|Math 20 Math 25 Math Tips davidvs.net|
Lane Community College emphasizes the core learning outcomes it wants students to acquire.
These core learning outcomes ensure all LCC classes are worthy educational opportunities. Math 20 might be a "remedial" college class for its math content, but it is not remedial as an overall learning opportunity
An LCC student who has never thought about the core learning outcomes might feel like "I am a homework-machine, turning in one assignment after another because the college is doing things to me."
An LCC student who has spent some time thinking about the core learning outcomes can instead feel like "I am a scholar, acquiring one skill after another because I am doing things at the college."
This page lists the core learning outcomes while briefly describing how they relate to our math class.
Your task is to pick four of the 27 criteria from the core learning outcomes. Elaborate with examples and explanations about more ways those four happen in our math class. What do they mean to you? How do they help you transition from homework-machine to scholar?
You may turn in your answers on paper, but most students copy-and-paste the four criteria to which they will respond into an e-mail and type their answers.
In my descriptions below, I intentionally write only one example for each criterion. I hope to help you get started thinking, while leaving the discussion wide open for student ideas. (As one example, for the criterion involving technology I only mention the class website. You could easily write something original about calculator use or Moodle.)
Definition: Critical thinking is an evaluation process that involves questioning, gathering, and analyzing opinions and information relevant to the topic or problem under consideration. Critical thinking can be applied to all subject areas and modes of analysis (historical, mathematical, social, psychological, scientific, aesthetic, literary, etc.).
A crucial skill learned in Math 20 and Math 25 is how to sort word problems by the best approach to solve them. Does the problem contain two numbers and is asking for a unit rate (use division)? Does it contain three numbers in two parallel situations, and is asking for a fourth number (use a proporton)? Does it contain two numbers and a percent, and is asking for a third number (use a percent sentence)? Or is it a wild card problem that requires a special approach?
Our class offers advice about how to avoid common traps in word problems. Do units of time match? In a percent sentence do the numeric value and percentage come from the same part of the whole?
Many word problems require an extra final step because of their particular situation. Does a proportion problem ask for how much a numeric value changed (requiring a final subtraction step)? Does an interest problem ask for the total amount owed (requiring a final addition step)?
Most math problems in our class have more than one method for finding a solution. This can be frustrating! The math topics would indeed be simpler if there was only one best method. But even if we adopt our favorite method for each topic, being able to understand when an instructor uses a variant method on the board or a classmate uses a variant method in a study group aids comprehension and collaboration.
We do a lot of work in a study group: during review in class, as the second portion of midterms, and hopefully outside of class for homework. When group members do not agree about a problem's answer, how does the group move forward? The ability to work as a group by sharing, comparing, analyzing, brainstorming, and tutoring is an incredibly important real life skill.
This is a more personal aspect of the previous issue. When I disagree with a group member about how to solve a problem, but am certain that my method and answer are correct, how do I defend my work within the group? Or when another student asks, "I think I might really like your method of solving that problem. Please explain it to me!" how do I clarify my reasoning?
Definition: Engaged students actively participate as citizens of local, global and digital communities. Engaging requires recognizing and evaluating one's own views and the views of others. Engaged students are alert to how views and values impact individuals, circumstances, environments and communities.
Classroom diversity happens because students work towards a common goal of mastering certain math topics despite having diverse starting points: distinct backgrounds, different foundational skills, varied assumptions, disparate emotional reactions, etc. Moreover, classroom camaraderie is the valuable enthusiasm from a sense of coming-together despite these diverse starting points. Speak up in class! It not only helps the math topics get taught, it helps the classroom environment flourish.
Students in our class have different reasons to value the math and consider it practical. Classmates whose futures include jobs involving (as examples) carpentry, baking, nursing, and computer programming will favor different methods for solving problems and prefer different ways of writing the answers.
Hm. I am not sure how this applies to Math 20 or Math 25. Help me out here.
