Desired Results
Having the ability to communicate what is inside a mind to an outside entity is at the heart of every discipline of learning and essentially is what the world is built on. People who can do this well, who can take their understanding, their learning, and transform it in some way so that others who come into contact with their ideas are they themselves transformed, are often able to find fulfillment specifically because they know they have made an impact on this world. It takes hard work, and both sides of the brain have to work together to create such communication.
My big idea is to provide opportunities for students to build their understanding of difficult, often abstract and hidden in the physical world, concepts and then to guide them through the process of making that knowledge visible to others. Seeing patterns and building blocks that are obscured in the visible world that we inhabit is not something that comes naturally to most, if not all, students. I want to give students the confidence to take the inert, head knowledge that so often accompanies mathematics instruction and create a visible display of that understanding through whatever media is able to convey the message most efficiently.
In his article in the Journal of Mathematics Education Leadership, Randall Charles gives several ways to group mathematics instruction. I have selected four core pieces of mathematic instruction that I would like to focus on:
These are all tough concepts for students to master within the subject of math, and they have an even more difficult time seeing how they connect to disciplines across the curriculum or in their own lives.
Using these three main concepts, I will focus in on the use of variables, ratios, and measurement. My ImagineIt project will have 3 iterations throughout the year. I am excited to see where the creativity of my students will take them as they #MAKEITVISIBLE!
Charles, Randall. "Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics." Journal of Mathematics Education Leadership 7.3 (2005): 9-24. Jaymctighe.com. Web. 6 Aug. 2015. <http://jaymctighe.com/wordpress/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf>.
My big idea is to provide opportunities for students to build their understanding of difficult, often abstract and hidden in the physical world, concepts and then to guide them through the process of making that knowledge visible to others. Seeing patterns and building blocks that are obscured in the visible world that we inhabit is not something that comes naturally to most, if not all, students. I want to give students the confidence to take the inert, head knowledge that so often accompanies mathematics instruction and create a visible display of that understanding through whatever media is able to convey the message most efficiently.
In his article in the Journal of Mathematics Education Leadership, Randall Charles gives several ways to group mathematics instruction. I have selected four core pieces of mathematic instruction that I would like to focus on:
- VARIABLE: Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.
- EQUATIONS & INEQUALITIES: Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.
- COMPARISON: Numbers, expressions, and measures can be compared by their relative values.
- MEASUREMENT: Some attributes of objects are measurable and can be quantified using unit amounts.
These are all tough concepts for students to master within the subject of math, and they have an even more difficult time seeing how they connect to disciplines across the curriculum or in their own lives.
Using these three main concepts, I will focus in on the use of variables, ratios, and measurement. My ImagineIt project will have 3 iterations throughout the year. I am excited to see where the creativity of my students will take them as they #MAKEITVISIBLE!
Charles, Randall. "Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics." Journal of Mathematics Education Leadership 7.3 (2005): 9-24. Jaymctighe.com. Web. 6 Aug. 2015. <http://jaymctighe.com/wordpress/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf>.
Performances of Understanding
#MAKEITVISIBLE. In my ImagineIt project, I see the term “understanding” having two facets, as defined by Wiggins and McTighe. They define it as, "Understanding as meaningful inference" and as "transferability." (Wiggins and McTighe, 5) First, students can understand if they can demonstrate their understanding by making connections. Understanding is also the ability to use knowledge in different ways, or, in other words, to be able know which skills and tools to use in a given situation or scenario and apply those skills effectively and efficiently. To demonstrate their understanding, students will have to make it visible in contexts beyond math learned in isolation and is decontextualized. That may seem to imply that students will have to create physical models of abstract concepts, but that is not necessarily the direction students will need to take. When given a challenge or situation,they will need to show what is happening behind their eyes, and they will have only the limitations of their own creativity to develop that performance of understanding.
