In this revision of my original lesson plan I want to evaluate my lesson in the context of the Universal Design for Learning (UDL) framework. I will first reflect on how my lesson fits within the UDL framework in it’s current state. I will then identify a set of revisions that will make it better aligned with the UDL framework, paying special attention to accommodating gifted and talented learners. UDL is an ever evolving framework that attempts to make learning as accessible as possible to as many students as possible.

**Lesson Plan in the Context of UDL (Current Form)**

The UDL framework is broken into 3 majors principles: (1) provide multiple means of representation, (2) provide multiple means of action and expression, (3) provide multiple means of engagement (Rose and Gravel, 2011).

*Multiple means of representation*

In it’s initial form my lesson only uses one or two means of representation. The main lesson is me talking at the whiteboard. This is fairly one dimensional and only provides representation through the visual means of accessibility. In addition, this leverages only one medium (text). This is problematic since the text medium creates barriers for some students (Rose and Gravel, 2011). I will consider ways to alleviate this shortcoming below. I also need to look at the ways in which I’m supporting transfer of knowledge to new problems in the context of calculus. Ultimately my goal is not to simply have this concept exist in isolation, but to make it so that students can effectively apply it outside of the lesson.

Even though this lesson only provides for primarily visual/text accessibility, there are other aspects of the principle that I do effectively. From the front of the room I do a very solid job of being explicit about the meaning of notation. It’s important to make sure everyone understands the symbols and notation that we’ll be using throughout the lesson. I also build on prior knowledge at the beginning of my lesson in order to help bring context to the concept. Barriers to learning occur whenever students either lack background knowledge, or have background knowledge that they don’t know is valuable to learning a particular concept (Rose and Gravel, 2011).

*Multiple Means of Action and Expression*

One aspect of this principle that I want to focus on improving is providing options for expression and communication. I currently have students expressing their knowledge collaboratively through the mega whiteboard activities and through their daily assignment. These are largely written means and some students can better express their knowledge through different means (Rose and Gravel, 2011). I will outline ideas for improving this aspect of my lesson below.

Another aspect of this principle that I do well at certain points during the lesson, but worse at other points is enhancing students capacity for monitoring progress. I think the beginning of the lesson needs a new technique for providing feedback on students immediate understanding and for helping students provide themselves with feedback. When students break into group work I do a much better job at listening to conversations and providing quick feedback. Students will also get feedback from their peers during this time.

*Multiple Means of Engagement *

This final principle of the UDL model, in the context of my original lesson, needs to be greatly improved. I currently provide very little to motivate the lesson, besides emphasizing the importance of the fundamental theorem in the context of calculus. If the information I’m presenting does not engage students in some meaningful way it “is in fact inaccessible” (Rose and Gravel, 2011). The lesson does not currently provide students much choice in terms of assessment, timing of tasks, or tools for gathering and contracting information.

The UDL framework also encourages fostering collaboration and communication. I do a fair job of this in the lesson. The group work time helps foster collaboration and communication. In addition students are asked to reflect on and communicate their ideas via a reflective blog post. The instructions for this blog post may be too vague, however.

**Revisions to Current Lesson Plan, Based on UDL Framework**

*Multiple Means of Representation*

In order to alleviate the fact that my lesson is fairly one-dimensional in terms of representation, I’d like to provide some sort of graphical representation of the concept. This will be inserted prior to the proof of the fundamental theorem. Students will be given the opportunity to explore graphs that represent the fundamental theorem and then asks to draw conclusions based on their observations. The is a pedagogical choice based on Bransford, Brown, and Cocking’s book *How People Learn: Brain, Mind, Experience, and School* (1999) where they cite the difficulties students have with learning “with understanding at the start” when they don’t “take time to explore underlying concepts and to generate connections” (p. 58). A digital component will be required (computers) as the exploration will utilize a Wolfram Alpha visualization.

*Multiple Means of Action and Expression*

I want to make sure that students have multiple ways to demonstrate and approach their learning. To do this I will have students not only do an assignment, but they will also be asked to explain their reasoning on certain problems to the class. I will also be frequently asking them during the group work to explain their reasoning verbally to me. I will also be pushing them to draw out deeper conclusions that might not be initially apparent. This is supported by Linda Sheffield, PHD, in her book *The Development of Gifted and Talented Mathematics Students and the National Council of Teachers of Mathematics Standard (1994), *when she says “Top students should explore topics in more depth and draw more generalizations” (p. xx). This technique adds verbal expression to the written expression already utilized (their daily assignment, reflection blogs, and lesson follow up on the next day).

In order to better monitor student learning for myself and to help students self regulate their learning I’d like to do some sort of back channeling during the proof portion of the lesson. This will force students to reflect on their learning (metacognition) during the proof and should help them evaluate their understanding. Students “need feedback to the degree to which they know when, where and how to use the knowledge they are learning” (Bransford et al, 1999, p. 59). Once the proof is finished I will be able to immediately give students feedback based on the backchannel. I think the best way to manage the backchannel is through a shared Google doc.

*Multiple Means of Engagement*

I want to first motivate students a bit differently. I think starting with an inquiry activity will be motivating in it’s own right. Following the inquiry activity I will discuss the implications of the fundamental theorem in the real world, just before going into the proof. This will hopefully make the lesson more relevant and therefore more engaging (Rose and Gravel, 2011).

As mentioned above, I think the blog post could use some more structure. Sheffield points out that gifted and talented students should “use and explain logical inductive and deductive reasoning” (1994, p. xvi). A good prompt for them to use in their reflection would be “What kind of inductive and deductive reasoning did you utilize in constructing your understanding of the fundamental theorem of calculus?” This will force students to reflect on *how *they came to their understanding*. *

*Conclusion*

As you can see, my revision didn’t focus so much on breaking down barriers to learning, but methods for extending and deepening learning. I have a fairly homogeneous group of students and many are gifted and talented. This lead me to focus on revisions that could better support that group.

References

Bransford, J. D., Brown, A. L., & Cocking, R. R. (1999). *How people learn: Brain, mind, experience, **and school*. Washington, D.C.: National Academy Press.

Rose, D.H. & Gravel, J. (2011). *Universal Design for Learning Guidelines (V.2.0).*Wakefield, MA: CAST.org. Retrieved from http://www.udlcenter.org/aboutudl/udlguidelines

Sheffield, L. J. (1994). *The Development of Gifted and Talented Mathematics Students and the National Council of Teachers of Mathematics Standards*. Storrs, CT: The National Research on the Gifted and Talented.

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