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Teaching Mathematics Students with Real-World Applications Stefan Baratto Clackamas CC AMATYC Conference (S178) 16 November 2014

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Skills (of course) Problem Solving (reduce fear) Critical Thinking (advance and improve)

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Technical Communication (the point of it all) Other? (barriers and anxieties)

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Learn Math Skills through Applications Learn their skills Students become more comfortable reading and solving problems Lead students to think critically about the content

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Difficulties Posed by Reading Level Developmental math & reading Relevant applications are easier to understand Difficulties Posed by Abstract Math We are not good at this

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Wason Selection Tasks Activity

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Teaches them my expectations Careful reading; critical thinking Easy, short Provides a wealth of teachable moments on the first day Especially when they ask, “what does this have to do with math?” Surprising how many get this activity wrong!

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Math is relevant, even to the developmental student Millennial generation needs relevance Finding applications that students care about and are within their abilities is a challenge

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Set of transferable skills that B&I feels that students should have when they graduate college B&I felt (1990s) that too many graduates didn’t possess these skills Some of these skills are best learned in math classes

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Communicating technical information is high on the SCANS skills list This involves the ability to read, take in, and think critically about technical writing It also involves the ability to communicate technical information This is important! It can be dull!

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Reading Percent Problems

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Relevance They all own iPods or the like; they can relate They all pay sales tax Critical Thinking Skills Rate: 107.725% If using 7.725%, then add back at the end

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Developmental Algebra Skill Distributing a negative sign always gives them trouble Easier to teach in context Distributing a Negative

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Introduce a topic with an application Demonstrate how the application requires the math they are about to learn Move to the math content, in the abstract

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Do examples; give students examples to do Return to the application and complete the math If time permits, students would have the opportunity to practice with an application, as well

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Do your students maintain their motivation when you transition to more abstract math? What have you done to help students be more successful with this skill?

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I introduce students to the basic business models of revenue, cost, and profit early in the course Students maintain their interest when we discuss these models in class I think they keep expecting me to switch to more abstract math; we don’t

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If I give students an input and ask them for profit, most students will compute the revenue and cost separately and then find the difference This works well for a single input This does not work well when constructing a model to use for many inputs Our job is to help them learn to generalize so that they can take advantage of the power of algebra

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I now allow them to find a profit by finding the difference between revenue and cost one time We talk about how they are subtracting the entire cost from the revenue They understand this

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My students gain a better understanding of the need to wrap the entire cost in parentheses More of them seem to understand that they need to distribute the negative sign to encompass the entire cost They gained a better understanding of the role of parentheses, in general

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We moved on to abstract examples More students were able to demonstrate mastery of this skill A month later, on their final exams, more students demonstrated that they had learned this well than in any other class I could remember This continues term after term

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I am stunned. And thrilled!!! I shouldn’t be This is classic Wason Test material It is still awesome!

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What works? What does not work? It is not enough to simply bring applications into the classroom Students need to be interested in the application But, inherent interest is merely a beginning

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Sometimes, I think that my students come to class just to tell me how much they hate math in general and word problems in particular Why is it that humanities and social science majors (students who “read for a living”) hate word problems?

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Teach students to read a word problem Help them discern the important “math” in a paragraph Separate the math into the parts of a problem and help students to understand how these parts fit together This is the basic challenge

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Of course, in order to motivate students, they need to find an application relevant How do you find your applications?

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Modern Items and brands Relevant Students “want” them Careers Surprises Up-to-date Prices

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Students know about gas prices and traveling Use what they know Rates

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Government National Weather Service (NWS) Bureau of Labor Statistics (BLS) National Center for Education Statistics (NCES) Commercial Amazon and Google Most popular lists Zillow Popular (upscale and trendy brands)

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Use the News Elections Events Math & Statistics

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Use what they like Math & Statistics

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Build on applications Use this same application when teaching pie charts Students understand and you do not need to completely introduce a new application Math & Statistics

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Many students who are less than strong in math see themselves as business majors. This explains a lot about our nation’s economic situation over the last decade plus Business and Finance can provide you with a rich source of applications which build one off of the other

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Speak with faculty in other disciplines on campus They know the employers that will hire their students You might be surprised at how willing they are to help Campus Data

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My students couldn’t care less about acid concentrations or alcohol solutions They do not envision themselves as chemists Nor do they care about the number of student or general admission tickets sold Count the tickets They do see themselves owning a business or in the health sciences fields

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Real-World Applications

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Have you worked with faculty in other departments to improve course content? Have you worked with them to find applications for your classroom? What careers are the developmental math students at your college likely to enter?

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Courses are sometimes jam-packed with content It is difficult getting to it all in a term without having to try and find the time to also do applications with students Do not think of apps as cutting into class time Applications and problem solving are what math is all about Apps are all about developing critical-thinking skills

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Good applications increase student interest Increased student interest increases student attentiveness Increased attentiveness increases student learning and retention

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How much of what you teach do your students actually learn and retain? Even your best students? Is it better to increase the proportion of content they learn by doing a better job with fewer topics?

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I want students to answer apps with sentences I’ve learned to actually write sentences on the board when I complete an app in class Students should write the answer to an application as a sentence This “forces” them to go back and re-read the problem “Did they ask for the discount or the original price?” Go back and see what the original question asked!

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Why is it that we assume they need help with the math (they do), but we also assume they are able to describe math in sentences? Why do we model the former but not the latter?

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Do you model what you want students to do? Do your students get to practice in class?

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Just like working with abstract math, students need classroom practice working with apps Strongly encourage students to work with their neighbors, especially when working on an application

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Students who watch us do math problems learn to watch us do math problems Always follow an instructor-led example with student work Many faculty members need to be taught this Use a computer, document camera, or hand- outs

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Give the students time to work on a problem, then ask questions about how to proceed Strongly encourage them to work with their neighbors Complete the problem for those who had trouble; write the answer as a complete sentence

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You can design these questions to elicit certain outcomes You can write a revenue problem so that they need to round up, even though the fraction part is less than a half You can write a cost problem so they need to round down, even though the fraction part is greater than a half Never pass up a teachable moment

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Teachable Moments Critical Thinking

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Do your students even reach really teachable moments when working with math in the abstract?

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Applications make the math feel important to the students They can relate to real world applications Build on an application They will feed off of your enthusiasm Working in groups gives the class a community feel and spirit

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Thank you for joining and participating Please Email me with thoughts, ideas, comments, or to request these files Stefan Baratto sbaratto@clackamas.edu Clackamas Community College Oregon City, OR Thank you for your hospitality Enjoy the rest of the weekend

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