Chapter 7 starts off talking about the same type of teaching methods as the other subjects. He says again that we need to take a look at our standards for math. We need to figure out if the standards we have are preparing students for their futures, and not just their educational futures, but their lives in the workforce. It seems our current system prepares kids for more math classes, but not necessarily for the way they will be using math in the "real world". Thought the chapter he reinforces the idea that most people do not sue more than basic math skills in complex situations. Most people don't use algebra in their jobs or lives. With that in mind, does it make sense for students to take certain classes if there is no connection to the real world? Schmoker also went right along with what one of our speakers at the conference said also; we need to teach fewer concepts, but teach them deeper.
From my experience I can agree that students need to take the basic math skills and learn to apply them in many different situations. Unfortunately students continue to struggle with word problems, even when it is an addition problem.
Schmoker also made the point that we need to make math more "real world". To do this, we need more reading, thinking, and writing in math. Math has two fundamental aspects: calculation and interpretation. Students need opportunities to express their "quantitative interpretations in arguments and proposals". We can do this with text books and real world documents. Schmoker had the idea of collections several really good newspaper articles that allowed student to read, think, write, and argue about while using numbers. I really like this idea. He suggested doing it weekly. He also stated that raw data is a great way to get kids talking.
Along with other chapters, he mentioned again that we need to teach kids to read the text book. He says that math problems can come down to understanding one word and if a kid isn't reading the book correctly they could be getting it all wrong. He says that we need to teach them to read the texts slowly and deliberately and make sure they understand every word and sentence. I liked the writing prompts on p. 213, I thought these would be a great way to get kids to write out what they are thinking and then they will be understanding math more deeply. I like these prompts better than the "explain" that is in our texts. Theses give a little more guidance.
The best thing I took from this chapter is having kids read articles and using those to get them to work out some problems using basic math skills. I am sure we have done this some, but doing it consistently could help a lot of our students.
First of all, I would like to say that I really enjoyed reading this book. I think that it contains many applications that can be implemented very easily in order to the way schools operate. However, at the same time, I feel as though it is kind of frustrating because schooling/teaching should be so simple, yet we have, over time, made it so complicated. Unfortunately, in order to implement some of the changes that the book mentions would require a huge change of thought for some and we know that can pose as an obstacle.
ReplyDeleteAnyways, as Kristin said, this chapter is very similar to the previous chapters with the substitution of either Science or Social Studies with Math. And I agree, implement reading, speaking, and writing into the Math curriculum as much as possible. I also really like how it focuses on a deep understanding of elementary skills. I was always a good Math student, and I enjoyed Math throughout my schooling. However, I am lost in regards to most of the content of the Math curriculum at the intermediate level. Those skills/strategies/etc. are not what students need to be successful in the real world. Over time, they will forget those skills. How much more could we benefit our students if we were able to focus solely on the skills that they will use for the rest of their lives?
I will conclude with a quote from page 197 that I really liked. Lynn Steen says abstraction is the enemy. "As the level of abstraction increases...links to meaning fade." As meaning fades, so does motivation to learn, understanding, course success, and - for many - college prospects. So what he is saying is really simple, if we want to truly get our students ready for college we must make their learning meaningful in a way that relates to their lives.
Something that came to mind when reading this chapter was finding ways to incorporate math with real world connections. They talked on pages 207-208 about using real data with students. I wonder if there is a way to use the data we already have from data teams to incorporate into math class. They could find out averages, increases/decreases in data, etc. How cool would it be if students were using their own data to interpret and draw conclusions in their own math classes? It would probably be much more meaningful to them since it is real data that they are part of.
ReplyDeleteI also like that Schmoker continues to stress the importance of writing in Math class. "Writing in math class requires students to organize, clarify, and reflect on their ideas" (212). I know from data teams that writing in math was extremely beneficial for Lindsey and it provided another chance for students to explain their thinking. Even though our focus was summarizing, Lindsey was able to see if students actually understood the concept being taught. And isn't that our ultimate goal?
If my math teachers had made me write in math, I think I might have caught on before I graduated from high school.
ReplyDeleteWriting in math will help students make connections, and examine their own process of thinking (without them realizing they are doing so). But this will also help them with those dreaded word problems. If they can take an equation and write their own word problem out of it, the fear will diminish. Writing can also help them by giving them another way to look at it. I know it seems difficult to see how writing and math fit, but I really feel like math would be one of the most beneficial subjects for additional literacy. Having them tackle and dissect a math text book will help them with other text books.
I will agree to disagree with Schmoker in this chapter—just a bit. I do think that students need to learn various types of math even if they may not encounter them in the real world. Maybe they will! Technology is ever-changing. I also think that math is great exercise for the brain, and definitely a different way of thinking…even if they don’t encounter some of the formulas or strategies; I do feel that the practice of working through it teaches more than the particular formula or strategy that is focused on. Perhaps I’m wrong, but those are my thoughts as of now!
