Here’s an idea for educators out there that I hope will help with answering ‘Why?’ – both for your students/parents and also for yourself. Instead of doing the classic ‘teacher thing’ and giving out a syllabus on day one, write your families a ‘Welcome Letter’ that outlines your most important beliefs (that families would do well to hear) on education and the reason your class is designed as it is. Really lay it out there – perhaps even choose a theme (as I did in the example below) and explain how each practice in your classroom contributes to that theme. I did this for my own class and found it very useful for my own understanding of my own classroom. The process even caused me to change some of the structures of my class for the better – hopefully you will encounter the same!
Here’s the letter I wrote to families about my classroom:
Welcome to Your 2019-20 Mathematics Journey
(A portion of the only 2019-20 school year you will ever have)
The goal of education is to help a society preserve humane values in the face of
economic and political interests that would be better served otherwise.
Your guide on this mathematical journey is I, mmm.
I graduated from Brown University with a degree in Biogeochemistry, and as both an environmental scientist and someone who didn’t know his multiplication tables in fourth grade, I never thought I would become a mathematics guide. But, after working in science laboratories for several years I took off on a 5,000 mile bicycle trip and learned that just talking to people was an effective way to spread environmental concerns. And, it’s fun! The natural extension of this type of communication is education.
So, I started teaching – AP Chemistry at first, and then I transitioned into mathematics because of my own experience of feeling that I was ‘bad’ at math for many years… at least, before realizing two fundamental facts. First, that anyone can learn mathematics with a knowledge of how to learn combined with requisite effort, and second, everyone – no matter what their natural aptitudes – has something to contribute to the dialogue of mathematics. It is through these two facts that I hope to invite you to learn and think about mathematics on a deeper level – not only so you can use the language and creativity of mathematics for your own personal financial benefit, but also so that you may play a part in helping to preserve humane values, whether environmental or intra-personal, in a changing world.
The vision of the RMSEL HS Mathematics program is described (in great detail) below through the medium of the ten Expeditionary Learning Design Principles.
The Primacy of Self-Discovery
We believe learning happens best with emotion, challenge, and the requisite support. People discover their abilities, values, passions, and responsibilities in situations that offer adventure and the unexpected. In mathematics students undertake tasks that require perseverance, mental fitness, craftsmanship, imagination, self-discipline, and significant achievement. A teacher’s primary task is to help students overcome their fears and discover they can do more than they think they can.
This translates into the mathematics classroom as much as it does on trips, manifesting in several ways. The first and most important way this manifests is that the classroom is at once a comfortable and uncomfortable place. This is because if the teacher’s primary task is to help students overcome fears, there must be a level of comfort for students to feel safe taking risks. Yet, on the flip side of that coin, there is no way to overcome fear without directly facing it – one step at a time. To illustrate, allow me to give a short anecdote:
I love to rock climb. Yet, a few years ago I realized that I would never actually get better as a climber unless I pushed myself outside the comfort zone and tried new things. It’s a delicate balance, though, between finding the point of eustress – positive stress that helps you grow – and cortisol-inducing stress, which can have a negative impact on learning new skills. I realized that I needed to try that challenging route and risk falling, all while not letting my mental fear interfere with my performance. I learned how to create the proper internal environment to allow challenge without anxiety. And of course, falls happen, and in the safe environment that we create by having extremely well developed protection systems, they are a fantastic learning experience.
The same thing happens in the mathematics classroom when a big test is coming up. Our students are playing with the balance between eustress and anxiety, and learning how to make the uncomfortable feel comfortable. They are risking failure, but learning how to create a mental environment in which they will succeed. Through this process, they are not only learning math – they are discovering how the body and mind they were blessed with works. They are in the process of self-discovery.
The Having of Wonderful Ideas
The mathematics classroom has two physical environments which can be thought of as separate from each other: the GroupThink Tables to the South, and the Presentation Area to the North. We believe that the GroupThink area provides space for creative thought, collaborative inspiration, and time to experiment and make sense of what is observed as well as struggle with new concepts. The presentation area provides space for subjecting ideas to a broader audience for critical review as well as an area for the whole class to learn new techniques or tools that may be useful in investigating new topics. Tools that are useful for success in both of these spaces are available (clipboards for notes to be taken in the presentation area and ‘math boxes’ with compasses, protractors, rulers, etc. in the GroupThink area).