Group discussions that focus on dialectic arguments (step-by-step reasoning) instead of rhetoric (emotional persuasion) are a vital component of democracy. Exposure to situations where group members say, "We disagree but know there is a best answer for this situation. Perhaps one of us has it. Perhaps we're all currently a bit confused. But together we can solve this!" is valuable in a society whose politics is increasingly rhetoric.
In one sense mastering the math topics in our class is like preparing to be a concert pianist or competitive sprinter: at the end of the term you must be able to perform by yourself, under the pressure of knowing that your effort will be recorded and evaluated. But getting to those last few hours "on stage" should be a group effort. Classmates are teammates.
Definition: Creative thinking is the ability and capacity to create new ideas, images and solutions, and combine and recombine existing images and solutions. In this process, students use theory, embrace ambiguity, take risks, test for validity, generate new questions, and persist with the problem when faced with resistance, obstacles, errors, and the possibility of failure.
Our syllabus concludes with a section entitled Truth, Wisdom, and Encouragement that challenges students to consider what "being good at math" really means, and whether they can achieve that during the few weeks we study together.
Hm. I am not sure how this applies to Math 20 or Math 25. Help me out here.
Our class website is so amazingly, potentially helpful that it can seem overwhelming. Exploring how to use the website as a resource is a vital part of class success.
Our midterms involve revising individual work to create a superior group project.
Do I really need to say anything about this criterion relating to a math class?
Each midterm involves analyzing which mistake were made and forming a study plan that includes both which specific math topics to work on and how those will be studied.
Definition: To communicate effectively, students must be able to interact with diverse individuals and groups, and in many contexts of communication, from face-to-face to digital. Elements of effective communication vary by speaker, audience, purpose, language, culture, topic, and context. Effective communicators value and practice honesty and respect for others, exerting the effort required to listen and interact productively.
My math students can ask me (and each other) questions during class, by e-mail, or over the phone. Each has its advantages and disadvantages.
Equations are a type of "clear language". Math has its own terms and gramar. How it is arranged on the page aids clarity and comprehension in a manner very equivalent to a spoken language's nonverbal communication.
The usual greeting at local dojo is a fist bump. This proclaims that no matter how the students are at different levels in skill, experience, and strength they will strive with each other, try their best, and provide honest feedback so all will grow better quickly. The dojo is not a place for complacent contentment (a side hug instead proclaims that everyone should be comfortable with nothing in-your-face or challenging) or inventing an imaginary opponent to strive against (a high five instead proclaims that together we overcame a common foe). A math class is also ideally a "fist bump" community. Real struggles, genuine effort, and honest feedback allow students to grow as quickly as possible. Even those students not yet ready for this type of kindly crucible become closer to ready through exposure: perhaps in their next math class they will be ready.
Students turn in four samples of chapter notes. These must demonstrate an appropriate blend of definitions, narrative explanation, example problems, and self-talk commentary that works together to explain a math topic and how to study it.
When students begin a new group work project, they might lack common language. Perhaps one student was absent when a relevant topic was discussed in class. Perhaps students use different methods of solving that type of problem. But that does not stop them. As students explain how they approach the math problems, common language is established and used.
Hm. I am not sure how this applies to Math 20 or Math 25. Help me out here. (I am picturing how some students loathe fraction arithmetic and others love it because to them canceling is fun. Surely there is something deeper.)
Definition: Applied learning occurs when students use their knowledge and skills to solve problems, often in new contexts. When students also reflect on their experiences, they deepen their learning. By applying learning, students act on their knowledge.
Recall the very first criterion, about sorting word problems by the best approach to solve them. This is amazing meta-learning! Not only do we learn how to do a variety of different math skills, we learn when to do them.
Word probems have nearly endless variety. The methods of solving them contain themes (proportions, percent sentences, unit analysis, geometrical formulas, etc.) but exactly how to apply those requires adaptability and ingenuity.
For this criterion I would prefer to hear what students say, in their own words. Help me out here.