I do agree that we need to have “less is more” become our mantra. And in doing so, math will be narrowed down. This will help more students become more confident and comfortable with their knowledge of math, but I worry that we’ll miss something. However, I guess if you don’t get it mastered, you can’t move on anyway. So perhaps if my teachers had this kind of approach years ago, I may have ended up a math teacher….I guess I’m still struggling with whether or not I agree or disagree with him.
Schmoker’s views on literacy in the math classroom stuck out to me the most. (Probably because I am a reading teacher!) He points out that close reading is an essential practice in math. I have never really thought of it that way – but agree! He explains how each little word holds a lot of meaning (might versus is for example). It is not that way with almost all other texts and students need to learn to meticulously read for math. I think modeling is the key to solving this issue. In thinking back – I probably didn’t do this enough when I taught math. But again, modeling shows students how to approach a situation and is a very powerful tool.
ReplyDeleteI also like his ideas for real world connections. Math is so abstract – and if you’re not a “math person” you know you’ll never use half of what you learn. I agree with Katie that it is good “exercise for the brain”. It helps students to problem solve. I don’t think Schmoker is saying to take that away – just make math a more practical area of study. If those complex subjects are needed to analyze real world connections – I think this is where you teach them. I agree with Schmoker that it is a waste of teaching them just for the sake of teaching it.
I think Amanda’s idea of students applying their learning targets to data team data would be awesome! It would also be a form of self reporting, which we all knows is essential. Something to think about!
In this chapter I think the emphasis on "what we teach" is critical. When we narrow our focus in math we really need to read and re-read the research Schmoker states throughout the chapter. I never thought of a math textbook and close reading...an area we should provide staff development/modeling. Spending months and not days on concepts was an "aha", too. It is a little easier to visualize when he talks about solving complex problems using non-fiction articles and data. I love Amanda's idea of students using their own data, their grade level data and maybe some building data (compared to district or other schools data?). I liked the quote Eric ended with and thought it is really applicable in all areas. I heard some conversations at all levels about application/meaning for students, but this year we can go deeper and really talk about current standards taught at an abstract level. Simple skills...reckoning with meaning (p.198) was the theme throughout this book, but consistent checks for understanding must happen for this to be effective. Schmoker talks about common standards maps. How would we implement this? Do you think all departments should do this? What modeling/practice should we provide? When would this fit in our vision for how we start our year? Would you want support from curriculum specialists at ASC or is this for JB only? I also think Scmoker's term "precision in language" when reading math textbook was something I did not consider ...we talk about math vocabulary, but I think what he is saying is really different and probably an important concept for all of our teachers to consider so they can help students see the difference. I agree with Kristin there are some good simple prompts presented in this chapter that teachers could implement. I really enjoyed this book and loved reading the blog to "hear" everyone's thinking. I wonder if we should print page 217 for all teachers...Schmoker did a nice job summarizing.
ReplyDelete_- Marianne
After reading this book, one thing I wish we could do is write in our text books. This would help with close reading and annotating. Math teachers, especially middle school teachers, for the years that I have been in the district have been frustrated with the amount of curriculum that we have to cover. We go a mile wide and an inch deep. Iowa Core/Common Core is going to change what we teach at each grade level. Hopefully when we make the changes necessary we will be able to figure out what the essential standards are.
ReplyDeleteI love Amanda's idea of implementing math writing with our data team data. This may help students take ownership of their data and work.
I think that writing fits great with our curriculum. I really liked Doug Reeves's idea on p. 212-213 where students have to explain why one of the multiple choice answers is wrong. Also, that students get credit for correcting their work and explaining why their answer is wrong and why the correct answer is right. The writing prompts on p. 213 are good.
I know we teach a lot of concepts that students more than likely won't need in the "real world" but what can we do about that?
Hi,
ReplyDeleteSorry again for being late, but Vincent has not posted yet either… J
It is hard to go last… Umm…
Page 195 and 208-209 - “The interplay of words” - Many of you said this. Math has a twisted version of reading comprehension within it. It is crucial to force students to READ and Reread in math in order to truly understand what is being asked or said. Math is the hardest subject matter to read and understand.
Page 197 - I was confused about how teachers might be able to help students press on even when frustrated and confused. I don’t think students or teachers are used to this (unfortunately). This will be a worthy challenge.
“As the level of abstraction increases…links to meaning fade.” POWERFUL for all subjects and SO true for math! As an observer in some math classes, I have often wondered what the practical use of some units might be.
It makes sense that future employers will want workers who can read, write, speak and communicate for practical purposes (p. 203). This should be the goal of all subject areas!
Page 206 - Like Kristin said, the use of articles can be so helpful. When teachers prompt questioning and model thinking, students begin to think this way. As Marianne said, we need to help our staff understand this.
Page 210 - I like the steps Schmoker notes here for helping students really understand. He uses a second grade example, but this concept is easy to see happening in 6th-8th.
Others of you mentioned this, but it is worth repeating. When students can write about a topic, they understand it. We know this is so true from the work with summaries we have done. We cannot give up on this. It is powerful and should be taking place more as a check for understanding.
I think 217 is a good review and will keep this group focused, but it might just be another piece of paper in a binder if we present it to the staff too soon.
-Rachel