Tuesday, July 10, 2012

Guided Math: Chapter 3


This post is part of my Guided Math Book Study. I will discuss each chapter in two sections: an overview of the chapter and my learning/wonderings and how this learning will affect my mathematics instruction. You can read the entire series of posts by clicking here. (Graphics for this post provided by Scrappin' Doodles.)



Using Math Warm-Ups in Guided Math



This chapter focuses upon how to get students engaged mathematically from the moment they walk into the classroom each morning. Most teachers are all about their set routines as we know that routines help students perform better and they help us maintain some sense of balance in what can often be a crazy-hectic day. 

First Sammons describes Math Stretches that can be used to begin each day. These are routines that are either done daily or done once per week on a rotating basis, with some form of routine done each day to start the day off mathematically.

Some of the Math Stretches described are (my comments in blue):
-Data Collection and Analysis
Students are asked to answer questions and then use the answers provided by the class to formulate a graph and analyze that graph. Additionally, if data is gathered over time, such as the weather for the month or how many days of indoor recess they have had in January, the students can interpret and analyze that data into a graph as well.
I really like this one because throughout all of the grades I have taught, my students have had a horrendous time with graphing. Something about taking the data from a table and putting it onto a graph or chart doesn't transfer for them. Repeated practice such as this, with items that are meaningful to the students, will provide practice over time and when discussed in the Math Huddle, misconceptions can be addressed immediately.
There are also some discussion types that are identified for use when having a classroom discussion about the data collection and the subsequent graph/chart made from that data.
Think-Aloud which provides the highest level of teacher support as the teacher is modeling relevant vocabulary, records analysis on chart and discusses the reason for choosing the method of representation
Guided which helps students to join in the discussion by carefully crafting questions to help students get through their thought process. The teacher is still a dominant part of the voice in this type of discussion.
Facilitated is when students take on more of the direct role in the discussion. The teacher may pose open-ended questions but mainly ensures students are staying focused on the discussion of their observations, what they've learned and how they represented their data
Independent is when students are in control of the discussion--the teacher may record some of the discussion on chart paper but it is usually done by students entirely and the teacher may interject as students share journal reflections to dispel misconceptions

-Number of the Day
We often think of using a Number of the Day pattern with younger children, say K-3 at the most. But Sammons shows us that you can use a Number of the Day (or Number of the Week as it were), with any age. Older students can use fractions, decimals, percents to represent numbers, all students can use arrays, ten-frames, base-10 models, etc to show numbers in different ways.
This is a strength of the Everyday Math curriculum in that we often ask students to represent numbers in a variety of ways, from as early as 1st grade. What I like about this, however, is that it becomes part of a routine. With older students, I wouldn't do this every day, I would do it weekly and use numbers based upon what we are working on. For example, if we are working on converting fractions, I might provide a fraction as the number of the day and see how many ways students could represent that number--either as an equivalent fraction, a decimal, a percentage, with pictures, etc.

-What's Next?
This math stretch needs to be done on chart paper so it can be displayed and discussed during the Math Huddle (it could also be done on a small white board that is in the meeting area). The teacher starts a pattern and leaves a blank space for each student in the class. The students each fill in the "next" part of the pattern until everyone has had a turn. If there are mistakes, the KIDS have to approach each other about it and discuss the error and AGREE to fix it.
I ♥ this stretch because it really promotes TALKING about WHY the answer is (or isn't) correct. All too often we teachers do the talking during math and this promotes that discussion for the students. My only thought was really about managing it - if the students do this as they come in, it can get crazy. Routines would be a MUST and have to be modeled explicitly over and over in order for this stretch to be meaningful and worthwhile.

-How did my Family use Math Last Night?
This stretch was promoted to be used in conjunction with a homework assignment. Once a week the students record a way they or their family were using math at home. It might be during cooking, measuring for something or whatever they used math for. The following day, they take this math stretch information to school they add the information to an ongoing chart of how math is used in their every day lives. Sammons also emphasizes that students have to learn to make "Math to Self" and "Math to World" connections just like they do with reading (compared to Text to Self and Text to World connections).
I think this is a great idea and a simple homework assignment that students could do. I feel it is very important for students to make real-world connections with everything we are doing. Why do you need to study algebra? Because you will use it here, here and here sort of thing. We have to make the learning meaningful but also authentic to help the students buy into it. I love the idea of a "Math to Self" connection so students can be encouraged to think of a time when they did a similar math problem or a "Math to World" connection when they can connect something their family has done to something a lot of people in the world might do. It will broaden their math sense but also provide them with connections to the real world.

-______ Makes me Think of.....
This is another stretch that promotes making connections in math. Students can make Math to Self, Math to World and Math to Math connections by sharing words that they think of when they hear another word. The example provided (pg 84-85) is that the teacher might write Fractions make me think of.... and then students will provide a word or phrase to describe what they think of. They can ONLY use words--no pictures or number representations and there can't be any repeats. 
This activity is one that I think would help promote connections between concepts that students don't often make themselves. At least the students I have taught in the past tend to be "boxed in" with one concept at a time and unless I bring the old learning back to their attention ("Don't you remember when we did.....?" "Ooooh, yeah!"), they often don't make connections on their own. This activity would encourage them to make the connections--it might be difficult for the students to come up with 25-30 different words/phrases but that would also encourage discussion about what other words might work which, in turn, can be seen as a vocabulary booster as well.



My school has been big into DDI Strategies in the last two years (which I have mentioned before). There is a  resource with that program called "Target Tabs". 


Basically as you "target" a specific area in reading (or math), the students record a response on the tab sheet. I have only used them for reading thus far....but as I read this chapter, I thought about how I might be able to integrate the Math Stretches with the Target Tab concept. It is something the students could keep in their binders daily as a record of their progress and would allow me to see who is having trouble and who isn't. Additionally, the target tabs would be GREAT for discussion purposes. Students could use clock partners or something similar before the Math Huddle to ensure they aren't always sharing ideas with the person next to them, etc. I think this is something that I would definitely like to "guinea pig" this coming year and see how it goes.

Another thought I had with the Target Tab idea of recording the math stretches is to have the warm ups be a 10 minute opener, allow 5 minutes for sharing and then come together for 15 minutes of Calendar Math and Math Huddle time. I think this would work out well to maximize the learning time but also to ensure that kids are engaged and reviewing. I'm not positive on it simply because I ♥ the Calendar Math materials I have seen around the blogosphere recently and it seems like it might be too much to try to do both. 

At any rate, this chapter has definitely gotten me thinking more about MATH and how to approach repetitive practice and mastery of certain skills like patterning throughout the year, even with older students. I'm not sold on the idea of doing the math warm-ups first thing in the morning because while I have taught math first thing the last three years, it doesn't mean my schedule will always allow me to do so. I think as long as I can dig out a 90 minute math block in my schedule, no matter where it is, that I can feasibly do these warm-ups with my class before we begin our math lesson.  If the schedule stays relatively the same as far as lunch and recess times for upper elementary next year at my school, I could easily do my math workshop after their morning recess and still have time to fit everything in before lunch. It is the only thing that Sammons hasn't 100% sold me on--I don't think it matters when you do the warm-ups as long as you do them before you begin the workshop time.


Stay tuned for my thoughts and reflections on Chapter 4: Using Guided Math with the Whole Class on July 12!
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