Friday, July 6, 2012

Guided Math: Chapter 1

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.)

Guided Math: A Framework for Mathematics Instruction

Chapter One provides an overview of the Guided Math model. The seven instructional parts are introduced and discussed briefly to provide teachers with a detailed framework in which to model their own instructional change after. I will discuss and comment on each instructional part (my comments will be blue).

1. A Classroom Environment of Numeracy: Students need to be immersed in a classroom that looks like math is taught there. Students need to be able to use manipulatives, compute math problems, compare math concepts, categorize math, using questioning, estimate, problem solve and write about their thinking process. Students need to talk about math and understand that numbers are more than just numbers--we use them every day, for many reasons and we wouldn't be able to do a lot of things we do without numbers.
Understanding numbers is vital to a classroom. This makes sense to me when I think about how often my students can't do mental math--they don't own the math concept therefore it isn't something they have really internalized. In order to foster that numeracy, we have to provide an environment that encourages numeracy. In other words, when people walk into my classroom, are they going to know by a quick glance that I teach math in there?

2. Morning Math Warm-ups and Calendar Board: Warm-ups take place when students enter the classroom. The daily tasks are either given daily or on a routine basis (ie. Number of the Day is always on Monday). Students may be asked to express number patterns, sequencing or any other concept that students need to learn and master. The Calendar Board encourage review of previous concepts, mental math skills and problem solving.
Usually I have thought of Calendar Math/Calendar Board as being something you only do with younger students as they practice tallies and place value. I see now, however, that my older students who are struggling with number sense can benefit from these daily routines to help them to master concepts that are more difficult. The biggest benefit is you can adapt problems as the year progresses to ensure that students are still practicing numeracy but are also required to think farther and deeper as the year progresses.

3. Whole-Class Instruction: This method is touted as a quick and easy way to engage all students in introducing the lesson and providing the objective for that day's learning. Teachers may use a mini-lesson engagement activity, read aloud math-related literature or review of previously taught concepts. Students also have the opportunity to meet as a whole group to discuss their math findings and share their learning with the whole class.
I love the idea of a "Math Huddle" where the class comes together to share what each pair or small group has discovered as they have worked on something that the teacher introduced in the mini-lesson or a concept they are reviewing. I also agree that whole group instruction needs to be short to ensure that students are engaged and stay engaged.

4. Guided Math Instruction with Small Groups of Students: Guided Math with small groups is similar to Guided Reading with small groups. Teachers assess students either formally or informally (a pre-test of the unit's concepts would suffice) and then group students according to where they are. Students are then given instruction at their level and teachers can better monitor student learning and achievement since they are working with smaller groups. Students who have already shown mastery (or very near mastery) may work more independently than a group who is having trouble with a specific concept. The small group framework allows the teacher(s) to spend as much or as little time with a group as needed based upon the needs of that group and the concepts being taught.
I am in love with the concept of small groups for math. I have done it a few times but never felt like it was the most effective. My "framework" wasn't very solid. Since I will be teaching a dual grade, it will be of the utmost importance for me to make sure I am maximizing every second I have with my groups--not having students who grasp the concept immediately continue to work on it because some students are just not getting it. By grouping them according to where they are with every concept, I can provide better instructional materials for students who need the enrichment and provide more hands-on and guided support for students who are struggling. 

5. Math Workshop: Math Workshop allows the students who aren't working directly with the teacher to be engaged in meaningful activities that provide review, enable students to work with manipulatives and other math materials. Students can be engaged with math games, investigation type activities, center activities, problems of the day/week, writing in a math journal or even engaging in paper-pencil review of previously learned concepts so that students are able to maintain the skills they have learned.
One important thing I really agree with is making sure the students who are more advanced with a concept are not just given "busy work". I never want students to think they shouldn't achieve because it just means "more work". Instead, providing the same concept but at a more challenging level will keep the students engaged and provide them with opportunities to be peer tutors if they are grasping concepts quickly and other students need just a bit of support. We use Everyday Math in my district and many of the games are really quite interesting for the students and allow them to work on previously taught skills. We also have Math Box activities that are a "spiral review" of what they have learned, even in previous grades. These boxes can also be differentiated for kids who you know have mastered a specific skill and those who haven't. 