Wonderful ideas may be had at either of these locations, or they may be had in solitude and reflection, while out on math solos (see the Solitude and Reflection section below). It is important to remember that wonderful ideas aren’t always new, they are always new to you. Sometimes the purpose of an activity is to re-create a formula that already exists – this is not a pointless endeavor! The process of innovating a formula leads to a depth of understanding unrivaled by the process of memorization! It is this depth of understanding that we seek through the curriculum used in this math course.
To support the development of this level of understanding, we focus on two differing concepts: development of the ‘mathematical toolbelt,’ and inquiry-based learning. The mathematical toolbelt represents all of the mathematical skills that students may need to use to solve an inquiry-based problem. Tools within the toolbelt include concepts like number, variable, and polynomial operations (addition/subtraction and multiplication/division), graphing, creating a table, simplifying expressions, rationalizing denominators, substitution, elimination, etc. Just as a carpenter needs to choose the proper tool for the job of building a cabinet (wouldn’t want to use a tape measure to place a nail properly…), mathematicians need to choose the proper tools for the job when engaging in inquiry-based learning. The key difference is that mathematics is often times abstractly representing reality, making it trickier at times to know if one is using the correct tool (although this comes with practice).
The Responsibility for Learning
Learning is both a personal process of discovery and a social activity. Everyone learns both individually and as part of a group. Every aspect of an EL Education school encourages both children and adults to become increasingly responsible for directing their own personal and collective learning.
The hope for educators at our school is that our seniors, after four years of engaging with the educative techniques that we offer, come to us and say with cheery excitement ‘Look at what I get to put in my portfolio! I chose this piece because […] !’ rather than [eye roll] ‘What to I have to have in my portfolio? Just tell me and I’ll get it done. Ughhh.” Everything that we do in math this year is hopefully working towards a comprehensive content understanding and that truly passionate engagement as described in the anecdote above.
To break into specifics of the course itself, two main tools allow students to take ownership of their own learning. The first is Google Classroom, which provides students with access to pertinent details on assignments like homework or projects. The second is Infinite Campus, which provides students with access to feedback on their learning success.
Announcements and Assignments for the class will be posted on Google Classroom daily (students will also have a ‘master list’ of all homework assignments), and students have the ability to check ‘done’ or ‘not done’ on various assignments, giving them an online assignment-completion tracking tool. However, students are encouraged to not rely solely on Google Classroom, as there are occasions (for example, a substitute hands out an assignment while an instructor is gone) when students will have an assignment that they are told about but that is not posted on Google Classroom. In these cases, students are still expected to complete the assignment for credit.
Grades will be posted to Infinite Campus weekly; missing assignments are also noted here. We suggest that parents and students get in the habit of checking grades together on IC weekly. Because allowing students and families to check their grades and assignments weekly encourages self-monitoring and ownership of the documentation of learning, I will not contact parents if a student’s grades are low or failing!
Once student work is graded, it is placed in a file folder on the shelf next to the sink. This allows students to have further ownership over their work as it forces them to go through the act of collecting their work. This is a small but important difference from being handed back their work!
Students are welcome and encouraged to communicate with me in a professional manner via email. In the event that an email is unprofessional (unaddressed, grammar/spelling errors, informal language, etc.) I will ask students to re-compose the email before returning their communication.
If students communicate with me in person and would like the contents of our dialogue to be communicated to parents, they may write an email that details such, send it to the parents with me carbon copied, and I will be able to respond to confirm our correspondence.
Empathy and Caring
Learning is fostered best in communities where students’ and teachers’ ideas are respected and where there is mutual trust. Learning groups are small in EL Education schools, with a caring adult looking after the progress and acting as an advocate for each child. Older students mentor younger ones, and students feel physically and emotionally safe.
The norms that we encourage in this class are based on some of Jo Boaler’s work and are listed below:
- Everyone Can Learn Math to the Highest Levels. Students are encouraged to believe in themselves. There is no such thing as a ‘math’ person. Everyone can reach the highest levels if they want to, with hard work.
- Mistakes are Valuable. Mistakes grow your brain – it is good to struggle and make mistakes. Go for it!
- Questions are Really Important. Always ask questions. Always answer questions to your highest capacity. Ask yourself: why does that make sense?
