ELA Common Core Resources

In my quest to unpack Common Core and to develop a deeper understanding of how to teach with the new standards, I have spent many hours researching the nuances within the CCS document, and I am still in the early phases. Common Core focuses on outcomes, but not the teaching process (with the  exception of close reading). While resources to support teachers are just beginning to emerge, there are a few great websites and blogs that are already in place. Below are a few that I have stumbled across:

New York State Department of Education 

http://schools.nyc.gov/Academics/CommonCoreLibrary/default.htm

New York has provided many free resources in relation to Common Core, including sample units, support videos, and descriptions of instructional shifts mandated by the new standards.

Achieve the Core http://www.achievethecore.org

This website maps out specific lessons for doing a close read with your students at a variety of grade levels, examines how to develop text-dependent questions, and a list of websites supporting Common Core.

The Reading and Writing Project http://readingandwritingproject.com

This website is led by Lucy Calkins and provides insights on perspectives about Common Core and  resources for teachers, including checklists and text lists.

Burkins & Yaris Blog http://www.burkinsandyaris.com

These two educators, one being a published author and another being a literacy coach, provide insightful thoughts in their exploration of common core.

Read Tennessee http://www.readtennessee.org

This website unpacks reading standards for grades K-3. They go into depth of concepts, ideas, and skills that support the standards, as well as look at the language of the discipline.

North Carolina http://www.ncpublicschools.org/acre/standards/common-core-tools

North Carolina has set about unpacking all the standards for both reading and math. This is a much more superficial examination compared to Tennessee, but may be a good starting point.

Whether you have begun examining the Common Core State Standards or not, you will need to in the near future. It is a daunting task. I hope that they sites may be a support to you in your learning journey.

Discourse and Debate

As a teacher, I have spent many years developing my understanding of children in the 7-9 year old range. Now that I have my own child, I find it infinitely fascinating to watch him grow from the ground up. I suppose that was the great interest of Piaget, and in watching my son, I realize he is a unique individual with unique experiences like all children. However, watching him make mathematical sense of our world is both delightful and entertaining at times. He was a late bloomer when it comes to speaking. It wasn’t until shortly after age two that he began really expressing himself verbally, and that we could gain some insight into how he processed his world. We had spent much time counting, especially the 13 stairsteps in our house. Counting to 13 seem to come easily to him, learning three numbers at a time. What was especially interesting was when he first began speaking in 2-3 word phrases and he noticed that both of his grandmas were in the kitchen with him. He looked back and forth out them, and said with delight, “Two gras!” Since then, he has shown how he explores our world mathematically by choosing to count different objects and people. Although he may not really understand the concepts, it is fascinating to hear him use mathematical terms in his daily conversation. He has expressed numbers such as 20 1/2, 100, and 1000, and looked at objects and said, “I’m trying to find how many inches,” as he demonstrates his own form of measuring. His learning is certainly not linear, and he is absorbing far more than what I intentionally work on with him.

So how does this relate to my topic? It is through conversation that I gain insights into my son’t thinking. As a toddler, these discussions are rather short, however, questioning still plays a role. How many do you see? Which is more? How much do you want? The importance of dialogue does not change as children get older. Unfortunately, we don’t have the leisure of much one-on-one time with a classroom full of students, and it is easy to fall into the pattern of teacher talking and students “listening.” However, learning is not a passive role, and without discourse, we don’t really know what students are thinking. Conversations play a central role to eliciting student misconceptions, conjectures, and big ideas. Conversations can allow for us to probe student thinking, scratch away the surface, and develop enduring understanding. Conversations will tell us more than any test alone.

So how do we give students more time to talk? Put them in the driver’s seat. Instead of leading the lesson, pose problem situations that students can grapple with and debate. Be the facilitator, rather than the leader of the classroom conversation. And when kids really don’t agree, then organize a debate. Students love this opportunity to defend their thinking, and it forces them to analyze the nuances of the problem to develop a greater understanding. It is also memorable, which has a lasting effect.

