This week in math…
1. What did I learn?
I have learned that is it much more difficult to explain my thinking than it is to just take what I am told at face value and use it. Especially if I need to have someone besides myself understand what I’m explaining! It’s a skill that I struggle with, but I guess being aware that I am “explaining challenged” is the first step in learning to be better at it. Practice, practice, practice!
And that goes for my students, too. I really like the thought of having the students do as much of the “explaining” as possible, and only add in my own thinking if I absolutely need to. If I follow up with a question instead of an explanation, it serves as an even more effective way to get new ideas out on the table.
2. What are the implications for classroom practice?
One thing that I’ve started doing when I’m teaching a math lesson, or any other lesson for that matter, is to make sure that when I ask a question about how someone solved a particular problem that I get more than one DIFFERENT way of having something explained. Even though I might have followed along with the first explanation and it made perfect sense to me, I can’t assume that it makes perfect sense to everyone. If I can get the kids to explain their thinking in more than one way, I will have a better chance that most of them will have something “click” and make sense to them to.
Yesterday, I had the satisfaction of watching a student realize a misconception in his thinking in the middle of his explanation. He got this “OH” look on his face and then he excitedly backtracked and came up with the right answer. And I could also see a few kids near him get the same look on their faces and then smile. It’s not always that clear when it happens, but if I had been the one trying to “explain”, I bet it wouldn’t have happened nearly so effectively.
Friday, February 4, 2011
Friday, January 28, 2011
Working as a group successfully!
From my own past educational experience, I don’t remember having been exposed to successful group work such as we have been learning about and experiencing during this Teacher Certification program. Sure, we were sometimes put into groups and given a project to do, but there was never any structure to the task and it never failed that certain people who were the overachievers (I’m guilty, I know) would take over and others who were quieter would just go along with whatever the rest of the group was doing. How much were we really getting out of it?
The article by Rachel Lotan (2003) is one that I know I will be keeping close by when I begin my new career as a teacher. It’s a whole new way of thinking about collaborative learning that I am excited by! Designing Groupwork by Elizabeth Cohen has also been added to my pile of books that I am waiting to read (found 1994 edition on Abebooks for cheap!) The planning for these types of lessons may be more intensive, but I think it’s not only more interesting and educational for the students, but for me as well.
By using group worthy tasks, we are not only helping the students to learn whatever subject(s) they are learning, but they are also learning vital life-skills that I think are maybe even more important in many instances. Learning how to work well with others does not come naturally for many people, but if we are able to aid them in learning these skills, students will carry those tools away with them and use them for the rest of their lives…even if they no longer remember exactly what it was they were doing in that particular project. This is an admirable goal, even apart from the math, science and history that they will be putting into a useful context while in these groups.
Well done group work makes learning interesting and accessible to all regardless of abilities. Taking into consideration your student’s strengths and abilities by giving them roles that will help them to be successful contributors to the group allows them to feel that they are a successful part of the learning community. What a wonderful goal to strive for!
The article by Rachel Lotan (2003) is one that I know I will be keeping close by when I begin my new career as a teacher. It’s a whole new way of thinking about collaborative learning that I am excited by! Designing Groupwork by Elizabeth Cohen has also been added to my pile of books that I am waiting to read (found 1994 edition on Abebooks for cheap!) The planning for these types of lessons may be more intensive, but I think it’s not only more interesting and educational for the students, but for me as well.
By using group worthy tasks, we are not only helping the students to learn whatever subject(s) they are learning, but they are also learning vital life-skills that I think are maybe even more important in many instances. Learning how to work well with others does not come naturally for many people, but if we are able to aid them in learning these skills, students will carry those tools away with them and use them for the rest of their lives…even if they no longer remember exactly what it was they were doing in that particular project. This is an admirable goal, even apart from the math, science and history that they will be putting into a useful context while in these groups.
