# Author Archives: Elin Anderson

### Worth The Wait

As educators, we have all heard of the benefits of wait time after you ask students a question. In this video, you will see proof of it. At the beginning of our pilot with K-2 teachers we shared many student videos and, although they noticed a lot of student’s math behavior, they also noticed how much wait time the teacher in the video gave the student and how objective the teacher remained in their prompting. This objectivity allows students to reflect on their thinking and often time self-correct.

In the video with Natosha (pseudonym), a 2nd grader, the teacher tells her she has 47 meatballs and then she is given 8 more meatballs. The teacher then asks her how many meatballs she has altogether. She uses her fingers sequentially to count up to 55. The teacher asks her to explain more about her strategy, and she is able to share that she uses her fingers to help her track the numbers she counts until she has counted eight. The teacher then shows Natosha a bag with little cubes in it and tells her that there are 17 cubes in the bag, but we want to have 31 cubes. How many more cubes would we need to add to have 31 cubes? Natosha uses her fingers sequentially again and says 14, then says 24. Here is where thoughtful prompting on the teacher’s part leads to self-reflection and validation that it is 14. The teacher could have jumped in and said, “You were right the first time, it is 14.” By asking the student to explain how she solved the problem, Natosha recounts again using her fingers sequentially and validates for herself that the answer is 14. How much more powerful is this for students in building their autonomy as learners?

In mathematics, we too often teach concepts in a way that makes it hard for students to connect, understand and apply those concepts in mathematics. Sometimes it is better to provide students with a collection of experiences that will help them **build their own understanding** of a concept. In the video, the big idea in subtraction is that it is the inverse of addition and we can use the understanding of this concept to solve problems quickly and efficiently. As teachers we try to teach this concept to students by exposure to the patterns students see in “fact families”. Sometimes all they see is the surface pattern and do not fully understand the concept itself. Next, in the video, the teacher says, “The bag now has 31 blocks, and I took out 14, how many blocks would be left?” Easy right?! All she needs to do is think about what she just did and know its 17. That is not what happens. Natosha approaches it as a whole new problem and, for her, it is. She is eventually able to solve a subtraction problem with a smaller minuend and subtrahend because the teacher attended to her mathematical thinking and was able to present her with problems within her “sweet spot.” I am sure that Natosha will eventually build an understanding of subtraction as the inverse of addition, but it will be because of her deep understanding of number. We as teachers have to be patient because a child’s understanding is “Worth the Wait!”

### That Moment You Realize…

Have you ever had one of those “aha!” moments when the light bulb goes off, and you come to understand something that makes your whole life easier? Or better yet as a teacher, you witness your students have one of those “aha!” moments. For us, at the AIMS Center for Math and Science, we have… Continue Reading

### Creating Centers in the Classroom – Part 3

This blog is the third part of a multi-part series titled “Creating Centers in the Classroom.” If you’ve missed the previous installments, you can read part 1 HERE and part 2 HERE. As we start the new school year, many teachers will try to create an engaging learning environment that meets the needs of all… Continue Reading

### Counting is Fundamental to Mathematical Reasoning

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… Continue Reading

### Putting the Cart Before the Horse (Mathematically Speaking!)

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

### Recognizing Is Not The Same As Understanding

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

### Manipulatives as Thinking Tools

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

### It’s Just an Art Lesson…or the Best Math Lesson Ever!

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

### Sharing Can be Rigorous Work!

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

### Understanding Cognition and the Concept of Number

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