The main point of my classes is to introduce new ways of thinking, not to solve problems by a given deadline. The only way to develop a new way of thinking is to keep trying to think in different ways. Without guidance, that can be tough. A huge part of this course is providing that guidance from me and, most importantly, from other students. The challenges and reflections that will be completed are designed to guide students' thinking attempts in productive directions.

I am trying something modern with this course. My plan is to help students as much as possible become more intelligent, persistent critical thinkers and problem solvers. There are a number of ways I feel that will best help me complete this mission.

A guiding principle of my class is:
"No answer ever creates student interest, but rather a good question."

Flipped Learning
In essence, I will be making video lectures for students to watch outside or inside of class. These videos will be no longer than 5 minutes at a time. I simply cover the basics in the video. I do not give a lot of examples in the videos, rather I focus on giving students understanding about how a certain math principle is. Once the students are in class, they will be the ones that use the video lectures among other resources to solve challenges. I will act as a facilitator and, because I will not have to lecture, I can provide one-on-one or small group help when needed. Besides video lectures, students are also able to utilize other resources such as textbooks, other students, Internet resources, etc.

Click here for more information about flipped learning.

Challenge-Based Learning
I have always had an issue with how traditional math teachers showing students how to complete a certain problem. Pardon my purity of motive, but isn't this what students should be doing? Do we really want students to be repeating a process rather than understand what it means, where it came from, and how to apply it to new situations? Don't we want students struggling through problems to teach them how valuable persistence is? You probably know my answer to these questions and this is why I am following a challenge-based learning model in my classroom. My students are expected to go through the problem solving themselves to figure out their answer. What I mean by this is that students will be solving real problems and not repeat "exercises" as is the case in traditional math classes.

Real learning and understanding comes from student thinking and questions as opposed to explicitly teaching students shortcuts to their learning and understanding. Another way of putting it would be focusing not getting from point A to point B the easiest possible way, but growing from the cognitive thoughts and road bumps along the way.

Grades are information. They are not meant to show a success or failure. They are meant to communicate how well a student is understanding the content.

Research has shown that the more students concentrate on grades, the more they do NOT focus on the learning.

Growth Mindset
According to growth mindset theory, intelligence can be developed and the brain is like a muscle that can be trained. It all starts of with one's mindset. If one has a fixed mindset when it comes to learning, research has shown that students are not able to reach the full potential. On the other hand, growth mindset has been shown to increase brain activity and improve intelligence.

So how do you improve? You can do any of the following:
  • Embrace challenges - you’ll come out stronger on the other side.
  • Do not tie your success to your self-image and how you will look to others - failure is an opportunity to learn, and so no matter what, you win!
  • The only way to truly fail is to give up trying.
  • Try your best! - effort is necessary to grow and master useful skills.
  • Criticism and negative feedback are sources of information - you can change and improve; negative feedback is not directly about you as a person, but rather about current abilities.
  • Embrace the success of others - this should be seen as a source of inspiration and information.
For more information on Growth Mindset Theory, listen to a TED talk from its creator, Carol Dweck:
Another psychologist also did a TED talk discussing Growth Mindset Theory:

Student Choice = Student Voice
Students will be solving problems as they choose. Many traditional classrooms involve students being shown how to solve a problem by a teacher, then they must repeat those steps a certain amount of times until the teacher feels that enough of the class has understood. Then, the students will be assessed. For this course, I am taking it in a different direction in the following ways:
  • Students can re-assess unit tests.
  • Students will not lose points for retaking unit tests.
    • Their new score on the assessment will replace their old score.
  • Students can make-up any part of the assessment that they want.
    • The entire assessment will not have to be made up.
    • If a student messes up a section of an assessment, only that part will have to be made up.
  • In-class work (Checkpoints) are leveled by Basic, Regular, and Advanced.
    • Students can choose which problems they want to start with.
    • The leveling of questions also helps with helping the students gauge where they are at in regards to the content.
  • Ideally, checkpoints are designed for students to start with the advanced problems first. If the advanced problems are too difficult, then can move to easier problems.
    • This is different in that rather than starting with the easiest problems first, students are recommended to start with the most difficult problems first. 

The pacing of this course is designed to help you maintain a steady pace. Most students are probably conditioned to think that success in math comes from working quickly (and many times alone) and getting the right answer as efficiently as possible. However, this course is about learning to think with a focus on the process rather than the product. Students will need time to understand and assimilate new ideas. Students will need to think and reflect often. This is probably something students are not used to doing in a math class. Please remember, a steady pace is generally better than a cram session!

Collaborative Student-Centered Work Environment
Rather than focusing on the standard model of a teacher-centered classroom, I focus on the students working together to solve problems that they do not already know how to do. Students complete these problems by working in groups, experimenting with concepts, getting hints from me, working with other groups, using online resources, etc. Furthermore, once a week, I have students present problems in groups to the class. The problems are created by the students and presented as if they were teachers themselves. They also walk around the room while the students are working on the problems and help them as if they were teachers.

Habits of Mind
Most, if not all students are never going to use the math content they learn in their classes. However, they will need the positive habits that they attained while learning the math. I try to focus on the following habits in order to make my class more meaningful.

The Habits of Mind are an identified set of 16 problem solving, life-related skills, necessary to effectively operate in society and promote strategic reasoning, insightfulness, perseverance, creativity and craftsmanship. The understanding and application of these 16 Habits of Mind serve to provide the individual with skills to work through real life situations that equip that person to respond using awareness (cues), thought, and intentional strategy in order to gain a positive outcome.
  1. Persisting
  2. Managing Impulsivity
  3. Listening with Understanding and Empathy
  4. Thinking Flexibly
  5. Thinking about Thinking (Metacognition)
  6. Striving for Accuracy
  7. Questioning and Posing Problems
  8. Applying Past Knowledge to New Situations
  9. Thinking and Communicating with Clarity and Precision
  10. Gathering Data through All Senses
  11. Creating, Imagining, Innovating
  12. Responding with Wonderment and Awe
  13. Taking Responsible Risks
  14. Finding Humor
  15. Thinking Interdependently
  16. Remaining Open to Continuous Learning
Setting Goals with High Expectations
Students maximize their academic success when, from the start:
  • Teachers are clear on their expectations
  • Teachers believe in their own expectations
  • Expectations are measurable, ambitious, and meaningful
Get Buy-in from Students & Parents
To promote buy-in from students and parents, I try to:
  • Convince students they can succeed and that they want to achieve.
  • Utilize role models through fellow students in the class, upperclassmen, family members, community members, other faculty members, historical figures, athletes, musicians, etc.
  • Give positive reinforcement for student effort
  • Create a welcoming, safe environment
  • Keep parents in the loop with a newsletter sent every two weeks
  • Invest students' families and influencers