Math Blog Final Reflection

All quarter we have learned about different manipulatives to use in our classroom.  Though intended for upper grades (5-8), these ideas for teaching math can be used in any grades (or variations of the ones shown during class).  Using these tools in the classroom will help students understand the “why” and “how” of concepts, which will help them find the importance, remember, and use them.  If not using manipulatives for whole class discussion, they can easily be used to differentiate instruction for students that are need additional practice, or for enhancement for students that need additional challenge.

I have already begun to use random manipulates in the classroom to demonstrate concepts, specifically on the lesson about fractions of different sized wholes.  In this lesson, I wanted students to understand that having the same fraction size, but a different sized whole, will not be equal.  To demonstrate this to my third grade class, I used two methods to demonstrate this concept, first with three different sized bowls and told two people they could each have half a bowl of pretend ice cream.  I then posed the question of if that was fair, in which students replied no.  Then, I said, “but they each get half a bowl” and students showed, using the bowl, how the halves of different sized bowls didn’t mean the same amount.  In the second situation, I used clear Starbucks cups and filled each size half way.  I then had students pour their halves into clear measuring cups to see that the halves were definitely different amounts.  Though this was not a manipulative like the ones that Robin had shown us, it was an object that students could use to see the concept and find understanding with (opposed to the books demonstrations).  I followed up with having the students create their own problems to assess their understanding and application of this concept.

Now having used manipulatives myself and seeing them used in the classroom, I can see that the use of manipulatives is helpful in teaching math concepts. They can teach the same concepts that the curriculum book wants them to learn, but even in less time and with more impact on overall learning.  Knowing this, I will be more aware of how I will teach math in the future. 

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What did I learn?

During class we had many discussions about various aspects of teaching math.  Of the many things that we discussed was the idea of begin frugal in the classroom and doing investigative work to find classroom resources that will help enhance students’ math experience.  For examples, Robin told us about the projectors that she was able to have when the school switched to doc camera and the computers she was able to obtain from small talk with someone whose company was updating their computers.  While this is good to know for new teachers, it is something that all teachers need to consider, not just math teachers. 

Another thing that we talked about was the mathematical teaching cycle:

All lessons need 4 things (Mathematical teaching cycle): 1. What do they know? (Rationale) 2. What do I want them to know?  What kind of math do I want them to know? (Objective) 3. How do I get them there? (Lesson)  4. Did they get there?  (Assessment)

Though we had covered the major concepts in other programs within the program, it was nice to have such a concise explanation of things that teachers need to have in mind.  At this point in the program, it’s nice to know that as long as we know these major things, we do not have to write out the long lesson plans for every single lesson that we teach, saving a lot of time and energy.

In addition to these things, I learned about tinkerplots and wolfram alpha websites.  Tinkerplots would be especially helpful for my main placement, since students are beginning to work with data.

What do I still have questions about?

How can we, as teachers, have the influence on students that math is important and being good at math isn’t a “stigma”, when parents may be influencing students the other way?  Robin had mentioned that some cultures don’t value girls being successful in math, and believe that males should be the ones that we give focus to, but how do we instill the values of math in every student?  Could we be angering parents with our intentions by doing so?

What are the implications for classroom practice?

Of today’s class, I will most likely use the mathematical teaching cycle as a short lesson when planning all of my lessons, not just math.  This is a quick, easy, to the point tool to use to make sure that everything is planned and accounted for.

Another thing I will use with my class is to use tinkerplots, and other tools, for students that are struggling to understand concepts.  This will be a way to differentiate instruction.

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What did I learn?

We began this class by completing an activity where we were fitting quadrilaterals into a shape.  This activity made me think about the various ways that different quadrilaterals can look and be altered to look like each other.  It was only with prior knowledge of quadrilaterals that this activity would be easy to complete, but in a classroom this type of discovery could help students remember the various properties of quadrilaterals.

What do I still have questions about?

What other websites have similar manipulates?  Are there physical manipulatives that would produce similar lessons?  I can think of the peg board that a use rubber bands or string, but that would be difficult to produce the same results.

What are the implications for classroom practice?

I have to admit that I had a tendency to playing with the online manipulative, instead of listening to the teacher, so I know that this is something that would have to be addressed in the classroom.  I would need to set clear expectations, clear time frames, or group work to address this.  I’m sure this is something that will be a problem no matter what, since students tend to be so fascinated with the use of technology that they just want to “play” (especially in the younger grades).

End of quarter tech update

All quarter I’ve been trying to figure out how to use an iPod Touch in the classroom, when there is only 1 iPod and many more students.  While doing so, I’ve found that my main use for this technology has been using it to record interviews, so I can be attentive to the student instead of busy writing notes.  I have also used the voice recording app to record conversations, mainly about behavioral issues, that I could not attend in person.  In this way, the iPod Touch has been very helpful.

Another similar use for the iPod would be to record lesson, so that absent students have access to the lesson in other forms and they listen to it once they return.  Dragon Dictation would be a good app for this, as well as giving students access to lessons when more visual methods of teaching were presented.

In literacy, or for ELL students, a similar tool would be helpful for students that have a hard time reading, so they could listen to a story to pick up the understanding by using visualizing strategies for comprehension.  Though books should not be completely abandoned with this approach, the student could use the book to reference either during or after listening to the story aloud.

There are many apps that are available for students to visualize mathematical concepts, similar to the ones that Robin showed us for the intermediate and upper elementary grades.  These tools give students access to manipulatives and can help students that are “visual” learners.  Additionally, mathematical apps can help students practice mathematical concepts that need the extra practice.

Students today seem to be over obsessed with technology and video games, and introducing technology they are comfortable with accesses their interests and engages them to the point that they may not realize they are learning.  This became evident during fall quarter while interviewing a first grade student about math.  We approached the math problems using video game characters in story problems.  After the interview we thanked him for working with us on math and he replied with, “we weren’t talking about math.  We were talking about video games.”

Though I have used (and found uses) for an iPod Touch in the classroom, I still struggle with the question: When I use the iPod with use a few students, how can I make it seem that I am being fair to the rest, since the others aren’t necessarily using the technology?  The students in my class seem to focus on being treated fairly and it seems like this would be an issue to the students.