Sunday, July 15, 2012

Guided Math: Chapter 4

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 Guided Math with the 
Whole Class

This chapter focuses upon how teachers can best utilize the Guided Math model with the whole classroom. Clearly the author is a proponent of using this with small groups as she has mentioned several times throughout the first three chapters how much she modeled this after Guided Reading. 

Advantages of Whole Class Instruction
There are many ways in which teaching the entire class is appropriate and even beneficial. Examples include:
-providing active engagement strategies
-reading aloud for math
-preparing for Math Workshop
-the Math Huddle
-practice and review
-tests or assessments that are more formal

Clearly whole-class instruction requires much less planning and preparation. Teachers are able to plan one lesson and present it to the entire class. If teachers are planning to engage prior knowledge, whole class instruction is very appropriate and worthwhile. Teachers are engaged with direct teaching during whole-class instruction which can maximize the amount of time students are being taught by the teacher rather than a peer or in self-guided work. 

Working with the whole class during a Math Meeting or Math Huddle allows teachers to create a sense of community, specifically focusing upon math and math-related concepts. When students engage in conversations about math, they are more likely to understand the concepts better than if they simply read about it or listen to it described. The student conversations during this time can be monitored by the teacher and misconceptions can be addressed immediately so students are not going into independent practice with misunderstandings about the concept or process being studied.

I agree that whole-class instruction can have it's place, no matter the subject. Gathering students together to explain directions, provide brief overviews or review of concepts is probably the easiest way to give the information to everyone all at the same time. I also feel very strongly after piloting a new math review system in our district this spring that students need to be able to EXPLAIN their thinking--not just how they got an answer but how they know the answer is correct. All too often, students know the process of getting an answer but they haven't internalized it in that they can't tell someone else how to do it. The Math Huddle, which allows the entire class to meet together daily, provides time for students to engage in this talk with the teacher there to provide help or correct misconceptions. It's meant to be a very brief time but can also provide a big "bang for your buck" when students do most of the talking and explaining. 

Challenges of Whole-Class Instruction
It is nearly impossible for any teacher, no matter how good they may be at delivering instruction, to meet the needs of every student in their class when engaged in whole-class instruction all the time. Students become distracted, get lost or bored during a lesson and may not have enough active engagement if the teacher is teaching to the entire class. 

Teachers have a hard time being involved with all students when they teach in a whole-group setting all the time. They won't know if little Susie did not understand a concept until perhaps a day after she has been working on something incorrectly and ingraining the incorrect procedure or process more deeply as she works. Additionally, feedback can't be provided as readily if the teacher is trying to engage the entire class at the same time because the teacher can't be with every student during their independent practice. 

Teachers know that a balance of summative and formative assessments provide the most effective feedback for teachers in order to design their instruction. The summative assessments provide an assessment of the learning that took place while the formative assessment demonstrations what students already know (or don't) so the teacher can plan continued instruction. It is stated that the use of assessments FOR learning allow students to have tremendous gains because of the immediate feedback and change in instruction to meet their needs (pg. 110). However, it is difficult to engage in conferences and conversations when teaching the entire class and thus, some of the formative assessment information is lost because observations and conversations don't happen as often as they might.

I am a huge proponent of formative assessment--I don't want to waste my students' time teaching them something that they know. I would never know where they are and how quickly they grasp concepts and are ready to keep going if I didn't use formative assessments. It's MUCH harder to use anecdotal notes when you can't meet with students to do the observations and ask students about their thinking.

Methods of Whole Class Instruction
There are several methods that can be used during whole class instruction to engage students and maximize learning. Mini-lessons, activating strategies, preparing for Math Workshop, Math Huddle, Practice and Review sessions  and Assessment are all areas in which teachers can effectively use a whole-class model.

Mini-lessons: Just like with reading or writing workshop, this time is meant to be very brief, no more than 10 minutes in length so teachers can identify the day's learning and get students started on the work for the day. Each mini-lesson consists of four parts (as adapted from Lucy Calkins' writing mini-lessons):
Connection: make a connection to prior learning or to a real-life experience outside of school that relates to the math concept. Utilizing the connections helps engage students with something they already know so teachers can move forward.
Teaching Point: the teacher clearly states the learning for the day and then models and demonstrates the strategy being taught or the concept being used. The modeling and demonstration is vital.
Active Engagement: then students have a very short time to practice what the teacher just demonstrated. This may be individual white-board practice, a think-pair-share or restate the teaching point in their own words.
Link to Ongoing Work: the last component is to link the teaching point to something the students have already been working on. The students need to leave the mini-lesson understanding that the teaching point is something that they should remember and use when appropriate.

This is a great way to keep those mini-lessons in check. I know I am guilty of not always linking the teaching point to something we have been working on or WILL be working on. I try to remember to give them a reason (we learn X in 2nd grade because in 3rd grade you'll add Y to it so make it more challenging) but it doesn't always happen the way I intend and sometimes when things are crazy in the classroom, this part is forgotten. 

Here's a brief sample I wrote up for determining Factors with 4th graders (pulled from CCSS). Very short and sweet.

