Math 20 Math 25 Math Tips davidvs.net

Math 20 Core Learning Outcomes

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.)

The Core Learning Outcomes

Think Critically

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.).

Identify and define key issues

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?

Determine information need, find and cite relevant information

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?

Demonstrate knowledge of the context and complexity of the issue

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)?

Integrate other relevant points of view of the issue

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.

Evaluate supporting information and evidence

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.

Construct appropriate and defensible reasoning to draw conclusions

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?

Engage Diverse Values with Civic and Ethical Awareness

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.

Recognize and clarify personal values and perspectives

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.

Evaluate diverse values and perspectives of others

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.

Describe the impact of diverse values and perspectives on individuals, communities, and the world

Hm. I am not sure how this applies to Math 20 or Math 25. Help me out here.

Demonstrate knowledge of democratic values and practices

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.

Collaborate with others to achieve shared goals

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.

Create Ideas and Solutions

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.

Experiment with possibilities that move beyond traditional ideas or solutions. Embrace ambiguity and risk mistakes

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.

Explore or resolve innovative and/or divergent ideas and directions, including contradictory ideas

Hm. I am not sure how this applies to Math 20 or Math 25. Help me out here.

Utilize technology to adapt to and create new media

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.

Invent or hypothesize new variations on a theme, unique solutions or products; transform and revise solution or project to completion

Our midterms involve revising individual work to create a superior group project.

Reflect on successes, failures, and obstacles

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.

Communicate Effectively

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.

Select an effective and appropriate medium (such as face-to-face, written, broadcast, or digital) for conveying the message

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.

Create and express messages with clear language and nonverbal forms appropriate to the audience and cultural context

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.

Organize the message to adapt to cultural norms, audience, purpose, and medium

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.

Support assertions with contextually appropriate and accurate examples, graphics, and quantitative information

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.

Attend to messages, check for shared meaning, identify sources of misunderstanding, and signal comprehension or non-comprehension

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.

Demonstrate honesty, openness to alternative views, and respect for others' freedom to dissent

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.)

Apply Learning

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.

Connect theory and practice to develop skills, deepen understanding of fields of study and broaden perspectives

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.

Apply skills, abilities, theories or methodologies gained in one situation to new situations to solve problems or explore issues

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.

Yes.

Integrate and reflect on experiences and learning from multiple and diverse contexts

For this criterion I would prefer to hear what students say, in their own words. Help me out here.