SCRATCH: The Contemporary Approach to Mathematics
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Overview
Review of Related Literature
Lesson Plan 1: Scratch Intro [Day 1]
Lesson Plan 2: Creating Sprites [Day 2]
Lesson Plan 3: Activity Cards [Days 3/4]
Lesson Plan 4: Mad Libs [Day 5]
Lesson Plan 5: Rock Paper Scissors [Days 6/7]
Lesson Plan 6: Interdisciplinary Project [Days 8/9/10]
Lesson Plan 7: Group Assessments [Day 11]
Lesson Plan 8: Assessment Implementations & Finalizations [Day 12/13]
Lesson Plan 9: Presentations [Day 14]





Introduction

This unit has been designed as one that will take place in the span of 14 days. Students will first orient themselves with what constitutes the Scratch Program. Throughout the following week, students will be assigned tasks in order to orient them with many facets of the program. Following the first week, students will create storyboards for the sake of an interdisciplinary project involving Scratch as the presenting component. Students will have days to work on their own projects, in groups, and then they will have a day to assess each other’s work. Students will then receive feedback and implement changes on their projects, while finalizing the entire project Day 13. On the fourteenth day, students will present their animations, stories, and conclusions.





Review of Related Literature

If I could start my math class with literature, I would. I'd have my class read a skit displaying the latest literature on mathematics and it's place in the 21st century. I'd have them learn that it is not their fault that they're not inclined to care for it, that math has been stripped of all that is interesting. Before I start a revolt, I'd like to introduce the idea of cooperative learning­––­that is to say, I'd like for my students to know that I understand their frustration with the math curriculum, but I want them to know that I'm there to work with them through it and this is just one of the things in life that we have to get through to go on to bigger things. I want them to know that as part of my empathy for them I will strive for higher learning and will make the class as interesting and as relevant in terms of doing them a service in the realm of free thinking and creative thought. They need to be aware that math is not just to learn the formulas but also to explore thought and ideas, to create, to destroy, to imagine.
Contemporary literati state the condition of mathematics education in the following terms: “Sadly, our present system of mathematics education is precisely this kind of nightmare…In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done—I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education” (Lockhart 2009).
As an alternative, many scholars in the field of mathematics education and curriculum are seeking inventive and innovative ways of presenting information to the twenty-first century learner. Research shows that “increased inclusion of visual and kinesthetic approaches helps students make connections among various representations of underlying mathematical concepts” (Mamolo 2011). Instead of memorizing facts and formulas, students will more readily adapt to themes through the introduction of manipulatives and open-ended questions as an appealing approach to mathematics for the 21st century learner. Play, as defined by learning theorists, is “the capacity to experiment with one’s surroundings as a form of problem-solving” (Jenkins 2007). To play is to begin to conceptualize, through one’s own findings, their relation to the world around them. Psychologists and anthropologists advocate play in its natural form and moreover denote that it “is key in shaping children’s relationship to their bodies, tools, communities, surroundings, and knowledge” (Jenkins 2007).
However, while the literature dictates learning is derived from a “playful” approach, mathematics curriculum has geared toward the other end of the spectrum. Instead of playing with numbers and patterns, students have been reduced to memorizing set formulas and maintaining them in their heads until the minute after the test is over. Lockhart states, “This is why it is so heartbreaking to see what is being done to mathematics in school. This rich and fascinating adventure of the imagination has been reduced to a sterile set of ‘facts’ to be memorized and procedures to be followed. In place of a simple and natural question about shapes, and a creative and rewarding process of invention and discovery, students are treated to this: A=1/2BH” (2009).
The 21st century learner is actively engaged in a participatory culture, which is a “culture with relatively low barriers to artistic expression and civic engagement, strong support for creating and sharing one’s creations, and some type of informal mentorship whereby what is known by the most experience is passed along to notices” (Jenkins 2007). Halmos (1975) states: “The best way to learn is to do—to ask, and to do”. As a 21st century learner of mathematics, the student should be able to express him/herself in a classroom that is engaging and geared towards a participatory culture in which the student is free to engage in vocal classroom material while feeling confident enough to fail at times.
