Differentiate
It would be ridiculous to think that the players on a baseball team would have exactly the same skills, abilities, and prior experiences. Coaches always have teams filled with players with a range of skills, experiences, and knowledge about the game. And just like students, one pitcher could have a great arm but needs to work on control, while another may know when to throw the right pitch, but can't remember where he should be on a sacrifice bunt when a guy is on third. Coaches and teachers need know where their players and students are along their targets to be able to help them improve.
High school baseball games are really just assessments of learning. During games, coaches collect data about their players and work with them on those skills during practices. Teaching is similar; teachers give students formative assessments to not only assess a students performance, but more importantly modify teaching and learning activities. Those activities will either ask students to practice skills or push students to a deeper understanding.
Summative assessments are a true assessment of learning. In my mind, a summative is the "big game." It's what you have spent weeks preparing for. A good summative assessment assesses what a student knows, understands, and can do is according to the learning targets. In a perfect world, every student should meet the standard on all the learning targets on a summative, because the teacher and student were able to redirect the student's learning along the way through formative assessments. Continuing the metaphor, this means that the team with the most wins should win the World Series! But not everything works as planned...
High school baseball games are really just assessments of learning. During games, coaches collect data about their players and work with them on those skills during practices. Teaching is similar; teachers give students formative assessments to not only assess a students performance, but more importantly modify teaching and learning activities. Those activities will either ask students to practice skills or push students to a deeper understanding.
Summative assessments are a true assessment of learning. In my mind, a summative is the "big game." It's what you have spent weeks preparing for. A good summative assessment assesses what a student knows, understands, and can do is according to the learning targets. In a perfect world, every student should meet the standard on all the learning targets on a summative, because the teacher and student were able to redirect the student's learning along the way through formative assessments. Continuing the metaphor, this means that the team with the most wins should win the World Series! But not everything works as planned...
Summative
Formative
Linear Systems - Algebra 2 - Formative
The goal of the formative assessment for the Linear Systems Unit is to see what part of the process of solving a system of equations a student can do and needs more work. The beginning of this unit should be review, but often students haven't solved a system in almost two years. After this formative, I broke the students into groups so that they could practice some of these specific skills before moving on.
Quadratics & Polynomials - Algebra 2 - Formative
The goal of the formative assessment for the unit on Quadratics is to see how well students can write equivalent quadratic equations, and factor polynomial expressions. The quadratic equations would be the latest concept taught, but factoring polynomial expressions will be a check in since the last formative. This will help guide the next couple of classes, exploring more quadratic equations and seeing if it necessary to review and practice factoring.
The goal of the formative assessment for the Linear Systems Unit is to see what part of the process of solving a system of equations a student can do and needs more work. The beginning of this unit should be review, but often students haven't solved a system in almost two years. After this formative, I broke the students into groups so that they could practice some of these specific skills before moving on.
Quadratics & Polynomials - Algebra 2 - Formative
The goal of the formative assessment for the unit on Quadratics is to see how well students can write equivalent quadratic equations, and factor polynomial expressions. The quadratic equations would be the latest concept taught, but factoring polynomial expressions will be a check in since the last formative. This will help guide the next couple of classes, exploring more quadratic equations and seeing if it necessary to review and practice factoring.
Feedback
Timely feedback is incredibly important. Ten years ago, I wouldn't have rushed to get a test or quiz corrected and handed back to my classes because I was in the mindset that grade was permanent and didn't necessarily change how students prepared for the next assessment. Now I recognize that each formative assessment not only builds my course of action for the unit but it also guides students into recognizing what skills they know and what they need to continue to practice.
One way students can get the most out of feedback is having them reflect on their own learning. Best Practices, a pedagogical mindset change that our math department started last year asks students to use structured discourse, explain mathematical reasoning, analyze mathematical evidence, and look for alternate ways to solve problems. A few times during each unit I plan to have students assess their progress on these skills as well as their habits of learning. I then give them feedback on their self-assessments allowing the students to compare their opinions on their progress and where I think they are. We do our best to provide evidence for each target. Minimally, this is a great way to get the conversation started about what students should be doing while studying mathematics.
Student Self-Reflection Assessment
One way students can get the most out of feedback is having them reflect on their own learning. Best Practices, a pedagogical mindset change that our math department started last year asks students to use structured discourse, explain mathematical reasoning, analyze mathematical evidence, and look for alternate ways to solve problems. A few times during each unit I plan to have students assess their progress on these skills as well as their habits of learning. I then give them feedback on their self-assessments allowing the students to compare their opinions on their progress and where I think they are. We do our best to provide evidence for each target. Minimally, this is a great way to get the conversation started about what students should be doing while studying mathematics.
Student Self-Reflection Assessment