Last week I learned about two more ways to engage students in math. We played with a couple of very neat math utilities: Fathom and Geometer's Sketchpad. What great classroom resources these would be! Geometer's Sketchpad looks like a particularly versatile tool that, according to its website, can help kids learn everything from geometry and algebra to proofs. For geometry, creating geometric shapes to fit over a clown's features - using only a limited number of available shapes - was a challenging exercise even for an adult! It really forced you to remember and apply your knowledge of the properties of geometric shapes.
Two questions I have are: 1) in what way can Geometer's Sketchpad facilitate algebra learning and 2) how much does it cost (I think this was mentioned, but I've forgotten). The next time I have free time on campus, I think I'll try and explore ways in which Geometer's Sketchpad can help students learn or practice algebra. If the algebra functions are as engrossing as the geometry exercise was, I think they'd be very useful in a middle level math class.
One implication for classroom practice is how to best utilize Geometer's Sketchpad when you only have a couple computers available for classroom use. Perhaps it would be best utilized as enrichment or remediation tool in that case - although if the software has a high pricetag, you'd probably want every student to have access.
Friday, February 18, 2011
Sunday, February 13, 2011
tangrams
This past week we had fun with yet another completely engaging math lesson - firing cotton ball "frogs" from paper clip launchers, then tracking the absolute and linear distances they traveled. While this way of teaching about distance was both fun and new to me, what I really appreciated about last week's class was learning how to use tangrams. I'd never worked with them before and knew nothing about them. In class, we used a set of tangrams to create a giraffe figure, then tried to construct a giraffe twice the size with multiple sets. This was not easy!
As I mentioned above, I'd never used tangrams before this class, and one question I have is about other classroom applications. They seem to do a good job of fostering spatial thinking. Do they have any applications at the 4th grade level? I'm wondering about a use that might help my main placement kids remember geometric shapes and their properties. Since the tangrams are geometric shapes they've studied, it might be a useful way to use them in my classroom.
The implications for classroom practice that I see are more engaging ways to get kids to connect to math. The exercise of doubling the size of the giraffe was very challenging -- my group never got there, in fact -- but was also very engrossing, no one wanted to stop trying!
As I mentioned above, I'd never used tangrams before this class, and one question I have is about other classroom applications. They seem to do a good job of fostering spatial thinking. Do they have any applications at the 4th grade level? I'm wondering about a use that might help my main placement kids remember geometric shapes and their properties. Since the tangrams are geometric shapes they've studied, it might be a useful way to use them in my classroom.
The implications for classroom practice that I see are more engaging ways to get kids to connect to math. The exercise of doubling the size of the giraffe was very challenging -- my group never got there, in fact -- but was also very engrossing, no one wanted to stop trying!
Sunday, February 6, 2011
moving from assessment to instruction
Over the past few weeks I've learned a bit about my buddy's needs, abilities, and interests. My buddy, whom I'll continue to call Katie, seems to genuinely enjoy reading. She particularly enjoys her reading textbook. During one of our informal reading conferences she neatly summarized what had been happening in one of the stories, highlighting both explicit and implicit details. For instance, she inferred why the main character, Maria Isabel Salazar Lopez, disliked being called Mary Lopez, a conclusion supported, but not directly stated, by the story. Katie's comprehension of the two assessment readings, Amelia Earhart and Early Railroads, was fairly good. She did miss some explicit supporting details, such as the sentence that told the reader who Tom Thumb was in the Early Railroads piece. This affected her comprehension of the analogy being made between the engine and Tom Thumb, and she stumbled on the comprehension questions that dealt with that analogy.
Additionally, Katie's reading of the assessment pieces was slower than average. She read Early Railroads at 93 words per minute - nearly 20 words per minute slower than an "average" 4th grade peer. In all her reading aloud for me, however, I noted a particular difficulty with names that really slows her down. Katie had a bit of trouble with the name Tom Thumb in Early Railroads and it almost felt like the name was a bit of a tongue twister for her. It took her a while to move on with the reading. At other times, though, Katie will elide an unknown word. That said, Katie generally reads in larger, meaningful chunks, until she gets to a section that trips her up. Occasionally she missed punctuation, too. Katie had 12 miscues during her reading of Early Railroads, which indicates that the text is at instructional level for her.
Given the results of the reading assessments and my findings during our informal reading conferences, I would say that Katie is at level 3 on the NAEP Oral Reading Fluency Scale. Katie sometimes read with meaning, but at other times read inexpressively and missed punctuation and phrasing. Although she sometimes read larger phrase groups with correct expression for long stretches, these stretches were punctuated by shorter word groupings and groupings that missed words and/or punctuation. She might be just a bit higher than a 3 with an instructional text.