The culture of my classroom has been of one with low engagement in the material and therefore, low engagement and achievement throughout the curriculum. As a result, my focus has been on developing self-confidence within the content area. Since the culture of my classroom has been one where attendance and exam-return rates are low, I’ve directed my research towards the nurturing of self-esteem within the content area. Research shows that “there are many ways in which people can feel good or bad about themselves…thus, a child can hold negative feelings about her ability as a student but feel great about herself socially” (Levine 2002). Students in my class have continually received low marks in mathematic subjects. Levine (2002) states,
Kids who think they’re not too bright keep on thinking that way. Kids who have confidence in their intellectual abilities continue to believe so. These kinds of self-perceptions often become self-fulfilling prophesies. If you truly believe you have intellectual ability, you are more likely to demonstrate intellectual ability than if you think you don’t have any.
In essence, student ability in mathematics is tied to low self-esteem with the content area and a disengaging curriculum, which lacks manipulatives and hands on exploration of the creativity-probing subject.
A contemporary Indian mathematician states, “A great mathematical creation could be a profound and potent idea creating a fundamental and revolutionary impact by its very simplicity and elegance, or it could be a deep technical work of great complexity and ingenuity” (Dutta 2002). We want to strive for long-term learning in the classroom, that which is achieved through high standards for all students and deep, interactive engagement with the content area. Lockhart (2009) constructs an argument for the art of explanation in mathematics:
By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes.
More and more we ask ourselves why students come into Geometry and higher level math classes unprepared and undetermined. But it is us who have said they cannot learn math the way we instructors know it, so let’s just teach them the basics. But the basics don’t mean anything without the explanation that led to the result. If we want students to “proof” in Geometry, we need to show them now how to think and how to arrive to conclusions by letting them experiment with the work, not just produce a response for a grade.
Today, more and more classrooms are geared toward the 21st century learner. Students are now required to be active learners, not the passive learners of the past. MIT has invested in today’s students by creating a program called Scratch, a program for students used to make video games and interactive digital media for what they call the Creative Learner, their term for the Creative Society, a label they gave the 21st Century. Embedded within the programming language are many mathematical skills and concepts used in the math classroom. Instead, students become familiar with them through computer programming, in which the language and concepts become second hand to them. In an MIT article, Sowing the Seeds for a more Creative Society, Resnick writes:
While visiting an after-school center, I met a student who was creating an interactive game in Scratch. He didn’t know how to keep score in the game, and asked me for help. I showed him how to create a variable in Scratch and he immediately saw how he could use a variable for keeping score. He jumped up and shook my hand, saying, Thank you, thank you, thank you.” I wonder how many eighth grade algebra teachers get thanked by their students for teaching them about variables.
Students welcome mathematical concepts once they unveil the relevance to their lives, and moreover, their usefulness and power, especially when placed in context. Students don’t have a natural aggression toward the subject but they have been taught to feel disconnected from it. As a result, many math teachers are confronted everyday with the question, “why does this matter?”

In an effort to perhaps attempt to answer that question, or rather, alleviate some of the aggression towards math, Adam and I have created a Unit Plan in which students interact with Scratch and properties of Mathematics in an applied context.





Lesson Plan 1: Scratch Intro [Day 1]:


Lesson Plan 2: Creating Sprites [Day 2]:

Lesson Plan 3: Activity Cards [Days 3/4]:

Lesson Plan 4: Mad Libs [Day 5]:

Lesson Plan 5: Rock Paper Scissors [Days 6/7]:

Lesson Plan 6: Interdisciplinary Project [Days 8/9/10]:

Lesson Plan 7: Group Assessments [Day 11]:

Lesson Plan 8: Assessment Implementations & Finalizations [Day 12/13]:

Lesson Plan 9: Presentations [Day 14]:


Sample Projects




Related Readings