Well done group work makes learning interesting and accessible to all regardless of abilities. Taking into consideration your student’s strengths and abilities by giving them roles that will help them to be successful contributors to the group allows them to feel that they are a successful part of the learning community. What a wonderful goal to strive for!
Saturday, January 22, 2011
Literacy Project 1: Analysis of S.’s writing with a Lesson Plan.
Analysis
This Analysis was based on a writing sample that we obtained from S, who is a girl in the 4th grade at a local Elementary school. The sample we were given was chosen by the student as one that she was proud of and interested in having us read. It was a 6+ page, double spaced and handwritten, rough draft of a story in response to a class-wide writing prompt about waking up to find out that your pet could talk. We also had a spelling inventory that was administered on January 18, 2011.
Ownership and Meaning of the Pieces
Even though this was in response to a writing prompt, S. seemed very involved in the story that she was writing. She told us that the cat named “Fuzzball” was based on her own cats and some of the funny things that they have done in real life. She also incorporated people that she knows and even details from her own life. For example, she told us that she put canning jars, or “water jars” in her story because she had recently been at the house of a family friend and she was canning peaches and it interested S. While reading this sample, it was fairly obvious to us that S. went out of her way to try and bring excitement and personality into her story, and that she was enjoying telling us about the day that Fuzzball talked.
S. definitely sees herself as a writer. She told us that she writes for fun, at home and not necessarily just for school purposes. Last year she wrote a story called “the Wheelbarrow” as a Mother’s Day present for her Mother. She says that she gets her inspiration from her own life and from reading a lot of books. She seems to be a prolific reader who reads many types of genres, among which are historical fiction, contemporary fiction and fantasy stories.
The Six Traits
Ideas: S. had a lot of good ideas and drew from her real life knowledge and experience. She included a lot of details, but the purpose of some of the details was not always clear and they did not always help with supporting her ideas.
Organization: Organization is one area that I believe that S. could use further guidance and support. The introduction to her story was the most thought-out and cohesive part of her story. It began very strong, with purpose and was very interesting. But after the first page and the introduction of the talking cat, her story continued on as a “bed to bed” story where she woke up and the day just happened as one thing after another without a real purpose or drive to the story. For example, she introduced the arrival of her friend Abby for a play date, but this whole episode in the story had no relation to the cat who talks, nor was it ever developed. It seemed to be there for no purpose. After the first page, the story is just a serious of random events, none of which help to forward a story, despite the use of energetic language and very good descriptors. The story ends abruptly, leaving us with many questions and no sense of cohesion.
Voice: S. has a very good sense of how to relate to her reader. She used phrases that conveyed interest and excitement. The entire piece reads as if she were energetically telling us a story, and she uses phrases such as “Much to my surprise…”, “Eagerly she blurted…” and “I had no clue what…” to draw the reader in. The narrative was personal and engaging, including personal details and an attempt at dialogue.
Word Choice: While reading this rough draft, it was clear that S. was making an effort to use words that were interesting and conveyed a mental picture. She would self –correct; crossing out words as she went and writing more interesting word possibilities above them. For example, at one point in the rough draft she changed “quiet knock” to “muted knock”. She also used many detailed descriptions within her story that created mental images, such as “fuzzy pink pillow”, “thin high heeled black shoes”, and “Abby started dancing around like a person in ballet”. I was also struck by her use of lively verbs, such as “blurted” and “plugged”. At a few spots in the piece it noticeable that she had discovered some of these more interesting phrases and she overused them, although this is something that might possibly be corrected in the editing stages.
Sentence Fluency: S’s sentences vary in length and structure and have a good feel to them. There was not a lot of repetitive sentence structure that detracted from the author’s voice, and she did a very good job of varying the beginnings of her sentences. There was a rhythm to her words, as if she were speaking them.
Conventions: Even though this was a first draft, S’s conventions were very good. She will need to revisit her paragraphing, although this might be corrected when an attempt is made to help her with the organization of her ideas and story. She self-edits as she writes. At several places she would cross out a verb and correct the tense above it. Her capitalization and punctuation is accurate, though she will need help in properly formatting the dialogue in her story.