- Math is About Creativity and Making Sense. Math is a very creative subject that is, at its core, about visualizing patterns and creating solution paths that others can see, discuss, and critique.
- Math is About Connections and Communicating. Math is a subject that is intricately interconnected to all of reality. Math is also simultaneously a form of communication. Strive to represent math in different formats (like a picture, words, a graph, an equation, a table, a flip-page cartoon, etc.) and link all of the formats.
- Depth is Much More Important Than Speed. Top mathematicians, like Laurent Schwartz, think slowly and deeply. It may be impressive to solve a known problem quickly, but it’s not indicative of your aptitude.
- Math Class is About Learning Not Performing. Math is a growth subject (like learning a language – think about how long it took you to learn to speak English as a baby… and you are still learning it!). It takes time to learn, and it’s all about effort.
Success and Failure
All students need to be successful if they are to build the confidence and capacity to take risks and meet increasingly difficult challenges. But it is also important for students to learn from their failures, to persevere when things are hard, and to learn to turn disabilities into opportunities.
Of course, success and failure requires a very fine balance. Countless times I have had students ask for help in tasks as varied as putting up a tent to solving a quadratic equation, and I have helped them by only encouraging them that they can complete the task on their own! After all, students don’t build confidence from success not earned on their own, yet, they also need the encouragement that risking a mistake is worth it. There exists a parable of a butterfly struggling to escape a cocoon who has a man help him out by slightly tearing the edges of the cocoon. It turns out, little to the man’s knowledge, that the butterfly was permanently crippled because the intense struggle of his escape was the necessary prerequisite to developing the strength to fly. We must remember this with our students, avoid crippling amounts of help, and provide lots of encouragement in tough times.
Collaboration and Competition
Individual development and group development are integrated so that the value of friendship, trust, and group action is clear. Students are encouraged to compete, not against each other, but with their own personal best and with rigorous standards of excellence.
The modality we use for discourse and collaboration in this class is Dialogue, as described by David Bohm. Although the practice of Dialogue is quite extensive, it is differentiated from discussion in that during a discussion, we are (sometimes subconsciously) seeking evidence that corroborates our current perceptions of the world or listening in order to create an effective response to our speaker. Dialogue, on the other hand, requires the listener to suspend assumptions, step into the listener’s shoes, and truly attempt to understand the speaker’s point of view.
Of course, just as in life, students are not entitled to be leaders or even members of a GroupThink no matter the actions they take. Instead, other members of the group are entitled to ask members of the group not practicing Dialogue to not participate. “He who cooperates because he sees the truth as the truth, the false as the false, and the truth in the false, will also know when not to cooperate – which is equally important,” J. Krishnamurti states in Life Ahead. The development of effective individual thought within a group in dialogue is included in the Dimensions of Observable Growth (DOG) rubrics in order to track changes and progress.
Diversity and Inclusion
Both diversity and inclusion increase the richness of ideas, creative power, problem-solving ability, and respect for others. In EL Education schools, students investigate and value their different histories and talents as well as those of other communities and cultures. Schools and learning groups are heterogeneous.
Students who learn in different ways are encouraged, but usually not forced, to work together. During this time, the Dimensions of Observable Growth rubric serves as a way to track metacognition of GroupThink.
In order to address a greater range of the issues surrounding Diversity and Inclusion, I will reference the ideas of Neil Postman, who recognized that the discrepancy between reality and the human brain’s way of processing reality may give way to the idea of ‘prejudice,’ in what he refers to as ‘the photographic effect’ of language.
We live in a universe of constant process. Everything is changing in the physical world around us. We ourselves, physically at least, are always changing. Out of the maelstrom of happenings we abstract certain bits to attend to. We snapshot these bits by naming them. Then we begin responding to the names as if they are the bits that we have named, thus obscuring the effects of change. The names we use tend to “fix” that which is named, particularly if the names also carry emotional connotations.
A variation of the “photographic” effect of language consists of how blurred the photograph is. “Blurring” occurs as a result of general class names, rendering distinctions among members of the class less visible. One of the most common manifestations of the lack of this kind of semantic awareness can be found in what is called “prejudice”: a response to an individual is predetermined because the name of the class in which the person is included is prejudiced negatively. The most obvious and ordinary remark made in cases of this kind, “They are all alike,” makes the point clear.