Activating Strategies: By using different strategies to activate prior knowledge and/or engage students before the lessons begin, teachers can again maximize the time they have for math instruction. Some sample strategies include:
KWL: Most teachers know what the KWL chart but there are modifications suggested for this common strategy when used with math. You can change the K to "Thinks I THINK I Know" which will help dispel anything the students thought were true about the concept but may have been incorrect. Another modification suggestion is to change it to "What do you know for sure?" "What are you trying to find out" and "Are there any special conditions in the problem?" By changing the questions to fit math, student engagement can go deeper and misconceptions can be addressed immediately.
I LOVE the modified KWLs, especially the "what do you know for sure?" question. Often students think they know a lot about how to do something and they have been doing the problem incorrectly for a long time. This will provide students with the level of comfort to still share but be open to being corrected if, in fact, their thinking is off.
Anticipation Guides: This is another strategy often used with reading. Students can provide a wealth of information to their teacher by identifying what they already know to be true or false about a concept about to be studied and can look back at the end of the unit to see their own learning. It's important to remember to explain to the students this isn't a "graded test", its purpose is to guide the instruction of the class or group so that everyone is getting their needs met. (There is a great anticipation guide sample on page 120.)
Word Splashes: Students can preview and learn vocabulary while activating prior knowledge by seeing words "splashed" across a page or charge that deals with a particular concept such as the relationships between fractions, decimals and percents.

Reading Math-Related Literature: Using stories that relate to students' lives but also teach about math can be a great way to bridge connections between concepts and reinforce ideas that students may be struggling with. 

Setting the Stage for Math Workshop: Teachers can use whole-class instruction time to set the stage for math workshop by introducing, modeling and reinforcing procedures and practices of the workshop. During the first weeks of school, procedures will be taught, practiced and reinforced. After the procedures have been taught and used successfully, time can still be set aside to discuss any problems occurring during workshop and/or for teachers to explain what students will be engaged with during individual learning time of the workshop.

Math Huddle: Like a morning meeting, this time focuses the students for learning and discussing math and math-related concepts. It can be teacher-led or student-led or a combination of both. Students share ideas, problems, solutions and provide proof during this time. Students can stretch their thinking when challenged by a classmate who may not understand how (or why) a student got a particular answer and the student who shared may experience growth as a mathematician while explaining their thinking and surely the students who are listening will gain insight as well. 
I really like the Math Huddle concept. It is important for students to discuss their thinking and engage with each other about math and other subject areas being learned. Having a set time every day for them TO engage in this kind of talk will encourage them to share, stretch their thinking and be prepared to provide proof if another student (or the teacher) isn't convinced by their statements.

Practice and Review: Students can participate in brief practice and review sessions as a whole class. Since most high-stakes state tests are done with paper-pencil, it is important that students can spend some whole-class time reviewing how to take these assessments and what they will look like. Games can be played to review math concepts as a whole class such as "Around the World" or games such as Jeopardy that use PowerPoint to be presented to the whole class.  Clickers can be used as well to review as a class where data about student responses can be graphed and displayed for students to interpret and analyze.
I love the idea of using the Clickers and we have them at my school...but the computers rarely allow them to connect so it's wasted time. There are many places around the internet to find games such as Jeopardy, Who Wants to be a Millionare? and more that are used with PowerPoint and can be played as review games with the class provided you have a computer and some kind of projection system.

Assessment: Assessment is usually conducted as a whole class so that all students can be engaged in the test at the same time. Most of the time these are paper-pencil tests and can be multiple-choice or constructed response (or a combination of both). These can be used as practice for standardized test-prep as well since most standardized tests are still done on paper.

I have done both whole-group instruction for math all year and done small group instruction for math all year. Regardless, it becomes necessary to teach the whole class sometimes, even if you are using some small groups either to provide directions or clarify things that the whole class had confusion about.

I will definitely be using the Math Huddle this year. I love the concept of it and how it doesn't have to be really long to be effective. 

I will also definitely make an effort to use more mini-lessons for math. The adaptation of Lucy Calkins' model is a great reference to have. When I wrote out that brief mini-lesson for Factors, it took me less than 10 minutes and even though I focused it for 4th grade, it is something 5th graders would benefit from reviewing (or learning!) as well. This may be a bit more challenging since I will be teaching a split grade, but I am hopeful that my using the CCSS for most of my mini-lessons I can provide a common lesson to my whole class that satisfies what both grades need to learn to maximize the time that I have with my students.

I am going to look at my math series and think about how I can integrate the Anticipation Guides and the modified KWL because I think those are strategies that would really benefit the students, especially the A.G. What better way to engage children than keep them accountable for their learning by going back to that A.G. at the end of the unit and notice how their own thinking has changed. 

Stay tuned for my thoughts and reflections on Chapter 5: Using Guided Math with Small Groups!

1 comment:

  1. YAY, Sunny! You're ahead of me--I just couldn't keep up. You're a rock star!
    I am hosting Chapter 8. Come over and link up when you get there. I love your summary notes and I love your commentaries even more!

    Finding JOY in 6th Grade