Spelling
S. made very few spelling errors in her first draft of this story, and many that she made she self-corrected as she went by crossing out and putting the correct spelling above. (staires-stairs, ansering-answering, and comepletely-completely). At one point in the story she used the world “cubbord”, tried to self-correct several times, and then went to get help because it was a word that she didn’t know. The correct spelling was written by the teacher in green pen. When we gave her the spelling inventory, she spelled all the words correctly except cellar (celler), civilized (civiliazed) and opposition (oppisition). From the words in these two examples, I believe that S’s spelling level is most likely somewhere around early to middle derivational relations (Bear, et al, 2004). S. might benefit from a review of word endings and suffixes, and help with identifying base words and their relationship to their derivatives.
Lesson Plan
Objective:
To help the student determine the message that she wants to convey in her story and narrow down her subject matter.
To help the student use a graphic organizer to organize her ideas, resulting in a more cohesive story containing both an introduction and a conclusion.
Standards:
EALR 1: The student understands and uses a writing process.
1.1 Prewrites to generate ideas and plan writing.
EALR 3. The student writes clearly and effectively.
3.1 Develops ideas and organizes writing.
3.1.1 Analyzes ideas, selects a narrow topic, and elaborates using specific details and/or examples.
3.1.2 Organizes writing using a logical organizational structure.
Materials: First draft of story, pencils, paper, post-its if desired for idea web.
Instructional Strategies: This lesson will take place as a one-to-one writing conference.
First, I will compliment her on her very good introduction, use of lively verbs, good descriptors and on some of the good idea that she has in her first draft. I will then transition into expressing my thoughts on the apparent randomness of the events in the story and how I was confused by a few things, such as the appearance of her friend for a play date. Did this have something to do with the talking cat, which was the main focus of the story? I will also point out that the lack of a conclusion left me with many questions and a feeling of wanting to know more about her interesting story.
I will help S. to use an idea web to organize her ideas into a cohesive story.
I will help her to focus on what are the main “happenings” of her story that she wants to tell her reader. Do these all relate to the main subject of her story?
I will remind her of how an idea web works, using her rough draft as we go through the steps. What should go in the large center bubble? The main idea, etc… What should the other main ideas of the narrative be? What details did you write about and where should they be on this graphic organizer?
What doesn’t need to be included to support your story, what is important to you? Is there a beginning, middle and an end?
After modeling how this is done and I am sure that she is confident in what she needs to do, I will send S. to her desk to work on her idea organization some more, emphasizing that what she wrote was a very good first draft, but this will just help us to make it a better flowing story.
After she has gotten to a point where she feels comfortable with her ideas, I will have another writing conference with her to see how she is progressing in rearranging her ideas into a cohesive story, emphasizing a beginning, middle and end.
Assessment: The teacher will check the student’s revised draft for a beginning, middle and an end. She will also be looking for the continued presence of good word choices and voice in the new draft.
This Analysis was based on a writing sample that we obtained from S, who is a girl in the 4th grade at a local Elementary school. The sample we were given was chosen by the student as one that she was proud of and interested in having us read. It was a 6+ page, double spaced and handwritten, rough draft of a story in response to a class-wide writing prompt about waking up to find out that your pet could talk. We also had a spelling inventory that was administered on January 18, 2011.
Ownership and Meaning of the Pieces
Even though this was in response to a writing prompt, S. seemed very involved in the story that she was writing. She told us that the cat named “Fuzzball” was based on her own cats and some of the funny things that they have done in real life. She also incorporated people that she knows and even details from her own life. For example, she told us that she put canning jars, or “water jars” in her story because she had recently been at the house of a family friend and she was canning peaches and it interested S. While reading this sample, it was fairly obvious to us that S. went out of her way to try and bring excitement and personality into her story, and that she was enjoying telling us about the day that Fuzzball talked.
