Kyle+Hollenbeck

**Name:** Kyle Hollenbeck


 * Context for using the text set: **
 * The topic or unit of study for this lesson would be that of Recursion or Defining Recursive Functions. Although a topic typically covered heavily through a Combinatorics-like course, Recursion can be sprinkled into an Algebra 2 course (Algebra 2 is typically taken at some point before senior year of high school) in order to build upon students' understanding of functions. Students will want to understand and be able to solve/recognize patterns in linear and quadratic (not necessarily required but helpful) functions before this lesson. However, the lesson can technically still be completed with no prior knowledge of functions at all.

[|CCSS.MATH.CONTENT.HSF.BF.A.1.A]
 * Content Objective: **
 * Determine an explicit expression, a recursive process, or steps for calculation from a context.

[|CCSS.ELA-LITERACY.RST.9-10.3]
 * Reading/Thinking Objective: **
 * Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.


 * A. Print Resources: **
 * Text #1: Recursive Sequences **
 * Citation:
 * Roberts, Donna. "Recursive Sequences." Regentsprep.org. Regents Exam Prep Center, n.d. Web. 01 Apr. 2014. .
 * Text Summary:
 * This page steps the reader through the basics of identifying and defining recursive patterns or functions. The information is presented in a streamlined and coherent manner. Images are provided to allow students to better visualize the concept.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">I selected this text due to it being easy-to-follow, well organized, and appealing to multiple intelligences through use of both words and visuals. This text would mostly benefit students with matchup gaps and mismatches as it would help describe and/or reinforce the topic of recursion being learned in class. The diagrams provided can also allow a student to step through the examples without necessarily needing the actual text, thus making this text applicable to ELL challenges as well.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">The text could be used as a supplement for students with matchup gaps who just need a bit of extra help. It could also be a primary source to learn from by students with mismatches who are lost on the material. ELL students could benefit from the diagrams walking students through the examples.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: See attachment #1 for a copy of this text


 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #2: Yon Yonson **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">"Yon Yonson."Wikipedia. Wikimedia Foundation, 30 Mar. 2014. Web. 01 Apr. 2014. <http://en.wikipedia.org/wiki/Yon_Yonson>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This poem/song was supposedly first written roughly a century ago by Jan Jansen of Wisconson. The poem emphasizes recursion in the way that it continuously repeats itself while each verse builds off the previous.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This poem could serve as an exceptional way to express a mathematical concept to students who consider themselves mathematically challenged. It could be applicable to all three types of students as it can help provide a more well-rounded view to more comfortable students, while serving as an alternate viewpoint for students with more difficulties.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Students would be given the text in combination with Text #3 and asked to describe each and any connection they see between the two. Thus, this could serve as a warm-up type activity for the lesson.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: See attachment #2 for a copy of this text


 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #3: Recursion Poster **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Digital image. Ginchens Blog. N.p., 10 Nov. 2013. Web. 1 Apr. 2014. <http://img1.ginchen.de/wp-content/uploads/2010/03/recursion.jpg>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">A poster depicting recursion in which the image is constantly redrawn on a smaller scale within itself.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">As with text #2 this image could reach out to all three profiles in different ways by either building on knowledge or serving as an alternative route to said knowledge. Also, due to its visual explanation of the concept, this text may be helpful in conveying the concept of recursion to ELL students.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This text would be used in combination with Text #2 to serve as a warm-up activity (described under Text#2).
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: See attachment #3 for a copy of this text


 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #4: The Recursive Mind: The Origins of Human Language, Thought, and Civilization **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Corballis, Michael C. The Recursive Mind: The Origins of Human Language, Thought, and Civilization. Princeton: Princeton UP, 2011. Print.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This text emphasizes how our minds work recursively and serves to prove its point throughout the entirety of the novel. The initial chapter covers the meaning of the word recursion and its application to Math.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This text could help provide a more broad view of recursion and its application to the world. I would most likely recommend this text to students who either have a strong understanding of the concept (matchup assets) or students who feel they lack the academic knowledge to make text-to-self connections with the topic of recursion (matchup gaps).
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">The text would serve as a side-track for students who are ahead, having extra time to more deeply understand the material, as well as a relational experience for students with matchup gaps and mismatches.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: This was an over 150-page book, so I did not include it.


