believe students need to be given the opportunity to assume more responsibility for their learning. I have given my third grade students similar problems to solve. We have just begun our next math unit which is the data analysis of temperature. They are so engaged in recording the daily temperature throughout the day. The students have developed a list of questions that they would like to have answered after they have organized their data. Since, they have been organized into several small groups the questions may different. It is a work in progress and I am hoping the students may choose to also write a letter to a local weather forecaster and share their finds or questions. Nothing is more important than when a student takes ownership of their learning.

  • 05 Mar 2013 8:51 AM
    Reply # 1234106 on 1231998
    Pam Meader

    I loved the examples shared in this reading.  Prior to the Accuplacer influencing what I teach, I used to have my algebra students pick a math project to apply the various graphing and algebraic skills they had learned. I kept it pretty open ended with just certain parameters such as a poster presentation, modeling graphs, etc.  I have a full notebook of these wonderful projects and like the teachers described here, found the tasks to be rich, engaged the students, and truly made the learning of mathematics realistic.  But then the pressures of “knowing” what was on the Accuplacer and time constraints left no time for these projects.  I know in my heart, however, that applications are where the true learning of mathematics is.   

  • 06 Mar 2013 3:11 PM
    Reply # 1235423 on 1231998
    Heather Dority and Kim Smallidge
    Loved the examples in the book. We wish had the gumption to create such rich, engaging examples on a regular basis! In our 4th grade math class, we are currently working on fractions. The closest we have come to a rich, engaging problem is the following: Grady and Andrew were having a combined birthday party. Their moms each made a cake for the guests. In addition to the cake for the guests, Grady’s mom made him his own cake, and Andrew’s mom made him his own cake. Grady and Andrew were told that they could eat as much cake as they wanted! Grady asked his mom to cut his cake into eighths. Andrew asked his mom to cut his cake into twelfths. Grady ate 6/8 of his cake. Andrew ate 9/12 of his cake. Who ate more cake, Grady or Andrew? If their moms had made 1 cake, would there have been enough for both of them? Prove it!This led to some interesting responses. 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. We sometimes feel like these more encompassing problems leave the struggling learners behind. How can we balance conceptual understanding with the ability to get an accurate answer? It seems to be a double edged sword given the way students are currently assessed....how do you strike a balance?
  • 07 Mar 2013 4:30 PM
    Reply # 1236472 on 1231998



    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.

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