S. definitely sees herself as a writer. She told us that she writes for fun, at home and not necessarily just for school purposes. Last year she wrote a story called “the Wheelbarrow” as a Mother’s Day present for her Mother. She says that she gets her inspiration from her own life and from reading a lot of books. She seems to be a prolific reader who reads many types of genres, among which are historical fiction, contemporary fiction and fantasy stories.
The Six Traits
Ideas: S. had a lot of good ideas and drew from her real life knowledge and experience. She included a lot of details, but the purpose of some of the details was not always clear and they did not always help with supporting her ideas.
Organization: Organization is one area that I believe that S. could use further guidance and support. The introduction to her story was the most thought-out and cohesive part of her story. It began very strong, with purpose and was very interesting. But after the first page and the introduction of the talking cat, her story continued on as a “bed to bed” story where she woke up and the day just happened as one thing after another without a real purpose or drive to the story. For example, she introduced the arrival of her friend Abby for a play date, but this whole episode in the story had no relation to the cat who talks, nor was it ever developed. It seemed to be there for no purpose. After the first page, the story is just a serious of random events, none of which help to forward a story, despite the use of energetic language and very good descriptors. The story ends abruptly, leaving us with many questions and no sense of cohesion.
Voice: S. has a very good sense of how to relate to her reader. She used phrases that conveyed interest and excitement. The entire piece reads as if she were energetically telling us a story, and she uses phrases such as “Much to my surprise…”, “Eagerly she blurted…” and “I had no clue what…” to draw the reader in. The narrative was personal and engaging, including personal details and an attempt at dialogue.
Word Choice: While reading this rough draft, it was clear that S. was making an effort to use words that were interesting and conveyed a mental picture. She would self –correct; crossing out words as she went and writing more interesting word possibilities above them. For example, at one point in the rough draft she changed “quiet knock” to “muted knock”. She also used many detailed descriptions within her story that created mental images, such as “fuzzy pink pillow”, “thin high heeled black shoes”, and “Abby started dancing around like a person in ballet”. I was also struck by her use of lively verbs, such as “blurted” and “plugged”. At a few spots in the piece it noticeable that she had discovered some of these more interesting phrases and she overused them, although this is something that might possibly be corrected in the editing stages.
Sentence Fluency: S’s sentences vary in length and structure and have a good feel to them. There was not a lot of repetitive sentence structure that detracted from the author’s voice, and she did a very good job of varying the beginnings of her sentences. There was a rhythm to her words, as if she were speaking them.
Conventions: Even though this was a first draft, S’s conventions were very good. She will need to revisit her paragraphing, although this might be corrected when an attempt is made to help her with the organization of her ideas and story. She self-edits as she writes. At several places she would cross out a verb and correct the tense above it. Her capitalization and punctuation is accurate, though she will need help in properly formatting the dialogue in her story.
Spelling
S. made very few spelling errors in her first draft of this story, and many that she made she self-corrected as she went by crossing out and putting the correct spelling above. (staires-stairs, ansering-answering, and comepletely-completely). At one point in the story she used the world “cubbord”, tried to self-correct several times, and then went to get help because it was a word that she didn’t know. The correct spelling was written by the teacher in green pen. When we gave her the spelling inventory, she spelled all the words correctly except cellar (celler), civilized (civiliazed) and opposition (oppisition). From the words in these two examples, I believe that S’s spelling level is most likely somewhere around early to middle derivational relations (Bear, et al, 2004). S. might benefit from a review of word endings and suffixes, and help with identifying base words and their relationship to their derivatives.
Lesson Plan
Objective:
To help the student determine the message that she wants to convey in her story and narrow down her subject matter.
To help the student use a graphic organizer to organize her ideas, resulting in a more cohesive story containing both an introduction and a conclusion.
Standards:
EALR 1: The student understands and uses a writing process.