 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #5: Applied Combinatorics **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Tucker, Alan. Applied Combinatorics. New York: Wiley, 1980. Print.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">A textbook covering combinatorics in detail (combination math and probability) and providing a multitude of example and homework problems. Recursion is one of the many topics covered by this text.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This would serve as the main text for the lesson. Students of all three profiles would be expected to read through the material yet, should they encounter troubles (as many probably would as the text can be difficult), the other 9 texts provided in this set could help in dissecting this one.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Students would be given a one-chapter excerpt of the text on recursion and use this as the main reference text for the lesson. Problems would most likely be assigned from this book.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: This was an over 150-page book, so I did not include it.


 * <span style="font-family: Verdana,Geneva,sans-serif;">B. Media Resources **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #6: Explicit and recursive definitions of sequences **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Khan Academy. "Explicit and Recursive Definitions of Sequences." YouTube. YouTube, 15 Feb. 2013. Web. 01 Apr. 2014. <https://www.youtube.com/watch?v=KRFiAlo7t1E>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">An instructional video uploaded by Khan Academy building on student's knowledge of functions and bridging the gap between iterative and recursive functions
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Seeing as this video assumes students' knowledge of functions but serves as an introduction to recursion, I would find it a good fit for students with matchup gaps for whom this could serve as an additional source of information. Also, since the problem is spelled out for the student with numbers and narrated, this could be an alternate source for ELL students who may have difficulty with reading rather than speech comprehension
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Students would be encouraged to view the video in their free time should they have problems with the homework or understanding the material.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: []


 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #7: The LONGEST time - Numberphile **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif;">Numberphile. "The LONGEST Time."YouTube. YouTube, 18 July 2012. Web. 01 Apr. 2014. <https://www.youtube.com/watch?v=1GCf29FPM4k>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif;">The is a video discussing the longest time possible, explaining how this number was decided upon and neat tricks surrounding it.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif;">This video is applicable because the number it revolves around is 10 raised to the 10th power multiple times which could be interpreted as a form of recursion. This video could appeal to all three profiles in the way that there is not much prior math nor outside knowledge required to follow along. This does, however, tie in both real-world and math academic knowledge, thus providing all students with a broader view of recursion.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif;">I would most likely play this video during my lesson to give students a practical example of how recursion can be used to solve real-world problems. Plus, a light-hearted video such as this would help mix up class a bit.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: []


 * <span style="font-family: Verdana,Geneva,sans-serif;">C. Online interactive resources **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #8: Khan Academy **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Khan, Salman. "Khan Academy." Khan Academy. N.p., n.d. Web. 1 Apr. 2014. <http://khanacademy.org>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Khan Academy is an interactive resource for students of all ages providing knowledge on a variety of concepts. The site provides instructional videos, Q&A, practice problems, and tests which grade students and determine their appropriate content proficiency/level.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Khan Academy is exceptionally applicable to all three student profiles. Students with matchup assets can use it to excel and further their knowledge, students with matchup gaps can access and practice any information which confuses them, and those with mismatches can use the highly instructive videos as an alternative source of information. ELL learners could also benefit from the site as it has a strong overall presentation and use of visuals.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">I would push all of my students to enroll and actively participate on Khan Academy each week. One available topic on the site is Recursion along with every other imaginable Math topic covered at a high school level. The site could be used both in and out of class assuming students had access to the required technology.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: []

