Soar With Common Core

Mathematical Understanding - A Teacher's Guide by Stephanie Pierce

What do teachers need to know to teach for mathematical understanding?

In the newly released California CCSS Mathematical Framework, there is a chapter devoted to instructional strategies. These strategies are designed to help students learn mathematics with understanding and teacher to know how to connect knowledge they are learning to what they already know. Further these strategies support students in constructing a coherent structure for mathematical knowledge they are acquiring rather than learning a collection of facts or disconnected skills. These strategies are designed to engage students in inquiry and problem solving and for students to take responsibility for validating their ideas with evidence.

One such instructional strategy identified in the mathematical framework is Cognitively Guided Instruction (CGI). CGI is an approach to teaching mathematics rather than a curriculum program. At the core of this approach is the practice of listening to children's mathematical thinking and using it as a basis for instruction. It's a tenet of CGI that there is no one right way to solve a mathematical problem and that teachers' professional judgment is central to making decisions about how to use information about children's thinking to support and facilitate their mathematical understanding. The research on children' mathematical thinking upon which CGI is based shows that children are able to solve problems without direct instruction by drawing upon informal knowledge of everyday situations. Direct modeling is an approach in problem solving in which the child, in the absence of more sophisticated mathematical knowledge, constructs a solution to a story problem by modeling the action or structure. Children may represent their thinking with manipulatives, drawing, writing or with numbers. For example, Fred had five marbles at school. On the way home from school his friend Joey gave him some more marbles. Now Fred has eleven marbles. How many marbles did Joey give to Fred?

Students may solve this problem by counting down from eleven or by counting up from five. With the use of manipulatives students would be able to represent their thoughts for this problem multiple ways. They might make a row of five counting blocks next to a row of eleven counting blocks and then compare the difference. These types of problems are representative of CGI as an instructional approach.

Zoom Into Writing by Eileen Moreno

Getting students to understand what we mean by “More detail!” or “More description!” can be a hair-pulling experience. In their head, the detail is there. In fact, they’re probably thinking, “Whaddaya mean? I can see it clearly in my head!” Finding ways to make the power of description more concrete to our students is golden. One of the best mini-lessons I used to help my students to enrich their writing with description was by enlisting the help of a book called Zoom by Istvan Banyai. Ironically, this is a wordless picture book but it helped me to show what I meant when I told my students to either “zoom in” on a scene---add more detail---or even to “zoom out”---give the big picture more clearly. As you start on page one of the book, you are greeted by the following illustration:

Hmmm…that’s interesting. Then you turn the page and…

Oh, okay. Let’s go on to one more page…

Get the picture? (pun intended) I don’t want to ruin the ending.

With each page, the camera zooms out capturing the big picture in greater and greater detail. By the end, students sit there with mouths agape. If you prefer, you can even start from the end of the story to show the story as it zooms in. Either way, it gets the point across to students about the powerful effect of details. Once you’re finished reading the story and marveling at the detail, send your students off to their seats to zoom in/out of a scene in their writing and add it to your mini-lesson toolbox.

Zoom can be found on Amazon for only \$4.51. Istvan Banyai also made a second similar story called Re-Zoom which is also on Amazon for \$7.19 but I must admit that the original is my favorite.

(Full disclosure J I think I got this idea when I attended a Barry Lane workshop about 15 years ago and it never failed to engage my students)

SBAC Universal Tools, Designated Supports, and Accommodations for Students with Disabilities, by Hope Michel

The Smarter Balanced Assessment Consortium (SBAC) strives to provide EVERY student with a positive and productive assessment experience. Therefore, SBAC is building a framework of accessibility for ALL students, including students with disabilities and English Learners. In order to generate a fair and accurate estimate of each student’s knowledge and skills, SBAC realizes students must have appropriate universal tools, designated supports, and accommodations when needed. The level of support for each student is determined by an educational team at the student’s school site. Since the SBAC is based on the CCSS, the universal tools, designated supports, and accommodations may be different from the ones provided when students were administered STAR assessments (i.e., CSTs and CMAs). Special education staff are currently aligning the assessment information on a student's IEP with SBAC assessment information. If there are significant differences, the special education case manager/teacher will schedule an IEP meeting with parents to make appropriate changes on the IEP.

Reaching New Heights with Technology by Laura Spencer

This week, some of the participants from our innovation grants shared their successes. From kindergarten to middle school, we heard about how the inclusion of technology has transformed the classroom. In kindergarten, two teachers discussed how students were learning to use technology as a tool in much the same way adults do, and less as a gaming device. Not only are they able to find the letters on the keyboard now, but they are publishing stories with their own drawings and narrations and sharing them with classmates. Their ability to use technology to see visual representations of math concepts has resulted in an increase in skill level for all students.

At the primary grades, technology has become a way to tap in to a student’s inner writer. Because the editing process is so much easier, students no longer dread the writing process. All teachers reported an increase in writing skills, as well as students’ ability to collaborate and communicate. Research has also become an important component of the classroom. Instead of waiting a week to go to the computer lab, or asking the teacher for help, students are becoming self-directed learners and seeking out their own solutions to issues. And once they find the solution, some classrooms have started creating video tutorials so other students can learn the same information.

In the upper grades, the focus is on inquiry-based learning. Students are doing all the thinking, allowing the teacher to become more of the facilitator. As June Richards explained, the dense learning now becomes relevant and meaningful because it’s not coming from a textbook, but from interactive, online experiences. When students make the connection, they call them “OHH!” moments. It has definitely changed classroom learning.

Many of the teachers mentioned similar apps and websites that they use in their classroom. Augmented Reality was one of them – like QR codes, Augmented Reality provides a portal to more information. The difference is that QR codes use a barcode to bring a person to a website. An “aura” in augmented reality uses a photo to bring a person to any other media – video, photo, music, audio text, or a website. Students are creating auras linked to book covers to share a book review; they are linking them to their writing to share photo slideshows; and teachers are using them to create instructional tutorials attached to posters in their classroom.

Before the teachers left, they were asked what tip they would give to teachers just starting a 1:1 technology roll-out. Almost in unison, they said to “take it slow.” Pick one thing and learn it, instead of feeling like everything has to be mastered at once. One of the kindergarten teachers commented that there are times his students know more than him, so it’s important to learn from as many people and resources as possible, to include Google, Twitter, and YouTube.