1.1 Prewrites to generate ideas and plan writing.
EALR 3. The student writes clearly and effectively.
3.1 Develops ideas and organizes writing.
3.1.1 Analyzes ideas, selects a narrow topic, and elaborates using specific details and/or examples.
3.1.2 Organizes writing using a logical organizational structure.
Materials: First draft of story, pencils, paper, post-its if desired for idea web.
Instructional Strategies: This lesson will take place as a one-to-one writing conference.
First, I will compliment her on her very good introduction, use of lively verbs, good descriptors and on some of the good idea that she has in her first draft. I will then transition into expressing my thoughts on the apparent randomness of the events in the story and how I was confused by a few things, such as the appearance of her friend for a play date. Did this have something to do with the talking cat, which was the main focus of the story? I will also point out that the lack of a conclusion left me with many questions and a feeling of wanting to know more about her interesting story.
I will help S. to use an idea web to organize her ideas into a cohesive story.
I will help her to focus on what are the main “happenings” of her story that she wants to tell her reader. Do these all relate to the main subject of her story?
I will remind her of how an idea web works, using her rough draft as we go through the steps. What should go in the large center bubble? The main idea, etc… What should the other main ideas of the narrative be? What details did you write about and where should they be on this graphic organizer?
What doesn’t need to be included to support your story, what is important to you? Is there a beginning, middle and an end?
After modeling how this is done and I am sure that she is confident in what she needs to do, I will send S. to her desk to work on her idea organization some more, emphasizing that what she wrote was a very good first draft, but this will just help us to make it a better flowing story.
After she has gotten to a point where she feels comfortable with her ideas, I will have another writing conference with her to see how she is progressing in rearranging her ideas into a cohesive story, emphasizing a beginning, middle and end.
Assessment: The teacher will check the student’s revised draft for a beginning, middle and an end. She will also be looking for the continued presence of good word choices and voice in the new draft.
Monday, January 17, 2011
Why using an IPod Touch to differentiate learning would help my students…
My main placement is in a “highly capable” classroom. These students, as well as many others, would benefit greatly from having the ease of access to information that the Touch would give them. Currently, they are working on 2 different assignments that they have to research and put together using computer generated end projects. If they don’t have to wait for the use of a computer, a lot more can be accomplished during the school day. This would also help for those instances where the student does not have computer access at home to do this type of research.
It is also a great gift to a teacher who has many of these "highly capable" students so that they could make use of the large number of educational apps, available for every subject, as extensions of their learning while they are waiting for others to finish their work. The teacher could tailor the list of possible activities for each student according to what they need to work on at that time.
I have one student in particular who has a difficult time getting ideas down onto paper. He is VERY verbally talented with an amazing grasp of vocabulary and he is an out of the box thinker with fantastic ideas if you verbally ask him questions. But when he is confronted with a blank piece of paper, he can’t start. If he had the ability to go somewhere and record what he says in response to the prompt given verbally, and then he could listen to what he said and start to write it down on paper, it might get him past that initial first step of brainstorming freeze.
Our school is fortunate to be taking place in pilot program for using netbooks in the classroom. I have seen firsthand that even the mention of using technology gets these kids excited about even the smallest task. Enthusiasm and attitude can play a major role in how quickly and willingly students will advance their learning. If we are able to add this relatively inexpensive and easily accessible form of technology to our classroom activities, the level of excitement that could be brought to everyday activities, such as literacy centers and learning math facts, could only help these students advance. The tech can be somewhat distracting at times and the kids tend to lose focus on other things that they need to do instead, but with proper classroom management this can be minimized and possibly be used in a positive way.
It is also a great gift to a teacher who has many of these "highly capable" students so that they could make use of the large number of educational apps, available for every subject, as extensions of their learning while they are waiting for others to finish their work. The teacher could tailor the list of possible activities for each student according to what they need to work on at that time.