To facilitate that, students will be making use of their Chromebooks. We are fortunate to have 1:1 Chromebooks in 6th grade. They will be using them to record their learning and creating an online portfolio. To create these portfolios, each child will be creating a Weebly site. For each iteration of the project, they will be publishing their progress and work. For progress, they will be creating a self-talk video where they explain their thinking once a week on the project. They will also be creating some form of visible representation of their understanding. That representation will have three phases. In the first phase, peer-assisted learning strategies will be employed. Students will be divided into heterogenous groups of 4, and then paired within those groups. These groups will collaborate daily on their learning and projects, creating a plan for their project. Mini-white boards will be used to record learning and work. Pictures will be take and uploaded to the student’s website daily. In phase 2, a teacher will provide online feedback on their plan developed in phase 1. Phase 2 will also consist of a face-to-face conference regarding the planned project. Phase 3 will consist of the implementation of the plan, and feedback will be at least once a week from the teacher, but will more likely resemble daily feedback as need arises. A final self-talk video will be used as a self-assessment as well as a summative assessment as the student discusses the project and the learning that took place.
Wiggins, G., & McTighe, J. Understanding understanding. In Understanding by Design, expanded 2nd Edition, ASCD.
To facilitate that, students will be making use of their Chromebooks. We are fortunate to have 1:1 Chromebooks in 6th grade. They will be using them to record their learning and creating an online portfolio. To create these portfolios, each child will be creating a Weebly site. For each iteration of the project, they will be publishing their progress and work. For progress, they will be creating a self-talk video where they explain their thinking once a week on the project. They will also be creating some form of visible representation of their understanding. That representation will have three phases. In the first phase, peer-assisted learning strategies will be employed. Students will be divided into heterogenous groups of 4, and then paired within those groups. These groups will collaborate daily on their learning and projects, creating a plan for their project. Mini-white boards will be used to record learning and work. Pictures will be take and uploaded to the student’s website daily. In phase 2, a teacher will provide online feedback on their plan developed in phase 1. Phase 2 will also consist of a face-to-face conference regarding the planned project. Phase 3 will consist of the implementation of the plan, and feedback will be at least once a week from the teacher, but will more likely resemble daily feedback as need arises. A final self-talk video will be used as a self-assessment as well as a summative assessment as the student discusses the project and the learning that took place.
Wiggins, G., & McTighe, J. Understanding understanding. In Understanding by Design, expanded 2nd Edition, ASCD.
Learning Experience
This will be my 8th year at Newberry Academy. We are a full lottery magnet K-8 elementary school. Most grade levels have two classes. Sixth grade, the one I will be teaching, is the anomaly. There are three classrooms, each with an enrollment of 32 students. I will be teaching three 90 minute sections of math. Traditionally, the sixth grade has been incorporated into the middle school, and our schedules would often be joined. This year, the sixth grade will be more a stand-alone entity, which will make the planning and implementing virtually everything so much simpler because we won’t have to fear messing up the schedule of multiple grades.
As mentioned in Phase 2, there are four main concepts that I want to address through the ImagineIt Project. First, the idea of comparison, specifically ratios.
The first two content big ideas focus more on the algebraic understanding for students in sixth grade. What is X? Why do we use X? What is the equal sign and how can we use it? These are all questions that need to be explored as students are beginning to encounter more abstract problems associated with the learning of algebra. To help make connections and build understanding, constructing mobiles and creating programs on Javascript will be used. Working with partners, the mobiles give a concrete representation of equality, as well as give students a chance to play with how a variable can be changed and manipulated based on the other numbers in an equation. Exposing students to Javascript will give them a chance to create variables. Then, individually,they can again play with the results of changing variables within a program. The visual representation of those changes will be a powerful learning tool as they delve into algebraic concepts.
Comparison is a very large topic in math, so my focus will be on ratios. My students have a difficult time with ratio problems for many reasons. The problems are usually situations that they have no context or background knowledge of, and they don’t see or understand the multiplicative relationship inherent in ratios. For this concept, students will be working in groups with music and architecture. In collaboration with our music teacher, students will use GarageBand and instruments to create pieces of musics that explore ratios. Students will also be working individually with ratios in their art class in terms of perspective and scale.
