Wow! This weeks readings were a bit intense. In our CGI book, I learned a lot about different types on math problems. I never thought that there was so much reasoning and processing behind the problems. Aside from the effort put into solving them, it takes a lot for teachers to choose the best work for their students. There is a lot of time that goes into pre-assessments, monitoring, and post-assessments. All three, however, are very important when it comes to strategically identifying the best problems for students.
In my placement, the class textbook is Harcourt. However, my mentor teacher said that she RARELY uses anything from it. She said that she creates and designs the majority of the worksheets, homework, and other relative assignments that she gives out. When I asked why not, she said that she thought it was the best choice for her students. She said that she has students that are not, yet, at the level of the text and she has students that are beyond it. I think that creating your own worksheets and assignments is a great idea, but I think that teachers should still use the textbooks. I say that because the textbooks are leveled, so they will have a better gauge to use with their students.
In addition to the CGI book, I also really liked the Cantlon article. My favorite part about it was when it mentioned teacher journals. Other than blogging and reporting-back in meetings and conferences, I have never really known for any teacher to keep a journal about their day-to-day teaching experiences. I think that it is an awesome idea, and I am inspired to keep one of my own. However, I feel that I will lose interest in it once I begin teaching for an extended amount of time, because it will get to the point where I will not have enough time to do it anymore.
I think that our readings have greatly challenged my perception of math teaching. After taking courses like MTH 201 and MTH 202, I was confident about math enough to teach it to younger grades. The only issue I had with them was that it felt like they taught math pedagogy as more of a "Follow the textbook" method. From what I have physically seen in field, and read in our articles and texts so far, I am understanding that it takes more to teach math than being able to solve an equation and explain formulas. For example, I never saw long division problems as being multi-operational problems. I knew that there were several steps, but I just never saw them that way. I am looking forward to the rest of this semester and, more importantly, learning about more underlying mathematical teaching practices.
I completely agree about this weeks readings, it was quite intense but there was much to take away from them. Personally, I would thoroughly enjoy and benefit from discussing these methods we learned about in the CGI chapters. I think it's vital that we review these strategies because it's one thing to read these methods in our own time but it would be another to utilize these in class discussion to make sure we fully grasp there understanding. For example, when the CGI book mentioned how we can take the addition and subtraction methods and use them to begin to understand multiplication and division methods. I would like to understand how these relate and that way if I can understand the connection than I can better teach my future students.
ReplyDeleteAs for the Cantlon reading, I agree with Valand that it really was inspiring to look at a current teacher whom is reflecting in such an elaborate journal. I'm not sure if I would be able to write a journal in my own time in the future however I do intend to be a reflective teacher in my future professional career.
In my placement my teacher does math a little differently than Valands'. At Post Oak in second grade they use "Investigation" math program. My MT says that the teachers use the teaching manual to copy pages from and use them as worksheets that the kids will fill out during lessons. My MT isn't much like Valand's, my teacher is a good educator and has much knowledge to share but I've realized she's not as engaging as I'd hope to see. She teaches a lesson in math and then the students are supposed to fill out the worksheet based on the lesson. Rarely does my MT do a hands on activity and it is sad to see. For example, the ONE activity I heard she did was to weigh fresh fruit and place the fruit on the necklace and then over time, as the fruit dries up, they weigh the dried fruit to measure the difference. I wish I could see more hands on learning for math and I have considered asking my MT if she has an ideas for hands on learning. Maybe she has ideas but doesn't do them anymore, it's worth a shot to ask! I could probably learn more from my MT teacher, and other teaching colleagues, than what I learned in MTH 201 and 202, in my opinion. In the MTH course here at MSU, I don't think I learn nearly as much as I need to be an engaging hands on educator!
The readings were insightful and it is beneficial to go over the strategies in the CGI chapters. I am in complete agreement with Kate when she makes the point that it would be even more helpful if we were to discuss and review these strategies in the class to make sure that we are comfortable and have a full understanding of how to implement the instruction in the book. I do like that the chapters give sequences in how to implement the strategies. For example, with multiplication and division, the authors suggest starting out with problems that have whole numbers as their answers. This makes it easier for students to grasp these skills and allows them to recognize that math can be implemented in real-world situations.
