Table of Contents
Introduction
Explicit Teaching
Lesson Planning
Opening and Teaching
Reflection Activity
Re-enforcement
Re-enforcement Strategy #1: Integration into Daily Lesson Plans
Re-enforcement Strategy #2: Integration into Class Culture
Re-enforcement Strategy #3: Using Knowledge from Grade Reflections
Conclusion
Introduction
I teach and re-enforce using past knowledge in new situations in order to help students become more well-rounded and successful learners and thinkers. While teaching “using past knowledge in new situations” is something that all math teachers implicitly teach through the nature of mathematics, it is important that students learn the language to articulate that they are applying past knowledge to new situations. This increases their long-term self-awareness and self-management so that they can be aware that they have this skill when put in an unfamiliar situation in the future (Costa and Kallick, 2009, p.21). I explicitly taught my students what it meant to “use past knowledge in new situations”, and then I re-enforced the concept frequently throughout the year through multiple strategies.
Explicit Teaching
I borrowed my lesson plan very heavily from the Curriculum for the Community Schools of Vermont Students, and modified the lessons according to the needs of my own students. This is a rigorous, evidence-based curriculum for teaching the habits of mind to all ages. The curriculum, however, could still be improved upon by customizing it to the needs of my students, which is exactly what I did.
Lesson Planning
Please see the links below for the explicit teaching lesson plan and slides:
Using Past Knowledge in New Situations Lesson Plan (Click here to zoom in)
Link to Using Past Knowledge in New Situations Google Slide (click here to zoom in)
Through discussion and reflection, by students did grasp the concept that using past knowledge in new situations means that they take a past experience it, learn from it, and then apply those lessons in a future experience. When they had to make a timeline of a an event in their life, students were able to complete the task with varying degrees of success. While most students were able to describe the event they regretted, some had initial difficulties identifying the “moment where it went wrong” and reflecting accordingly. This provided for an interesting class conversation, where students acknowledged that while we learn from past situations, it can take deep and explicit reflection to figure out how to prevent making the same mistake again.
Opening and Teaching
At the beginning of the lesson, students learned the difference between being given perfect knowledge of an upcoming situation and utilizing knowledge they learned for a brand new situation. We had a class discussion in the context of something most students were familiar with, a quarterback in football.
We then discussed as a class what it would mean to use past knowledge in a new situation in math. We talked about how, for example, in elementary school students learned how to add, then how to add decimals, and now in middle school, how to add both positive and negative numbers. Students drew on past knowledge in order to understand new concepts. We also talked about how knowledge we learned in math class could be used outside of math class, such as adding and subtracting money. Knowledge they already had, how to to add and subtract decimals, could be used in a new situation.
I modeled for the class how I learned from a past mistake for a new situation. While I did not get a chance to re-take a math final I failed, I was able to learn what worked and didn’t work when I had tried to study for it. I was able to apply this knowledge for a new semester of math in order to use better study methods and bring my grade up.
Reflection Activity
This student reflected on how their grade dropped when they skipped class in the past. In future situations, they know they can use that knowledge to not skip class and instead get their grades back up.
This student reflected on how they struggled in school when they did not ask for help when they were confused. They learned to ask for help, and are now less confused since they consistently ask for help.
Learning about what it means to learn from past knowledge and apply it to a new situation takes time and practice. This lesson began the regular conversation in my class about both how mistakes are learning opportunities and how new knowledge tends to build on past knowledge.
Re-enforcement
After learning about “using past knowledge in new situations” in the context of life, students frequently began to do so in the context of math. For many math lessons, I began to have a section of the board where I asked a student to come up and write “where have I seen this before in the past?”. This helped students realize that not every lesson is “completely new”, and feel more successful with it. I frequently tied both past mathematical and life knowledge into day-to-day lessons so that students could practice this skill. Students’ achievement went up as a result of them being able to walk into each lesson viewing it as an addition to their existing knowledge instead of a brand-new concept.
Below, I have linked my general plan for re-enforcing using past knowledge in new situations:
Plan to Re-enforce Using Past Knowledge in New Situations (click here to zoom in)
Re-enforcement Strategy #1: Integration into Daily Lesson Plans
Math, by its nature, always requires that students use past knowledge in new situations. No mathematical topic is learned in isolation from past mathematical truths. When students learn how to factor, they need to use their knowledge of multiplication. When students learn about volume, they must use their knowledge of area. When students simplify expressions, they still must keep the order of operations in mind. I intentionally design my lessons to call upon past knowledge frequently, and make note in class what past mathematical and/or world knowledge we are bringing to a new lesson.
As an example of the types of lessons I develop to re-enforce using past knowledge in new situations, please see the attachments below:
Re-enforcement Lesson Plan A (Includes References, Click here to zoom in)
The first lesson plan, linked above, has students discover the area of a parallelogram by using their knowledge of the area of rectangles. Students physically cut apart parallelograms and re-arrange them as rectangles in order to develop their own algorithm. Students were very engaged in the lesson and felt empowered that they were able to discover how to find the area of a new shape on their own.
Re-enforcement Lesson Plan B (Includes References, click here to zoom in)
In the second lesson plan, linked above, students were able to use their mathematical knowledge in order to solve an open-ended mathematical question. While they knew about how to add and subtract integers, they had not applied this knowledge to a generalized proof before. This lesson required students to use their past knowledge in an unusual, open-ended question. Students enjoyed this flexible thinking and realizing that they knew more math than they had initially expected.
Students regularly complete tasks, such as the ones pictured above, that require them to apply past knowledge to a new situation. For example, in the task above, students had to take their knowledge of area and try to apply it to unfamiliar shapes. This was using past knowledge (area) in a new situation (different shapes).
Re-enforcement Strategy #2: Integration into Class Culture
I have a section of the board where we brainstorm as a class what past knowledge we can already use for this lesson. A student volunteer, as pictured, typically writes this on the board. This initial brainstorm re-enforces the norm that everyone in the class already comes with useful knowledge and that no lesson is taught in isolation from everything we already know. It is a staple of our class’s daily culture to think about “where have I seen this before?” and “what do I already know?”. This daily re-enforcement in small ways keeps “utilizing past knowledge in new situations” in the forefront of students’ minds.
Re-enforcement Strategy #3: Using Knowledge from Grade Reflections
Above, I have pictured the grade reflections students regularly completed in my class. This type of exercise encourages a growth mindset and lets them reflect on where they went right and wrong in the past in order to improve in the future. By reflecting on the past, students are able to figure out how they should improve in the future. While day-to-day lessons and class culture re-enforce this concept as it relates to mathematics, grade reflections re-enforce this concept as it relates to personal growth. Students complete these grade reflections at least twice per a quarter.
Conclusion
I explicitly taught using past knowledge in new situations through a research-based curriculum. I then regularly re-enforced in my class that we use past knowledge in new situations through my daily lesson plans, class culture, and the way in which we reflected on our grades. As a result, students came away from my class with the lifelong knowledge that they have lots of useful past knowledge from both triumphs and failures to use in new situations.
Mary (Vansuch) Silverglate 