Guided Math Book Study-Chapter 1

Well my book finally arrived from Amazon and I am eagerly reading the first few chapters to get myself caught up. If you are interested in joining this awesome book study please check out the Guided Math Book Study hosted by Primary Inspired. This is a book I have wanted to read since last summer when I had a goal of implementing math learning stations into my 7th grade math classroom for the 2011-2012 school year. I am hoping that other middle school math teachers join this books study to share ideas on how this framework would work in a middle school math classroom. Here is the link for Chapter 1. Please join in!

Traditional, whole class instruction is what most students still encounter in school today.  This type of whole group instruction can mislead students into thinking that there is only one "right" way to do math.  We need to get students to develop a strong conceptual foundation so they are able to move to abstract thinking (and really understand why the algorithms work, not just plug numbers in).

Teachers juggle students that need extra challenge with those who are skill deficient or lacking in conceptual knowledge.  We cannot continue to teach students math with a "one size fits all approach".

The instructional components of this model include:

1. A Classroom Environment of Numeracy  
2. Morning Math Warm-ups and Calendar board Activities  
3. Whole-Class Instruction  
4. Guided Math Instruction with Small Groups of Students
5. Math Workshop
6. Individual Conferences
7. An Ongoing System of Assessment  

Classroom Environment of Numeracy:  (Daily)

• Environments rich in mathematical opportunities
• As students recognize how numbers and problem solving affect their everyday lives, math becomes more meaningful to them
• Children learn best through active engagement in authentic opportunities to use and extend their number sense
• Encourage students to use manipulatives, compute, compare, categorize, question, estimate, solve problems, converse, and write about their thinking processes
• Through mathematical dialogue, students construct the meaning of mathematics, developing enduring understanding of the "big ideas" or concepts as they also develop procedural and computational fluency

What can teachers do to make Guided Math work in their classrooms?

• Foster the strong social aspects that are integral for learning
• Teach behaviors that promote constructive conversation
• Organize the physical aspects of their classroom for immersing students in an environment of numeracy
• Provide classroom procedures for students that allow student participation in all components of the Guided Math framework

Calendar Math and Morning Work:  (Daily)
Morning Math Warm-Ups
Math warm-ups take place in the morning to set the tone for the day.  As students arrive, they have assigned tasks to complete.  During calendar board the class discusses and analyzes their results.  Students may complete a number of the day chart.

Teacher briefly reviews previously covered mathematical skills, previews upcoming skills, provides practice in basic counting or math facts, encourages mental math skills, and engages students in problem-solving activities.

Whole-Class Instruction:  (Your choice)
Whole-class instruction remains an option within the Guided Math Framework, but rather than being limited to the traditional lesson format, a variety of instructional structures are available to teachers.

Whole-class instruction is an excellent method for presenting activating strategies or literature connections at the beginning of lessons, as well as for ongoing review of mastered concepts.

Teachers may choose to present mini lessons or model problem-solving strategies, thinking aloud as they do so.

Small-Group Instruction:  (Your choice)
Teachers use informal or formal assessment to group them according to their proficiencies at a given skill.

Groups are homogeneous, yet fluid, as students’ levels of understanding change.

Teachers work with small groups that are determined by student achievement and need.

Using this small-group instructional model, teachers can vary the amount of time they spend instructing students according the the specific needs of the student.

Offers teachers an efficient way to provide differentiated instruction to meet the needs of diverse learners.

Math  Workshop:  (Your choice)
Students who are not engaged directly with the teacher must have meaningful work to do and know how to follow established and practiced procedures for independent individual or group work.

Students are taught to work independently, and the teacher establishes expectations and routines during the first few weeks of school.

Students learn how to access materials they may need, follow rules for working with manipulatives, handle any questions they may have, and learn what to do if they complete their assigned work.

Workshop tasks might be inquiries or investigations, math-center activities, math games, problems of the week, Math Journal writing, or written practice to maintain previously learned skills.

Conferencing:  (Daily)
One-on-one work is needed to aid the teacher in assessing student understanding of mathematical skills or concepts, to clarify or correct student misunderstandings and errors, or to extend or refine student understanding.

These conferences provide rich information about how to best work with individual students.

This helps teachers identify specific teaching points for individuals and for the class as a whole.

Assessment:  (Daily)
Provides teachers with  timely information about class and individual student needs.

To maximize student learning, students themselves must be involved in assessing their own work based on criteria, rubrics, or exemplars.

Review and Reflect (My thoughts are in red)
Think of the way you currently teach mathematics.

1. What aspects of it are successful? I think that I do a lot of formative assessment to see where my individual students are at. I adapt my instruction based on that information. I think I do a good job of developing conceptual understanding in general, but there are areas I could improve. I think I do a good job of having rich discourse in my class. My students collaborate very well.
2. What aspects of it trouble you? Why? It's always finding that balance of challenging the higher level students, while also working with struggling learners. I definitely see the need for the daily review from calendar math or morning work, but as a middle school teacher I need to find something age appropriate that will serve the same purpose. I always start the year strong with daily warm-ups, but as we get going and are crunched for time, that seems to fall by the wayside.
3. Does your math instruction lead your students to a deep conceptual understanding of the math standards they are learning? If so, what are you doing that contributes to that? If not, how do you think you would like to change your teaching? I am really excited about our new math curriculum, Carnegie Learning. From what I have seen of it, it seem to do a great job of building conceptual understanding. It will be nice to have a curriculum that is common core aligned, instead of having to find materials on our own to teach the common core.