I have one student in particular who has a difficult time getting ideas down onto paper. He is VERY verbally talented with an amazing grasp of vocabulary and he is an out of the box thinker with fantastic ideas if you verbally ask him questions. But when he is confronted with a blank piece of paper, he can’t start. If he had the ability to go somewhere and record what he says in response to the prompt given verbally, and then he could listen to what he said and start to write it down on paper, it might get him past that initial first step of brainstorming freeze.
Our school is fortunate to be taking place in pilot program for using netbooks in the classroom. I have seen firsthand that even the mention of using technology gets these kids excited about even the smallest task. Enthusiasm and attitude can play a major role in how quickly and willingly students will advance their learning. If we are able to add this relatively inexpensive and easily accessible form of technology to our classroom activities, the level of excitement that could be brought to everyday activities, such as literacy centers and learning math facts, could only help these students advance. The tech can be somewhat distracting at times and the kids tend to lose focus on other things that they need to do instead, but with proper classroom management this can be minimized and possibly be used in a positive way.
Friday, January 14, 2011
Algebra Tiles...what else don't I know about?
This week in class I was completely amazed by the Algebra tiles. I had never seen them before, and I can only speculate as to how my experience with Algebra in the past might have been influenced it they had been offered to me as an option. I remember loving math up until Algebra 2, which is when it all became a struggle and completely frustrating to me. Unfortunately, I had a series of teachers over the course of that year, none of which went out of their way to explain things in different ways. They all took the “memorize the formula or rule, just do it and don’t ask why” approach to teaching math. This made it nearly impossible for me to come up to speed when I hit Calculus. If even one of them had tried to explain it in a different way, such as using the Algebra tiles, might it have made that little bit of difference that I needed? If those teachers had had the training and experience to use these other manipulatives, would they have understood the math better themselves, allowing them to in turn better explain it to me?
I know I will never teach upper level Algebra, but this line of thinking helps me to realize that I will need to be constantly looking for different ways to think about the math that I am teaching. I need to listen to my students and how they are thinking and remember what works for some may not always work for everyone. And I would like to think that unlike those “old school” math teachers that I had, I will do my best to try and figure out what I can do to help that kid who is lost “get it”. Because I believe that all students can understand, it just may not take place at the same rate or in the same way as everyone else. By giving the students multiple opportunities in different formats, and allowing them to explain their thinking to their classmates and in turn listen to how others think, they will have so many more opportunities to solidify their mathematical understanding.
I know I will never teach upper level Algebra, but this line of thinking helps me to realize that I will need to be constantly looking for different ways to think about the math that I am teaching. I need to listen to my students and how they are thinking and remember what works for some may not always work for everyone. And I would like to think that unlike those “old school” math teachers that I had, I will do my best to try and figure out what I can do to help that kid who is lost “get it”. Because I believe that all students can understand, it just may not take place at the same rate or in the same way as everyone else. By giving the students multiple opportunities in different formats, and allowing them to explain their thinking to their classmates and in turn listen to how others think, they will have so many more opportunities to solidify their mathematical understanding.
Saturday, January 8, 2011
My latest time consuming project
In December, I went to the Scholastic Warehouse Book Sale. It was an amazing event to experience, but a bit overwhelming. I found that I was constantly saying to myself "Do I have that book already? I can't remember...". The same thing happens when I wander into Half Price Books or any other place with books that are "great deals". Over the years I have accumulated a wide variety of books that live upstairs on a number of bookshelves, but I have no idea what exactly IS there. Now that I am shopping with some future classroom in mind, it's become more important to me to figure out what I already have before I start spending money.
So an organization idea was born. I don't have an IPhone, and until this week I didn't have access to an IPod Touch. I'm sure that there might be a comparable app that can be used to do this same type of thing. I'll leave that to someone else to figure out since I've already embarked on this adventure with the technology that I do possess and will continue to use after our Certification Program is completed. This is time consuming as it is, without trying to use two different interfaces!!