6. Individual Conferences: Conferring for math is described as being similar to conferences for reading or writing. It allows the teacher to meet with students individually (or in a small group if they are working on the same concept for review) and make notes of the strategies the student(s) uses and can help identify the needs of each child individually. These conferences can also lead to helpful information for forming small groups--if a bunch of children are not mastering prime factorization, as noted through conference records, one or two small groups can be formed to focus upon that skill and provide remediation and differentiated practice to work students toward mastery.
I will admit I have always struggled with finding TIME to confer. This past year I really made an effort to keep up on it and ensure that I was working with each child individually at least once a week. It made a huge impact on what they retained from conference to conference. I love the idea of extending this to math. In theory, you could meet with each child up to three times per week (one for writing, one for reading and one for math) if your setup and timing allows you to do this. At the very least I would be able to see each student twice a week (one for literacy and one for math). I personally feel that this provides a more meaningful student-teacher relationship as well because you can spare 30 seconds to chit chat and ask your students how things are going with a pet or whatever and then spend 3-5 minutes on the task at hand and still make the most of the conference.

7. An Ongoing System of Assessment:  Formative and summative assessments must be provided throughout every unit in order to ensure students aren't being taught something they already know. By conferring and reviewing student work (which can be considered a formative assessment) and analyzing quizzes or chapter assessments, teachers can more easily determine which group a child should be in. Because there are so many concepts to be taught in math, it is important for teachers not to feel like they need to move from "page to page" in the chapter or unit but rather make sure they are teaching the concepts that students need to know based on state and district standards.
I whole-heartedly agree with the concept of NOT just following the textbook page-by-page. Students who clearly understand Area and Perimeter should  not have to sit through 4-5 lessons on the same topic unless the topic pushes them farther in their thinking. Unfortunately I think a lot of math curriculums regurgitate concepts without adding anything "new". It's a waste of valuable learning time to have students spend time on something they already know. With the Common Core Standards being integrated in Michigan, I consider THAT to be my curriculum and Everyday Math to be a RESOURCE. Therefore, if I am finding that EM doesn't cover something my students need to know, then I will find extra materials and resources to ensure that they are being taught the standards. It might mean more work for me but if my students go to the next grade level with the skills they need, then it's worth it!

Already in the first chapter of this book, I have found a lot of things to agree with and even some things I hadn't thought of before. I know I will definitely be integrating the following into my mathematics instruction:

1. Math Warm-Ups/Huddle -- I love the concept of providing a similar type of warm-up every day or on set days of the week to maintain a routine. Students have the chance to work independently (or maybe with a partner) and students have time to DISCUSS their thinking and learning. I think this is vital. This past spring, my district implementing a new type of review for our standardized test and it emphasized student TALK. The students had to EXPLAIN how they knew something or why they were right. While I have always pushed my students to be able to tell how they know, the Math Huddle concept will give all students an opportunity to be engaged and will provide me with a quick way to dispel misconceptions and guide students to the correct conceptions (or better yet for the kids to guide each other!).

2. Mini-Lessons for Math -- I think this is an amazing idea. Since I will start with a split, I will ask my principal if I can veer off the beaten path and provide instruction with similar topics, even if they aren't in order. For example, if my 4th grade group is studying geometry, my 5th grade group should be as well. This will provide me with opportunities to each across the grades for students who need enrichment or remediation (ie I can put 4th graders in the 5th grade group or vice versa as appropriate). If that isn't possible, I will then examine my standards and determine a topic that BOTH grades need to understand and provide some practice as a whole group with that before moving into my small groups. That may mean that the mini-lesson doesn't have anything to do with the content lesson for the day but there isn't much I will be able to do about that if I do end up teaching a split all year.

3. Math Workshop -- This is something I definitely want to perfect. I have been digging through my old resources and plan to make some math games for my kids to use during workshop. Some will include work with ten-frames, tallies, base-10 and games using decks of cards. I have always struggled to ensure that my students have enough meaningful activities to do during their independent time because over the years they have tended to get very loud, very fast if I am not right there with them. I am also considering a Daily 5 Math type of concept for the workshop so students have set things they need to do throughout the week but are given a choice of what to work on which day to keep their interests up and their engagement high as well.

4. Conferences -- I bought the Confer app for my iPhone and iPad earlier this spring. I definitely plan to use it for all of my conferences (math, reading and writing). It will provide me with super easy ways to group my students and track the progress I see with each child. This is vital for me because often the paper trail bogs me down and I start to feel like it isn't worth it. The Confer app and the fact that I can use it on both of my devices will make things SO much easier and save a TON of paper! It will also give my students an opportunity to work with various different groups as they master some skills and need more help on others.

Stay tuned for my thoughts and reflections on Chapter 2: Using Guided Math to Create a Classroom Environment of Numeracy on July 8!


  1. WOW, Sunny... you're a fast learner!

    Great summary!
    And... after reading this, I think I've decided to splurge and get an iPad--WITH the confer app!

    Thanks for the motivation... I loved reading this!

    Finding JOY in 6th Grade

    1. I actually read this chapter two weeks ago!! I'm on chapter 4. So posting 1-3 will be easy and then I can focus on the last 4 :)