Author Archives: Beverly Ford
One of the best experiences as a teacher for me is when you see a child have an “ah-ha” moment. The look on their face, their body language, their emotion. These moments bring me so much joy. I have seen so many of these moments working with 1st graders over the last few years. I was so proud of the perseverance students had as they would solve problems multiple times, growing to be confident in their responses. Now, myself and Grace Florez, an AIMS colleague and fellow contributor to this blog, have the exciting responsibility of being able to take what we have learned from the research and utilize it as we work in classrooms every day this fall. This will be a thrilling experience for us both. At the AIMS Center, we want to see this research at work in our valley classrooms before we translate it for teachers.
In my last blog, I talked about how I view learning slightly differently than before since I have come to know radical constructivism. As a radical constructivist, some essential elements of learning are perturbation and reflection. Heading back into a classroom everyday, one of my priorities will be creating the space to reflect on my decisions as the math teacher and the mathematics of my students. I know time is something teachers never have enough of, so it is important for me to explore realistic ways to reflect on both of these things. It will be interesting for me to see what I notice when I am with the students everyday. Some questions I wonder about in my own reflection are: what am I drawn to reflect on? When does my reflection lead to change? What are the ways I reflect best?
One advantage a classroom teacher has is the amount of time they interact with the student, so they can develop a scheme of that student. In other words, they know when the student is engaged or not, when they are thinking hard, and many other telling behaviors. I’m looking forward to being a teacher in the classroom again, so that I can have that knowledge of the students and be able to notice the reflective moments they are having. I just can’t emphasize enough the value of reflection in learning, so I have already warned Grace she will have to be my accountability partner to make sure it is happening. I look forward to sharing with you more about Bev and Grace’s Great Adventure in the classroom in the months ahead.
Today I want to write about how the mathematics of students helps me to see my role as a teacher and learning a bit differently. In my last few posts, I have been telling you the story of Grace. Today, I wanted to share Grace’s story because it is an example of a time where… Continue Reading
One of my favorite questions to ask a toddler is, “How old are you?” They will often proudly hold up two, three, or four fingers. Most of the time these fingers come up all at once. This is their first experience connecting a number word and their fingers and can be a foundation to building… Continue Reading
In my first blog about the Mathematics of Grace, I mentioned that by the end of our six week study she was able to answer 98 + 5. This was exciting for me because when we first interviewed her she wasn’t able to combine 19 + 3. She was limited to solving sums within 20.… Continue Reading
In my last blog I wrote about one of the first things I noticed about the mathematics of Grace. She used her fingers to solve addition situations like 7+4 by constructing more advanced finger patterns, where one finger could mean one or eleven and six fingers could mean six or sixteen. This allowed her to… Continue Reading
The mathematics of students is a powerful tool for a teacher. It allows a teacher to hypothesize what is happening in the mind of a child and plan a next step that will allow that child to construct more sophisticated understanding. Today I want to look at the mathematics of a student we call Grace… Continue Reading
Are there any dangers in training your students in the “strategy” of counting-on? After reading Dr. Les Steffe’s work, I would argue it is harmful. He calls counting-on a non-teachable scheme. This means that if you want counting-on to be meaningful for students you can present situations that would promote their construction of counting-on, but… Continue Reading
In my last blog I talked about how the research I have been studying focuses on the “mathematics of children” and I claimed that research that articulates “mathematics of children” can provide powerful tools for a teacher. Many of us experienced elementary school a long time ago and this creates a challenge for our teaching.… Continue Reading
I have had the privilege of being a part of the AIMS Center from its birth. Having been a teacher, coach, and staff developer for the last 15 years, the world of a teacher is something I have experience with. I am now called a Research Associate and my role is to be a bridge… Continue Reading
Have you ever given your students an experience with manipulatives and then found when you shifted over to a textbook that the students didn’t make the connection between the two experiences? As a curriculum developer and researcher, I am constantly looking for more ways for students to make connections from the concrete (manipulatives) to the… Continue Reading