I have a Windows 7 phone (Samsung Focus), which has the capability of linking to my Windows Live Account.
It serves a similar function as Google docs. I am able to create documents, Excel spread sheets, PowerPoint presentations, store photographs and more, virtually, to be accessed from other locations, just like Google Docs. I decided to set up an Excel Spreadsheet containing an organized list of what books I currently have at home, so that if I am out and come across a "great deal" unexpectedly, I can use my phone to quickly check to see if it's something that I already have, or look at my wish list for ideas of what I need.
I was able to set up categories such as Picture book, Easy Reader, and Non-fiction, and alphabetize (by title) as I went. It will take me quite a while to enter my library into the spreadsheet and I will probably be working on it off and on for the next few months as time permits. But once it's there, I will just add titles as I buy and keep going from there.
After entering quite a few titles, I stopped to check to see how easy it would be to find a particular title. I searched for the word "Fancy", wanting to pull up which Fancy Nancy books I have and it took me immediately to the entry with a link to the cell in the spreadsheet that I could click to go to.
Wednesday, January 5, 2011
There in not just one right answer!
It was fascinating to see how many different ways we all looked at the same problem. It was almost as if we were doing the same jigsaw puzzle but some of us started with the edges, while others started in the middle, and still others started sorting by color. We all got there in the end, but we all went about it in very different ways that made sense to us personally.
I found myself wondering why I instinctively headed toward one method over another, while the person next to me always seemed to choose a clearly different route. I was very fortunate to sit next to someone who thought about those math problems in a different way than I did. It made me realize that I have been too dependent on the “only one right answer” way of learning math. Everyone should do it the same way I do, right? Now I see that is not only incorrect, but a very limiting and boring way of going about learning. I really enjoyed seeing what other people did! And every time a new way was introduced, I found myself saying “wow, that’s cool, and it DOES make sense to me. I didn’t think about it like that.”
After discussing the first problem, I solved the second one by going with my first instinct. But this time after I finished, I caught myself looking over my neighbor’s shoulder to see what she was doing. Not to cheat or in search of some validation of my answer, but out of a wonderful sense of curiosity.
If we were able to get our students to foster this sense of curiosity, what a great learning environment we could create! Not to mention how much it would help those students who just don’t solve things in the same way as the teacher, but can maybe glean some understanding when another student explains it to them in a different way! And once a student can understand a concept in one way, they are much more likely to be able to proceed onto understanding it from different angles, increasing their overall understanding and knowledge base for future learning.
Some people just NEED to sort out the colors first, while I always need to separate out the edges. There is no one “correct” way of getting the puzzle done. And it’s very important to always keep that in mind!
I found myself wondering why I instinctively headed toward one method over another, while the person next to me always seemed to choose a clearly different route. I was very fortunate to sit next to someone who thought about those math problems in a different way than I did. It made me realize that I have been too dependent on the “only one right answer” way of learning math. Everyone should do it the same way I do, right? Now I see that is not only incorrect, but a very limiting and boring way of going about learning. I really enjoyed seeing what other people did! And every time a new way was introduced, I found myself saying “wow, that’s cool, and it DOES make sense to me. I didn’t think about it like that.”
After discussing the first problem, I solved the second one by going with my first instinct. But this time after I finished, I caught myself looking over my neighbor’s shoulder to see what she was doing. Not to cheat or in search of some validation of my answer, but out of a wonderful sense of curiosity.
If we were able to get our students to foster this sense of curiosity, what a great learning environment we could create! Not to mention how much it would help those students who just don’t solve things in the same way as the teacher, but can maybe glean some understanding when another student explains it to them in a different way! And once a student can understand a concept in one way, they are much more likely to be able to proceed onto understanding it from different angles, increasing their overall understanding and knowledge base for future learning.
Some people just NEED to sort out the colors first, while I always need to separate out the edges. There is no one “correct” way of getting the puzzle done. And it’s very important to always keep that in mind!
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