Article 1: “Can Kindergartners do fractions?” by Julie Cwikla
Julie Cwikla in her article “Can Kindergartners do fractions?” examines the capability of children ages 4 to 6 to understand fractions. Cwikla performed an experiment with the end goal of trying to discover how much knowledge children have of fractions before the concept of fractions is even introduced. She tests 30 students who all attend the same Montessori school. The selected students were given different problems to solve involving sharing. One problem given was “Jade wanted to share six carrot sticks with her four friends. How could she do this fairly?” The students were given paper and asked to draw their solutions to the problems as well as orally explain the problems to Cwikla. The results of the experiment showed that the younger students could easily separate the whole pieces, but struggled to separate the pieces that needed to be broken up into halves or fourths. The older students were also more likely to know the mathematical terminology such as half, fourth, and whole. Cwikla says, “The student work demonstrates that children between the ages of three and six indeed have a pre curricular understanding of fair sharing and fractions” (p.362).
Cwikla’s purpose in writing this piece is to present the findings from her experiment as well as share her discovery that young students are capable of understanding the basic fair sharing approach to fractions. She is writing to herself and her own classroom as well as other early childhood teachers and lower elementary school teachers.
This article has showed me that even though my students haven’t been officially introduced to the concept of fractions; they may still understand the basics without even knowing. I can better seen know how I can draw upon my students’ prior knowledge of sharing without them realizing that they know so much about fractions already. This article has shaped my unit in helping me realize that I need to use visuals and introduce terminology to better help my students grasp a more concrete definition of fractions.
Cwikla, J. (2014). Can kindergartners do fractions?. Teaching Children Mathematics, 20(6), 354-364. http://www.jstor.org/stable/10.5951/teacchilmath.20.6.0354
Cwikla’s purpose in writing this piece is to present the findings from her experiment as well as share her discovery that young students are capable of understanding the basic fair sharing approach to fractions. She is writing to herself and her own classroom as well as other early childhood teachers and lower elementary school teachers.
This article has showed me that even though my students haven’t been officially introduced to the concept of fractions; they may still understand the basics without even knowing. I can better seen know how I can draw upon my students’ prior knowledge of sharing without them realizing that they know so much about fractions already. This article has shaped my unit in helping me realize that I need to use visuals and introduce terminology to better help my students grasp a more concrete definition of fractions.
Cwikla, J. (2014). Can kindergartners do fractions?. Teaching Children Mathematics, 20(6), 354-364. http://www.jstor.org/stable/10.5951/teacchilmath.20.6.0354
Article 2: “Math Games Can Target Key Instruction Areas” by Nanci Smith
In her article “Math Games Can Target Key Instruction Areas”, Nanci Smith presents the impact games can have on mathematical learning. In her article she is addressing teachers to show them how beneficial games can be in math instruction, and how teachers can go about implementing games in their classroom. She talks about how beneficial games can be for students to learn mathematical concepts and ideas and how games make it easy to differentiate learning for all students. Nanci Smith provides two ways that games can benefit math instruction. “The easiest way to use games to differentiate math instruction is by offering a variety of choices within the games… Another way to use games as a vehicle to differentiating instruction is to address different students readiness levels through the games.” She clearly demonstrates how games can benefit many students of different levels.
Nanci Smith also talks about how math games can even affect the attitude students have towards math. “The biggest impact I have seen from using games in math might be in the area of affect. Suddenly students are engaged in mathematics and do not see math as the class they hate or cant do. Math becomes more fun, energetic, and cooperative.” This is the main point that struck me as I was planning my unit plan. I want my students to come away from math, excited about math and engaged. I don’t want to see me students bored in math or not excited about math, because that can just lead to negativity towards math down the road, when so many students have such a big potential to be good at math.
As I prepare my unit plan I really liked the concern that Nanci Smith brings up. She says, “One problem I have seen repeatedly with teachers who try to use games in math is that students don’t do the math correctly, but often do not know they are not. Because of this they reinforce errors and misconceptions. It is important that there is some way for students to be accountable for the way they are doing the math when playing the game.” This is definitely a concern that I have with my students, that if we play a game the students become to concerned with the competitiveness of the game and stop thinking about the math aspect. I have previously used a math game with my students and it helped keep the students engage, so I plan on incorporating varying games into my unit plan as different style of instruction.
Delisio, E. R. (March 8, 2010). Math Games Can Target Key Instruction Areas. Education World. Retrieved from http://www.educationworld.com/a_issues/chat/chat256.shtml
Nanci Smith also talks about how math games can even affect the attitude students have towards math. “The biggest impact I have seen from using games in math might be in the area of affect. Suddenly students are engaged in mathematics and do not see math as the class they hate or cant do. Math becomes more fun, energetic, and cooperative.” This is the main point that struck me as I was planning my unit plan. I want my students to come away from math, excited about math and engaged. I don’t want to see me students bored in math or not excited about math, because that can just lead to negativity towards math down the road, when so many students have such a big potential to be good at math.
As I prepare my unit plan I really liked the concern that Nanci Smith brings up. She says, “One problem I have seen repeatedly with teachers who try to use games in math is that students don’t do the math correctly, but often do not know they are not. Because of this they reinforce errors and misconceptions. It is important that there is some way for students to be accountable for the way they are doing the math when playing the game.” This is definitely a concern that I have with my students, that if we play a game the students become to concerned with the competitiveness of the game and stop thinking about the math aspect. I have previously used a math game with my students and it helped keep the students engage, so I plan on incorporating varying games into my unit plan as different style of instruction.
Delisio, E. R. (March 8, 2010). Math Games Can Target Key Instruction Areas. Education World. Retrieved from http://www.educationworld.com/a_issues/chat/chat256.shtml