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 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #9: Shodor Interactive: Recursion **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">"Recursion." Shodor.org/interactive. Shodor Education Foundation Inc., n.d. Web. 01 Apr. 2014. <http://www.shodor.org/interactivate/activities/Recursion/>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This interactive site provides students with an online program allowing them to experiment with recursion. Descriptions and information regarding recursion, along with instructions on how to use the tool itself, are provided.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">The site allows students to devise their own recursive functions, putting themselves on the opposite end of the typical problem set. Students with mismatches may have difficulties, but students with matchup gaps would most likely find this application of recursion manipulation to be helpful in understanding the material. Students with matchup assets should have no problem at all using this application and could also benefit from doing so. ELL students could also benefit from the use of graphs and the reliance on trial-and-error/numbers rather than words.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">I would most likely use this site for an in-class activity. Students could work in groups, containing a variety of profiles, to design a recursive formula, graph it, explain how the two relate, and then swap values with another group who would then have to solve that recursive formula.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment:[]
 * <span style="font-family: Verdana,Geneva,sans-serif;">D. Instructional Resources **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text #10: Investigating Investment Formulas Using Recursion **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Citation:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">"Lesson Plan: Investigating Investment Activities Using Recursion."Http://ims.ode.state.oh.us/ODE/IMS/Default.asp?bhcp=1. The Ohio Department of Education, n.d. Web. 01 Apr. 2014. <http://dnet01.ode.state.oh.us/ims.itemdetails/lessondetail.aspx?id=0907f84c8053106a>.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Text Summary:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">A lesson plan for teaching recursion through the use of Investment Activities as a real-world aspect.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Rationale:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">The lesson plan is certainly well designed and appeals to multiple intelligences. All three profiles of students are addressed through the differentiated instruction portion. ELL students may find the level of vocabulary used in examples daunting, although the writer has made a note of new and difficult vocabulary pertaining to this lesson and would, as such, most likely cover this vocabulary in class.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Use of text:
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">This lesson plan is obviously designed for teachers rather than students, but I would certainly use it as a reference point when designing a lesson plan of my own regarding Recursion.
 * <span style="font-family: Verdana,Geneva,sans-serif;">Attachment: See attachment #10 for a copy of the table of contents


 * <span style="font-family: Verdana,Geneva,sans-serif;">Which texts/tasks selected for each type of learners: (indicate by listing the # of each resource selected for that population) **
 * <span style="font-family: Verdana,Geneva,sans-serif;">Students with Matchup Assets: 2,3,4,7,8,9,10
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Students with Matchup Gaps: 1,2,3,4,6,7,8,9,10
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Students with Mismatches: 1,2,3,7,8,10
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Non-native English speakers: 1,3,6,9,10


 * <span style="font-family: Verdana,Geneva,sans-serif;">Using these texts together in the classroom: **
 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">In designing my lesson plan, I would use Text 10 as a reference point as I find it to be exceptional in its instruction of Recursion. Texts 2 and 3 could be used as a warm-up activity to introduce the idea of Recursion. Text 5 would have been assigned reading for the night before (students would be instructed to mark up the text if they had trouble understanding) and reviewed in class. I would print and pass out a compilation of the diagrams provided from Text 1 and cover a few of its examples. Text 7 would be viewed in-class. Text 9 would be used for an in-class activity. Students would be encouraged to work on their own through the use of Text 8, Khan Academy, outside of class. Text 6's and Text 1's links would be provided to students should they still feel uncomfortable with the topic at the end of the lesson. Text 4 would be recommended to students seeking a broader view on the topic of Recursion.


 * <span style="font-family: Verdana,Geneva,sans-serif; line-height: 1.5;">Attachments: **
 * <span style="font-family: Verdana,Geneva,sans-serif;">**[|Text #1]**
 * <span style="font-family: Verdana,Geneva,sans-serif;">**[|Text #2]**
 * <span style="font-family: Verdana,Geneva,sans-serif;">**[|Text #3]**
 * <span style="font-family: Verdana,Geneva,sans-serif;">**[|Text #10]**