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.

Closing a lesson - an alternative to exit tickets

Many teachers have implemented exit tickets, which are are great closure to a class and a great way to check for understanding.  If you are interested in changing it up a bit now and then, here are some ideas.  Many of these ideas can also be used inside the lesson for quick reviews and breaks.

Teachers use closure to:

• Check for understanding and inform subsequent instruction
• Emphasize key information
• Tie up loose ends
• Correct misunderstandings

Students find closure helpful for:

• Summarizing, reviewing, and demonstrating their understanding of major points
• Consolidating and internalizing key information
• Linking lesson ideas to a conceptual framework and/or previously-learned knowledge
• Transferring ideas to new situations

Like contracting your bicep at the top of a dumbbell curl, closure squeezes an extra oomph into a lesson. See my favorite closure strategies below!

Creative Closure Activities

1. Snowstorm

Students write down what they learned on a piece of scratch paper and wad it up. Given a signal, they throw their paper snowballs in the air. Then each learner picks up a nearby response and reads it aloud.

2. High-Five Hustle

Ask students to stand up, raise their hands and high-five a peer -- their short-term hustle buddy. When there are no hands left, ask a question for them to discuss. Solicit answers. Then play "Do the Hustle" as a signal for them to raise their hands and high-five a different partner for the next question. (Source: Gretchen Bridgers)

3. Parent Hotline

Give students an interesting question about the lesson without further discussion. Email their guardians the answer so that the topic can be discussed over dinner.

4. Two-Dollar Summary

Kids write a two-dollar (or more) summary of the lesson. Each word is worth ten cents. For extra scaffolding, ask students to include specific words in their statement. (Source (PDF): Ann Lewis and Aleta Thompson)

5. Paper Slide

On paper, small groups sketch and write what they learned. Then team representatives line up and, one and a time, slide their work under a video camera while quickly summarizing what was learned. The camera doesn't stop recording until each representative has completed his or her summary.

6. DJ Summary

Learners write what they learned in the form of a favorite song. Offer extra praise if they sing.

7. Gallery Walk

On chart paper, small groups of students write and draw what they learned. After the completed works are attached to the classroom walls, others students affix Stickies to the posters to extend on the ideas, add questions, or offer praise.

8. Sequence It

Students can quickly create timelines with Timetoast to represent the sequence of a plot or historical events.

9. Low-Stakes Quizzes

Give a short quiz using technologies like Socrative, BubbleSheet, GoSoapBox, or Google Forms. Alternatively, have students write down three quiz questions (to ask at the beginning of the next class).

10. Cover It

Have kids sketch a book cover. The title is the class topic. The author is the student. A short celebrity endorsement or blurb should summarize and articulate the lesson's benefits.

11. Question Stems

Have students write questions about the lesson on cards, using question stems framed around Bloom's Taxonomy. Have students exchange cards and answer the question they have acquired.

12. So What?

Kids answer the following prompts:

• What takeaways from the lesson will be important to know three years from now?
• Why?

13. Dramatize It

Have students dramatize a real-life application of a skill.

14. Beat the Clock

Ask a question. Give students ten seconds to confer with peers before you call on a random student to answer. Repeat.

15. Find a First-Grade Student

Have kids orally describe a concept, procedure, or skill in terms so simple that a child in first grade would get it.

16. Review It

Direct kids to raise their hands if they can answer your questions. Classmates agree (thumbs up) or disagree (thumbs down) with the response.

17. CliffsNotes, Jr.

Have kids create a cheat sheet of information that would be useful for a quiz on the day's topic. (Source (PDF): Ann Sipe, "40 Ways to Leave a Lesson")

18. Students I Learned From the Most

Kids write notes to peers describing what they learned from them during class discussions.

19. Elevator Pitch

Ask students to summarize the main idea in under 60 seconds to another student acting as a well-known personality who works in your discipline. After summarizing, students should identify why the famous person might find the idea significant.

20. Simile Me

Have students complete the following sentence: "The [concept, skill, word] is like _______ because _______."

21. Exit Ticket Folder

Ask students to write their name, what they learned, and any lingering questions on a blank card or "ticket." Before they leave class, direct them to deposit their exit tickets in a folder or bin labeled either "Got It," "More Practice, Please," or "I Need Some Help!" -- whichever label best represents their relationship to the day's content. (Source: Erika Savage)

22. Out-the-Door Activity

After writing down the learning outcome, ask students to take a card, circle one of the following options, and return the card to you before they leave:

• Stop (I'm totally confused.)
• Go (I'm ready to move on.)
• Proceed with caution (I could use some clarification on . . .)

Download the PDF cards for this exercise. (Source: Eduscapes)

Discourse!

. DEVELOPING MATHEMATICAL DISCOURSE Sponsored content brought to you by Curriculum Associates

Strategies to support mathematical discourseDeveloping rich mathematical discourse in the classroom is important for building mathematical reasoning and conceptual understanding. Join us for a discussion with mathematics expert Dr. Gladis Kersaint on how teachers and administrators can support the development of productive mathematical discourse in the classroom through well-planned and well-sequenced discussions of student work.Register

Teaching Mathematics

Recently, there was a study done based on results from the Programme for International Student Assessment (PISA).  The results showed that countries who scored higher on the assessment used less memorization techniques in class.   I have linked the report as well as an article regarding memorization findings from the report below.

This supports our efforts to teach starting with the concrete level.  Students need to know how the numbers work and be able to process through problems rather than apply rules and procedures.

Article
PISA Publication