Students have diverse learning styles brought on by cultural and language differences, social schema, and even psychological differences. Some learners are spatial learners, others are systematic and procedural in style, some learn best with technology, and still others learn best when manipulating their own environment. The number of students in a classroom is often equal to the number of different learning styles. Teachers have the challenging task of maximizing learning for each student by playing to these learning differences.
Goal:
I will use various teaching strategies in the classroom including using physical manipulatives, technology, and modeling with real life situations to maximize student understanding of the Utah Core Standards for Mathematics.
Goal Reflection:
Last year, I walked into an empty classroom. Even though it had previously been a math classroom, it was left bare of the essentials including calculators and rulers. It was also completely devoid of other more interesting math teacher supplies like algebra tiles, scissors, compasses, and protractors. Last year my students really struggled with factoring and completing the square because I didn't have algebra tiles to demonstrate the ideas behind the algebra. My students also struggled with transforming functions because we didn't have calculators with which to experiment transforming functions. And when it was time to perform reflections and do rotations without Miras and tracing paper to aid in the process, my students were stumped again. I used my legislative and school money and some of my own money to make an investment in the necessary supplies, and the school used Trust Lands money to buy me a set of TI Nspire calculators with Navigator communication system. With so much money invested, I promised myself I would utilize the investment by creating fun and engaging lessons that were more than just lecture and notes.
I used algebra tiles when we introduced factoring and completing the square, and occasionally would break them out when students were having a hard time adding like terms or solving equations. I used patty paper, compasses, and homemade reflecting plastic when we started our geometry unit. I used various other crafting supplies to derive the equation of a circle and understand the relationship between slopes of perpendicular lines. I also used the TI Nspire calculators to explore and understand many topics including the equation of a circle, the relationship between inscribed, circumscribed and central angles of a circle, cyclic polygons, triangle congruence, transformations of functions, and correlation coefficients just to name a few. As the year draws to a close, we will even get outside of the classroom to model real life situations involving the math we learned in class. With my College Prep students we will launch soda pop rockets and use the time in the air to determine the maximum height of the rocket. My Math 1 and Math 2 classes will collect experimental data and use it to make predictions to help a Barbie doll safely bungie jump from the second floor of the school. I have seen such an improvement in my student's understanding of these topics over last year. Not only are they more engaged, being able to physically manipulate their learning tools is very powerful to increasing their depth of knowledge as these activities develop concepts rather than mathematical procedures. I am excited to continue to develop more activities like this to engage more learning styles.
I used algebra tiles when we introduced factoring and completing the square, and occasionally would break them out when students were having a hard time adding like terms or solving equations. I used patty paper, compasses, and homemade reflecting plastic when we started our geometry unit. I used various other crafting supplies to derive the equation of a circle and understand the relationship between slopes of perpendicular lines. I also used the TI Nspire calculators to explore and understand many topics including the equation of a circle, the relationship between inscribed, circumscribed and central angles of a circle, cyclic polygons, triangle congruence, transformations of functions, and correlation coefficients just to name a few. As the year draws to a close, we will even get outside of the classroom to model real life situations involving the math we learned in class. With my College Prep students we will launch soda pop rockets and use the time in the air to determine the maximum height of the rocket. My Math 1 and Math 2 classes will collect experimental data and use it to make predictions to help a Barbie doll safely bungie jump from the second floor of the school. I have seen such an improvement in my student's understanding of these topics over last year. Not only are they more engaged, being able to physically manipulate their learning tools is very powerful to increasing their depth of knowledge as these activities develop concepts rather than mathematical procedures. I am excited to continue to develop more activities like this to engage more learning styles.
Evidence:
This image and lesson plan show my use of manipulatives in the math classroom to help students understand complicated algebraic concepts. The algebra tiles are used throughout the year during class and especially in after school tutoring sessions. I allow students the use of algebra tiles on tests and quizzes to accommodate learner differences. |
Below you see evidence of the same lesson taught multiple ways. Once using paper and scissors to physically manipulate right triangles to obtain the equation of a circle. Again using TI Nspire calculators to virtually create infinitely many right triangles with a hypotenuse that is 6 units. The combination of these infinite right triangles trace out a circle with a radius of 6. |
Reflection:
No two students learn and comprehend in exactly the same way. By providing multiple methods of instruction, I am able to keep more students engaged and motivated to learn. In a scheduled observation with the principal, the class worked with algebra tiles to factor and complete the square before developing an algebraic strategy. Principal Hamm was very impressed with my use of math manipulatives in a secondary classroom.
Although there is something very valuable gained from holding and manipulating something in your hand, technology is also a very powerful tool to explore mathematical relationships, and I have great student engagement any time I do calculator activities. In a surprise observation with a district mentor, the mentor noticed 96% of my students were engaged in my lesson, which involved a calculator activity. She was impressed to see such engagement in a math classroom, but the truth is I was appealing to a wider audience by using technology to explore triangle congruence than if I were to just lecture to a bored class.
These calculator activities, algebra tile lessons, or other hands-on activities usually seem to be the most memorable lessons for students. Later when students struggle with a related concept, I remind them of the algebra tiles or the calculator activity, and the light bulbs in their heads turn on as they relate the physical or technological manipulative to the algebra in front of them. I did not have these tools available to me during my first year of teaching, and I have seen much better results in student understanding my second year of teaching as I have used these tools. Furthermore, using the TI Nspire calculators as manipulatives serves to prepare students a bit better for the haptic-style questions they encounter on the SAGE test, which is a great added bonus.
Although there is something very valuable gained from holding and manipulating something in your hand, technology is also a very powerful tool to explore mathematical relationships, and I have great student engagement any time I do calculator activities. In a surprise observation with a district mentor, the mentor noticed 96% of my students were engaged in my lesson, which involved a calculator activity. She was impressed to see such engagement in a math classroom, but the truth is I was appealing to a wider audience by using technology to explore triangle congruence than if I were to just lecture to a bored class.
These calculator activities, algebra tile lessons, or other hands-on activities usually seem to be the most memorable lessons for students. Later when students struggle with a related concept, I remind them of the algebra tiles or the calculator activity, and the light bulbs in their heads turn on as they relate the physical or technological manipulative to the algebra in front of them. I did not have these tools available to me during my first year of teaching, and I have seen much better results in student understanding my second year of teaching as I have used these tools. Furthermore, using the TI Nspire calculators as manipulatives serves to prepare students a bit better for the haptic-style questions they encounter on the SAGE test, which is a great added bonus.