ReplyDeleteIn my classroom, I have observed that my MT does a great job of starting off with "the basics" and working with the students to build on those skills to more complex problems. Currently the class is focused on fractions, decimals, and percents. My MT began the unit by defining fractions and showing the students multiple examples of various fractions. She likes to provide the students with various means of presenting information so in addition to showing students fractions on the whiteboard and illustrations, she provided them with tactile objects to help them grasp the idea of fractions. In addition to explaining and modeling, my MT enjoys providing the students with fun, hands-on activities. Once she observed that students were comfortable with the idea of fractions, the class began to focus on equivalent fractions. Again, she used the tactile items to show students equivalent fractions and help them understand. Once the class seemed comfortable with the concept, she introduced equivalent fraction bingo. In this game, she called out a fraction and the students were able to place a bingo marker over any fraction that was equivalent to the fraction called. Another engaging activity that the students enjoy involves calling random students up to the front of the class and making a rule based on a fraction of the group. For example, the teacher might say, "2/8 of the group has the rule." Students make hypotheses on what the rule may be based on observing the students. Not only does this engage students in the subject, but it allows them to see how math concepts can be used in the real world. Today, the class was focused on equivalent fractions and changing them into percents. It is refreshing to observe a teacher who adequately explains concepts, monitors the progress before continuing on, and introducing hands-on activities for the students to really grasp what it is the teacher wants them to get from the lesson. By starting out with the basics and progressively building up the students' knowledge, it is obvious that they are understanding each new concept that is being introduced.
In agreement with both Kate and Valand, I do think it would be really beneficial to reflect on my teaching in the future using a journal. I do believe that it may be hard to keep up with the journal after some time, but at least for the first couple years of teaching I think it would be interesting to use my reflections to alter my teaching each year to make lessons more beneficial for students. It would be an insightful tool to use in order to see what works and does not work for students in math. Being that I am not too comfortable with teaching math, this would be really helpful!
I completely agree with all of you ladies. I think that it is extremely important for students to be able to solve problems, using the best method for them. I feel that there is, however, a limit to doing the problem. The limit should be that the students are able to use a method that can be explained, whether it was taught by the teacher or not. I really liked what Tracy mentioned about technology on the classroom, because it is an issue that I have often discussed in many of my classes. I call it the "calculator controversy". There are a lot of educators that feel that students should be able to use calculators. Some feel like calculators should not be given to students until they are old enough for simple math to be a thing of the past. In other words, they should not be learning about calculators and adding and subtracting with double-digits, while using calculators to solve he problems at the same time. Then, there are those that feel that calculators should be banned from school all-together. They feel that they should only be used at the college level. Regardless, I think that it is more important to focus on making sure the students truly know what they need to know about mathematics.
DeleteIn the Five Practices book, chapter two talked a lot about selecting appropriate math problems for students. I found this reading very helpful, because it gave me ideas of what I need to consider when assigning math problems. I think that many teachers get caught up in worksheets and book work, that they forget to make up individualized assignments. I think it is one thing to assign some math problems. But, it is something completely different to be able to find structured and appropriate work for your students.
I agree with you all as well about students being given the freedom they need to solve math problems the way that they see fit. My MT does not provide students with various ways to solve problems and i feel as though this is hindering the students learning ability. When most of the lessons are introduced my MT shows the students the way she would like to see the math done, then she sends them off into groups to work on their own. I have noticed that even though she shows them the way to solve the problem, when they are in groups many of them come up with their own strategy to solve the problems. Even though she explains the concepts that she is introducing, i would like to see her spend more time on the problems to ensure that everyone understands before they get into groups and copy each others work. i appreciate Tracy bringing up technology because i have yet to see any incorporated into the math lessons. Even if its using computer games online, i feel as though it would give students a chance to see the math manipulated in another way.
ReplyDeleteI like the strategies introduced in the CGI book. Now that we have read about these strategies i think that it is important for us to try and identify them in the classroom. It would be helpful to go over these concepts in class so that we can become comfortable enough with them to teach to students and to show them multiple ways to solve problems. By becoming more comfortable with these strategies it would aide us in selecting appropriate math problems for students. we could them select problems that would be easily worked through using the different strategies discussed in the book.