Number Talk Training

Teachers from Paine Primary recently attended a Number Talk workshop. A Number Talk is a short, ongoing daily routine that provides students with meaningful ongoing practice with computation. A Number Talk is a powerful tool for helping students develop computational fluency because the expectation is that they will use number relationships and the structures of numbers to add, subtract, multiply, and divide.  
Pictured are teachers Catherine Finkley, Penny Moore, Emily Wolfe, and Cynthia Weyerman. 

Math Practice Standards in All Subject Areas

As a math teacher, I would ask my students to write. They would complain that it was math class and they should not have to write in math. I would tell them that there's no such thing as "math day" out in the real world. Outside of school, math is integrated into everyday tasks and work tasks. While numbers in isolation are rarely useful, writing about what the numbers mean is important for clearly communicating ideas.
Mathematics is modeled in almost any field. Common Core standards ask students to do research, look at real-world contexts, make sense of the world around them, and be able to reason and justify conclusions. The eight Common Core Standards for Mathematical Practice can be applied in any subject area. Here are some suggestions for how we can all be teachers of the Common Core math standards:

1. Make sense of problems and persevere in solving them. (CCSS.MATH.PRACTICE.MP1)

Any subject area can ask students to make sense of problems. Rather than giving students step-by-step instructions where everyone's outcome is the same, pose an interesting problem or question for students to figure out the solution. The problem does not have to be a math problem -- every subject has things that students can figure out. The solutions need to be more than a quick answer. To persevere, students should work their way through solving a multi-phase problem. The answer to one part becomes information they'll need to answer the next part.

2. Reason abstractly and quantitatively. (CCSS.MATH.PRACTICE.MP2)

Use numbers to reason. All subject areas have data that can be analyzed. If teachers are posing DOK 3 and DOK 4 problems, students need to look at evidence, make sense of it, and draw conclusions. This is done with textual evidence as well as numerical data. Have students analyze the water crisis in California. Part of that is looking at the data on rainfall, crop irrigation needs, farmers' crop outputs, household water use, etc. Every class should have students looking at this data, analyzing it, making charts, and drawing conclusions.

3. Construct viable arguments and critique the reasoning of others. (CCSS.MATH.PRACTICE.MP3)

Piggybacking on the previous standard, students should defend their arguments with data that they've reviewed. Viable arguments don't have to be about numbers. Every subject should have students construct an argument. Doing peer evaluation allows each student to critique others and defend his or her own reasoning. Students can also critique the reasoning of authors of texts. This can be done in any class.

4. Model with mathematics. (CCSS.MATH.PRACTICE.MP4)

Math is present in everyday applications. How does your subject area utilize math? Whether in art, music, history, economics, or science, we all have uses for math. How are math concepts represented in your subject area? Make an effort to expose your students to the ways in which your subject area models math.

5. Use appropriate tools strategically. (CCSS.MATH.PRACTICE.MP5)

When students are faced with a problem, do they realize that they need to utilize a ruler, protractor, computer, or spreadsheet to solve it -- without your telling them? All classes can use spreadsheets to organize information. Tools do not need to be math tools specifically. In the course of their everyday lives after graduation, students will need to decide whether they should they use a text document or spreadsheet, create a flowchart or timeline, use one of many collaborative or web 2.0 tools, or punch numbers into a calculator. Now is their chance to learn the best strategic use for these tools and many others.

6. Attend to precision. (CCSS.MATH.PRACTICE.MP6)

Students tend to give vague answers, so we must work with them to be specific and back up their statements with evidence. This evidence doesn't have to be with mathematical numbers. When dealing with data and numbers, students should be able to come up with a precise answer whenever it is required.

7. Look for and make use of structure. (CCSS.MATH.PRACTICE.MP7)

Every world language has patterns and structure for students to observe and analyze. Looking for patterns and structure in history should already be occurring. In any subject area, students could be seeking patterns and structure to give them a deeper understanding of a problem.

8. Look for and express regularity in repeated reasoning. (CCSS.MATH.PRACTICE.MP8)

All students should be continually evaluating the reasonableness of their intermediate results. Throughout the process of solving any problem (not just a math problem), students look for things that repeat. When writing an essay, they're using a similar structure throughout the writing process.
As you construct your lesson plans, consider which of these eight mathematical practices you can include. Quite possibly, you're already including some of the practices in your Common Core lessons. If we want to strengthen students' reasoning and numerical literacy skills, we can't just relegate the mathematical concepts to math class. The more cross-curricular thinking we apply to our lesson plans, the more opportunity students will have to find value in what they're learning.

How do you use the Common Core math standards?


Alice Keeler is a Google Certified Teacher, New Media Consortium K12 Ambassador, Microsoft Innovative Educator and LEC Admin & Online and Blended certified. Professor of Curriculum, Instruction and Technology at California State University Fresno and Teacher on Special Assignment at ACEL Charter High school. Alice Keeler has developed and taught online K12 courses as well as the Innovative Educator Advanced Studies Certificate (cue.org/ieasc). A believer in the importance of connectivity she founded #coffeecue (cue.org/coffee) and #profchat. Masters in Educational Media Design and Technology. Doctoral student at Boise State University in EdTech with a focus on gamification. Passionate that kids are not failures, using technology to change the way we approach learning and grading. Alice tweets @alicekeeler and blogs at alicekeeler.com.

Teachers Participate in OGAP (Ongoing Assessment Project) for Math

Paine Primary math coach, Donna Brumlow and teachers Gina Lackey, Donna Walker, Jeanette Cerisano, Kay Shumate, and Beth Ann Marshall recently participated in OGAP training with other regional coaches and teachers.

The OGAP formative assessment system is based on the belief that teachers make more effective instructional decisions resulting in improved student learning when they: (a) are knowledgeable about how students develop understanding of specific mathematics concepts and about preconceptions and misconceptions that interfere with learning these concepts; (b) have tools and strategies that allow them to systematically monitor their students’ understanding prior to and during instruction; and (c) receive professional development focused on that knowledge, those tools, and those strategies. Four principles about effective instruction and assessment underlie OGAP’s design:

1. Build on students’ pre-existing knowledge. Ignoring students’ initial thinking risks students developing understandings that do not match what the teacher intended (NRC, 2001b).
2. Teach (and assess) for understanding. Because teaching for understanding “improves retention, promotes fluency, and facilitates learning related materials” (NRC, 2001b), OGAP items and tools are designed to elicit conceptual understanding.
3. Use formative assessment intentionally and systematically. Research has shown that learning gains from systematically implementing formative assessment strategies into instruction are larger than gains found for most other educational interventions (NRC, 2001a).
4. Build assessments based on the mathematics education research. A key recommendation from Knowing What Students Know (NRC, 2001a) is that assessments should be built on research on how students learn specific mathematics concepts.

OGAP is both a product and a process: professional development focuses on research about how children learn mathematics, providing a rationale for the design of the item bank and frameworks. It also shows teachers how to use those tools, and models routines that allow them to use them well.

Source: http://www.cpre.org/ogap