Mathematical Fluency

I have been reflecting on and discussing with colleagues ways to help students achieve greater math fluency and number sense. I have had an epiphany:

Having students practice and memorize math facts isn't enough.
When we help students learn to read, we don't just have them read and read and read. According to my expert Language Arts friends, I have learned that students receive direct instruction on tools for comprehension and fluency.  Just like reading, math facts fluency and number sense requires assistive teaching. Students need to be taught to see the patterns, reflect on them, verbalize them, translate them into their own language, and thus understand them.

One of the great problem solving strategies is to solve a simpler problem. However, it is only when we learn something from the simple problem that can be applied to a greater problem that this strategy works. Similarly, when students complete math facts, they must learn to see the patterns and lessons hidden within in order for number sense to take hold and assist them with understanding numbers.

One way to do this, is to have students complete a math drill and then lead them through the process of looking for and identifying patters.

Ex:

1 + 9
10 + 9
20 + 9
30 + 9
40 + 9
.
.
.
Most students can complete this task, possibly easily and quickly; however, until we have them look back and see the pattern, and discuss the pattern, they aren't going to learn number sense. We need to directly and intentionally teach them the patterns of math, thus helping them discover number sense.

Habits of the Mind: Successful Differentiated Instruction

Differentiated math instruction is most successful when teachers do the following:

1. Believe that all students have the capacity to succeed at learning mathematics. 
2. Recognize that multiple perspectives are necessary to build important mathematical ideas and that diverse thinking is an essential and valued resource in the classroom.
3. Know and understand mathematics and be confident in their abilities to teach mathematical ideas.
4. Be intentional about curricular choices; that is, think carefully about what students need to learn and how that learning will be supported.
5. Develop strong mathematical learning communities in the classroom.
6. Focus assessment on gathering evidence that can inform instruction and provide a variety of ways for students to demonstrate what they know.
7. Support each other in their efforts to create and sustain this type of instruction.

This is taken from the book: Math for All, Differentiating Instruction by Linda Dacy & Karen Gartland.

I believe that our CTT structure can support this list and help our mathematical instruction improve. I know that some teachers lack confidence in their mathematical abilities. If you ever feel unqualified to confidently approach a concept, please reach out to your CTT, Cami Parry, or myself for help.

Quickwrites 

A quick, effective way for students to recall and understand what they know is to have them engage in a brief writing exercise called a Quickwrite. This strategy helps students access prior knowledge and discover what they already know.  

When a student writes, he/she is thinking critically. One way to engage students in writing is the quickwrite, a one- to five-minute response to a prompt that helps students access their prior knowledge on a topic or record ideas on a stated topic. Quickwrites are focused and yet not threatening, because they are short, and students are usually responding to a prompt that stimulates their thinking.

Quickwrite responses can be categorized into four types: 

1. application of a concept, 
2. imaginative ideas, 
3. offering an opinion, and 
4. justifying a point of view 

The key to successful quickwrites is interesting the students in the prompt so that they provide thoughtful responses.

You might ask students to:

• Summarize an experiment they design or a piece of literature/reading.
• Justify a point of view.
• Draw conclusions from a demonstration, lab, or event.
• Write about their background knowledge or learning process for new material.
• Respond to an open-ended question. 
• Describe or explain a process. 

My Favorite AVID Strategy!

Welcome back to school! 
Probably my favorite AVID strategy is 10-2-2.

Why?
10-2-2 Chunks your lesson into manageable bites for students.
Slow the lesson down-just a bit.  Students need time to process. Think about it, you are talking and writing and discussing.  Students have to hear the information, process it, decide what should go in their notes, and write it down, not to mention spelling and organization of what they write.  That is a lot of brain usage in a short amount of time. 10-2-2 gives students a chance to stop and think about what was just said, do they really understand it? It also provides time for collaboration and interaction with the students' notes.  Even with younger students who may not be writing anything down, it gives an opportunity to discuss what just happened with a partner. A brief description is below. You can find the pdf instructions on the team drive (link below). Feel free to change it up to meet your students' individual needs and capabilities.  The whole point is to give students a chance to pause and think about what just happened.

Getting WICOR into your lesson: this strategy uses Writing, Organization, Collaboration (possibly even a little Inquiry and Reading sprinkled in as well, depending on the usage).

10-2-2 

(pdf with details can be found in the AVID Strategies and Resources Team Drive)

The structure involves the following:

• 10 minutes: Presenting information/note-taking
• 2 minutes: Processing information
• Students pair up to share their notes, fill in gaps and identify questions.
• Students could work in partners to answer a question relating to what was just discussed or an activity that was just completed.
• 2 minutes: Summarizing information
• After partnering, students work alone to write a brief (1 sentence) summary of just that chunk.  Students can share their summaries to lead to more discussion as a class.