Other tools for giving students more talk time include pair-share thinking frequently throughout a lesson, conferring with students one-on-one, in pairs, or small groups during independent work time, and strategic student share outs. When students are ready to support each other in their learning, I put them in collaborative groups to discuss their strategies and efficiency with concepts. I call these small group  activities “Math Chats.” They are differentiated cards that groups of 3-4 work with to discuss their thinking behind a concept. Students are encouraged to offer different perspectives and analyze how their strategies make the problem friendlier.

Subitizing: More Than Meets the Eye

Subitizing is a relatively new concept for me. Sadly, it is not an integrated part of the mathematics curriculum yet. Therefore, children often have little experience with subitizing. When I first learned about this concept, I thought it pertained only to kindergarten, first grade, and struggling students beyond those years. However, I have now seen that children of all ages benefit from subitizing.

What is subitizing, and why is it important? Clements and Sarama (2009) define two types of subitizing. The first, perceptual subitizing, pertains to the ability to both perceive intuitively and simultaneously the amount in small number sets. No counting is neccessary, you just know the amount when you see it. Children develop the prerequisite skills for perceptual subitization at a young age. According to Clements and Sarama, children begin naming collections of 1, 2, and 3 from ages 1-2. By age three, children can also create collections made of 1-3 objects, sometimes 4. Perceptual subitization up to a collection of 4 occurs at age four, and the recognition of sets of 5 develops at age five. To encourage the development of perceptual subitizing, parents and teachers should play snapshot games where children see an organized picture of dots, squares, and other simple geometrical shapes organized in a linear fashion for couple of seconds, then determine the number.

The second type, conceptual subitizing, relates to the ability to instantly see the parts, and join them together to make a whole. For example, given the picture of five arranged with three and two dots, a conceptual subitizer would see 3 and 2, and know that makes 5. Again, no mathematical operations may be consciously enacted, but rather, an instant recognition that the parts make that whole. As children progress, subitizing helps with the visualization of operations and mental math. Conceptual subitizing to five and ten begins at age five. By age six, children are able to conceptually subitize to 20. At this age, five and ten-frames are helpful organizers for promoting subitizing at these higher levels. Skip and counting and place value with subitization begin at age seven, and by age eight, children see multiplicative relationships, such as 5 groups of 10, and 4 groups of 3, which makes 50 and 12, so 62 dots. As you can see, children benefit from subitizing activities well into third grade and beyond. Below is a table to organize these milestones in subitizing.

Trajectory of Subitizing

Age	Type of Subitizing	Example
1-2	Precursor to subitizing: Name small collections up to 3	I see two grandmas.
3	Precursor to subitizing: Create small collections up to 3 or 4	I can count three crackers.
4	Perceptual up to 4	**** I see four stars.
5	Perceptual to 5	***   I see five stars.    **
5	Conceptual to 5	***  I see three and two **   stars. There are five stars
5	Conceptual to 10	* * * * * * * I see 3, 3, and 1, which makes 7.
6	Conceptual to 20	* * * * * * * * * * * * * I see 5, 5, and 3, so that makes 13.
7	Conceptual with place value and skip counting	I saw tens and twos, so 10, 20, 30, 32, 34.
8	Conceptual with place value and multiplication	I saw groups of tens and fours, so 5 tens makes 50, 4 fours makes 16, so 66.

All information adapted from Clements and Sarama (2009)

I encourage you to try out subitizing with your students or children. Where are they in their development? I have seen eight year olds that are conceptual with place value and multiplication, and 14-year olds who are at perceptual to 4. Experiences with numbers, both counting and visualizing, are crucial for number development, regardless of the age. Once foundations are set, subitizing can be used to teach more complex topics. I have used both subitizing and arrays to develop understanding of multiplication, algebraic properties, and division. If you are new to teaching Common Core, then my new unit on teaching multiplication using subitizing and array cards may be just for you! These cards are intended to be part of a program that also includes problem solving. You can check out my 17 page free download to see for yourself!

Clements, D.H., Sarama, J. Learning and Teaching Early Math The Learning Trajectories Approach (2009). Routledge: New York, NY.