Author Archives: Elin Anderson
As I write this, The AIMS Center for Math and Science Education is in the final stages of planning and preparing for the kick-off of our pilot program with Kindergarten through Grade 2 teachers. We will start with a week of professional learning this summer. In the midst of synthesizing all that we have been reading and learning, I have been thinking about how to connect what we are doing to the Common Core Mathematics Practice Standards, in particular, Math Practice 2: “Reason abstractly and quantitatively.” Sometimes the eight practices seem a little nebulous because they try to communicate the “habits of mind” we want to instill in our students during mathematics instruction, and the practices encompass Kindergarten through 12th grade. What this practice looks like in kindergarten is very different than what it would look like in 12th grade. I wanted to know more so I decided to look at the California Framework for Mathematics, specifically the separate chapters for TK, Kindergarten, Grade 1 and Grade 2 to see what they say. When I looked at the first couple of sentences from each grade level description on Math Practice 2: Reason abstractly and quantitatively I noticed something interesting. See below:
Transitional Kindergarten: Counting things for a reason—or just to get better at it—is important. Young students love to count things and to practice the counting sequence.
Kindergarten: Younger students begin to recognize that a number represents a specific quantity and connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.
Grade 1 and 2: Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a representation of a problem while attending to the meanings of the quantities.
First of all, creating many meaningful opportunities for young students to count is critical in students’ development of quantitative reasoning (being able to work with and think about numbers). More importantly, it is necessary for students to have a context or reason for counting and be able to communicate that purpose to others so they start to see that math is all around them. For example, students could count to see how many pencils are in a container and connect that amount with a numeral. As students get more sophisticated with their counting they notice that there are 7 blue pencils and 8 red pencils. They might want to be able to communicate what they have counted in a more efficient way “7 blue pencils plus 8 pencils equals 15 pencils all together” or “7 + 8 = 15”. In other words, students create a symbolic representation of a problem while attending to the meanings of quantities. Believe it or not, that is a lot to hold to in a child’s mind! How can we as teachers support them in their understanding? Stay tuned for my next blog post!
In my experience as a teacher, I had many students that were learning English as a Second Language (EL). Maybe this is your experience as well, or you may have had the experience of trying to learn a second language yourself. When introducing new vocabulary around a concept, I would tap into to students background… Continue Reading
My previous blog post, “Sharing can be Rigorous Work!”, I shared that part of the work we have been doing in the last few months investigates how students develop fractional reasoning based on the work of Dr. Les Steffe. When I taught 2nd grade under the previous California Standards it included exposure to fractions where… Continue Reading
As the school year winds down, at the AIMS Center we too are wrapping up our work with students. The tasks we asked second and third graders to engage in this year had students working with various manipulatives (cubes, blocks, bags, strips, etc). This made me think about Math Practice 5: Use appropriate tools strategically.… Continue Reading
In my last blog post I wrote about how the sharing activity we are engaging second and third grade students with, although seemingly very simple, is actually very rigorous. In my observations I have been amused by how fascinated and excited the students are to be doing something where they are allowed to use glue… Continue Reading
The term “rigor” has been highlighted in education since the Common Core Standards have been adopted. The Common Core Standards have been deemed to be more rigorous and, therefore, students should be engaged in more rigorous lessons. What does it look like for students to be engaged in a rigorous task? Especially in the K-2… Continue Reading
How do children come to understand a concept? More specifically, how do they develop a concept of number? This is the underlying question to the work we do at the AIMS Center for Math and Science Education. In seeking the answer to this question, we have been reading research around cognition. Needless to say, we… Continue Reading
In my last blog entry I talked about laying the foundation for fractions in K-2 by thinking about the standard for measurement 1.MD.2 as foundational for the conceptual understanding of fractions. In this entry, I am going to talk about what it means for a student to coordinate units. The word coordinate, when used as… Continue Reading
This spring, the Coordinating Units team will begin looking into how students develop an understanding of fractions. We have been reading the research in this area done by Dr. Leslie Steffe. In his research with students he theorizes that if students have a fully developed whole number sequence and are able to use it flexibly,… Continue Reading
***This is part 5 of a series. Click the links to go back and read part 1, part 2, part 3, and part 4*** For the past four weeks our team has been sharing the Towers Task activity progression in our blog posts. Last week, Darrell shared that, as students become adept at working with… Continue Reading