Overall, I think Katie needs work on fluency. While fairly good, her comprehension would improve if she had better fluency. This week, I plan to have Katie read the level 3 texts.
Additionally, Katie's reading of the assessment pieces was slower than average. She read Early Railroads at 93 words per minute - nearly 20 words per minute slower than an "average" 4th grade peer. In all her reading aloud for me, however, I noted a particular difficulty with names that really slows her down. Katie had a bit of trouble with the name Tom Thumb in Early Railroads and it almost felt like the name was a bit of a tongue twister for her. It took her a while to move on with the reading. At other times, though, Katie will elide an unknown word. That said, Katie generally reads in larger, meaningful chunks, until she gets to a section that trips her up. Occasionally she missed punctuation, too. Katie had 12 miscues during her reading of Early Railroads, which indicates that the text is at instructional level for her.
Given the results of the reading assessments and my findings during our informal reading conferences, I would say that Katie is at level 3 on the NAEP Oral Reading Fluency Scale. Katie sometimes read with meaning, but at other times read inexpressively and missed punctuation and phrasing. Although she sometimes read larger phrase groups with correct expression for long stretches, these stretches were punctuated by shorter word groupings and groupings that missed words and/or punctuation. She might be just a bit higher than a 3 with an instructional text.
Overall, I think Katie needs work on fluency. While fairly good, her comprehension would improve if she had better fluency. This week, I plan to have Katie read the level 3 texts.
Saturday, February 5, 2011
current thoughts: differentiating instruction with an ipod touch
I'll confess to finding some uses for an Ipod touch in the classroom over the past few weeks. I particularly like its usefulness for recording student interviews and assessments. I've also run across some apps I really like which might have value in the classroom. One app, Logic Box, could augment mathematics instruction by fostering spatial and geometric thinking. Another app, NASA looks like an excellent supplement to an astronomy unit. I like the Whiteboard Lite app, too, for its potential to eliminate noxious dry erase fumes from the classroom - although the iPod screen is a bit small for any detail.
As far as differentiating instruction with an iPod goes, though, my opinion hasn't changed much. In fact, a few things that have happened in my classroom recently have further convinced me that our efforts are better spent - at least in my school - ensuring that all of our kids have equal access to a quality education before springing for dozens of iPods. If we were reasonably close to that goal, I'd be open to exploring iPod touches for instructional use. One certainty is that kids would love being able to use an iPod touch in school!
As far as differentiating instruction with an iPod goes, though, my opinion hasn't changed much. In fact, a few things that have happened in my classroom recently have further convinced me that our efforts are better spent - at least in my school - ensuring that all of our kids have equal access to a quality education before springing for dozens of iPods. If we were reasonably close to that goal, I'd be open to exploring iPod touches for instructional use. One certainty is that kids would love being able to use an iPod touch in school!
paper folding
Last week in math class I learned that paper folding is very mathematical! It was really interesting to see how the simple act of folding an origami box uncovered so many mathematical challenges. It was a truly rigorous way to explore geometry and proofs - I personally had difficulty expressing the reasons why I knew a given shape was what it was! Particularly challenging was finding a way to articulating why one folded line was parallel to another.
One question I have is how best to elicit the proofs. Is it best to have the whole class work independently and volunteer answers? Or would it be better to have students work in teams or groups? I'm personally inclined to say groups, because I know I could have used someone to bounce ideas off of when we did this in class.
I think this is a great way to explore geometry and practice articulating mathematical proofs in the classroom. While we engaged in this activity as a way to explore and provide proofs, I'm personally planning to adapt this activity into a lesson for 4th graders. My kids had some trouble with geometric shapes when they were learning about them last fall. I think (and my master teacher agrees) that examining geometric shapes while folding an origami box will help them better understand and remember what they learned. It helps that most of my class is rather origami obsessed, too!
One question I have is how best to elicit the proofs. Is it best to have the whole class work independently and volunteer answers? Or would it be better to have students work in teams or groups? I'm personally inclined to say groups, because I know I could have used someone to bounce ideas off of when we did this in class.
I think this is a great way to explore geometry and practice articulating mathematical proofs in the classroom. While we engaged in this activity as a way to explore and provide proofs, I'm personally planning to adapt this activity into a lesson for 4th graders. My kids had some trouble with geometric shapes when they were learning about them last fall. I think (and my master teacher agrees) that examining geometric shapes while folding an origami box will help them better understand and remember what they learned. It helps that most of my class is rather origami obsessed, too!
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