The third iteration of the project will focus on measurement. Specifically, using our understanding of ratio, students will be designing a scale model of a dream home, room, or structure. Individually, they will be able to use Sketchup, Google Drawing, or paper and pencil to create their models. Field Trips to the Thorne Rooms at the Art Institute of Chicago and the Great Train Story at the Museum of Science and Industry will aid in the design process.
I believe students will benefit greatly from the individual and group projects. Consistent feedback and the understanding that they can always improve upon their work will help create an environment where they can feel free to be open with their understanding and/or misunderstandings. I will be able to see whether they truly understand, or if they are still basing their understanding on a faulty foundation.
Charles, Randall. "Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics." Journal of Mathematics Education Leadership 7.3 (2005): 9-24. Jaymctighe.com. Web. 6 Aug. 2015. <http://jaymctighe.com/wordpress/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf>.
As mentioned in Phase 2, there are four main concepts that I want to address through the ImagineIt Project. First, the idea of comparison, specifically ratios.
- VARIABLE: Mathematical situations and structures can be translated and represented abstractly using variables, expressions, and equations.
- EQUATIONS & INEQUALITIES: Rules of arithmetic and algebra can be used together with notions of equivalence to transform equations and inequalities so solutions can be found.
- COMPARISON: Numbers, expressions, and measures can be compared by their relative values.
- MEASUREMENT: Some attributes of objects are measurable and can be quantified using unit amounts.
The first two content big ideas focus more on the algebraic understanding for students in sixth grade. What is X? Why do we use X? What is the equal sign and how can we use it? These are all questions that need to be explored as students are beginning to encounter more abstract problems associated with the learning of algebra. To help make connections and build understanding, constructing mobiles and creating programs on Javascript will be used. Working with partners, the mobiles give a concrete representation of equality, as well as give students a chance to play with how a variable can be changed and manipulated based on the other numbers in an equation. Exposing students to Javascript will give them a chance to create variables. Then, individually,they can again play with the results of changing variables within a program. The visual representation of those changes will be a powerful learning tool as they delve into algebraic concepts.
Comparison is a very large topic in math, so my focus will be on ratios. My students have a difficult time with ratio problems for many reasons. The problems are usually situations that they have no context or background knowledge of, and they don’t see or understand the multiplicative relationship inherent in ratios. For this concept, students will be working in groups with music and architecture. In collaboration with our music teacher, students will use GarageBand and instruments to create pieces of musics that explore ratios. Students will also be working individually with ratios in their art class in terms of perspective and scale.
The third iteration of the project will focus on measurement. Specifically, using our understanding of ratio, students will be designing a scale model of a dream home, room, or structure. Individually, they will be able to use Sketchup, Google Drawing, or paper and pencil to create their models. Field Trips to the Thorne Rooms at the Art Institute of Chicago and the Great Train Story at the Museum of Science and Industry will aid in the design process.
I believe students will benefit greatly from the individual and group projects. Consistent feedback and the understanding that they can always improve upon their work will help create an environment where they can feel free to be open with their understanding and/or misunderstandings. I will be able to see whether they truly understand, or if they are still basing their understanding on a faulty foundation.
Charles, Randall. "Big Ideas and Understandings as the Foundation for Elementary and Middle School Mathematics." Journal of Mathematics Education Leadership 7.3 (2005): 9-24. Jaymctighe.com. Web. 6 Aug. 2015. <http://jaymctighe.com/wordpress/wp-content/uploads/2011/04/MATH-Big-Ideas_NCSM_Spr05v73p9-24.pdf>.
Teacher Demonstration
For my teacher demonstration, I am going to work with the teachers and students on ratios. Specifically, we are going to use GarageBand to create some simple rhythms using two different instruments. Using those rhythms, the teachers and students will change the ratio of the different instruments and of the time signature. They will be required to create a rhythm that is 3/4, and then they can create their own rhythm. The assessment will be to give them a rhythm and they have to figure out what the ratio is. I think this will be a fun and engaging way for teachers and students to get familiar with GarageBand and to really see the power of ratios.