One way that we teach this in the mathematics classroom is through GroupThink sessions (and the accompanying DOG) – we relate these somewhat philosophical and esoteric ideas to relatable situations. To paraphrase Postman’s thoughts again, we teach the fact that human biology clearly dictates that you cannot avoid making judgements, but that you can indeed become more conscious of the way in which you make them. This is critically important because once we judge someone or something we tend to stop thinking about them or it. Which means, among other things, that we behave in response to our judgements rather than to that to which is being judged. People and things are processes. Judgements convert them into fixed states. This is one reason that judgements are often self-fulfilling. The relatable context for students, of course, comes from a classroom setting. If a boy, for example, is judged as being “dumb” and a “nonreader” early in his school career, that judgement sets into motion a series of teacher behaviors that cause the judgement to become self-fulfilling. What teachers need to do then, if they are seriously interested in helping students to become good learners, is to suspend or delay judgements about students. Our students, then, can ask themselves if they have been exposed to judgements that created self-fulfilling prophecies, and can have dialogue about it. They can also practice suspending judgement themselves.
The Natural World
A direct and respectful relationship with the natural world refreshes the human spirit and teaches the important ideas of recurring cycles and cause and effect. Students learn to become stewards of the earth and of future generations.
In math, students will get outside into the natural world in several ways. Math solos (described below) are a chance for students to experience solitude and reflection while diving into a new and challenging problem. Field work is designed to capture rich and engaging problems from the world around us… which serves as the foundation for the language of mathematics.
Because the environment is our first teacher, and because much of our time is spent in the classroom environment, we hope to provide students with a practice of being environmental stewards even within the context of the indoor educational environment. By developing a sensitivity to disturbances (a declining organization of the classroom) and the responsibility to restore the environment (for example, cleaning trash from the room at the end of class), we hope to develop a transference to our outdoor pursuits.
Solitude and Reflection
Students and teachers need time alone to explore their own thoughts, make their own connections, and create their own ideas. They also need to exchange their reflections with other students and with adults in the form of Dialogue.
The following is an excerpt from Roots, ed. Emily Cousins:
If students are to tap into their own creativity, personal renewal, and thoughtfulness, schools must structure time for meaningful reflection to be valued. “I don’t retreat from the world to escape,” Robert Frost said, “but to return stronger.” Solitude is cocoon time. It helps develop powers of concentration. It requires silence, commitment, and an imaginative use of existing space. It does not cost any money; it can happen every day. Scientists and artists alike attest to the ‘click,’ the unanticipated connections they make when constructively immersed in solitude – an experience virtually unknown today in public schools.
Essential for character development, solitude and reflection also enhance academic learning. David Kolb suggests that learning requires explicit time set aside for reflecting on experience (Kolb, 1984). His work describes a learning cycle that has four key elements: concrete experience and observation, considered reflection, synthesis and abstract conceptualization, and testing of concepts in new situations. Kolb’s model is especially pertinent to the experience-based field work that makes up much of each learning expedition.
Solitude and reflection in the mathematics classroom comes partially through ‘Math Solos,’ which occur at or near the introduction of a challenging Project. Math Solos are a time where students find a peaceful spot in the park, by themselves, and begin to tackle a challenging problem on their own. This gives students the chance to develop their own ideas before engaging in collaboration with a group.
Service and Compassion
We are crew, not passengers. Students and teachers are strengthened by acts of consequential service to others, and one of an EL Education school’s primary functions is to prepare students with the attitudes and skills to learn from and be of service.
In my mind, crew is often confused with ‘family,’ when the premise of the idea derives from ships at sea. Out on the water, every crew member has a specific task that – if not completed – may cause the ship to sink. If and when one crew member is feeling sick or weak and cannot complete their task, in order for the ship to keep moving the rest of the crew must step in to support the necessary work. It is this commitment that creates familial bonds.
In the mathematics classroom, we (as a ship) have to keep moving, and it is up to the attitudes and actions of our crew members to keep us from sinking.
Components of The Vision
As you may be able to sense from the information above, you will be challenged this year to push your thinking beyond what you even knew possible! However, because the information listed above was largely the essence of how math class will run, the precise details are given below.
Class structure and physical space:
Class begins upon the ringing of the tuning rod, at which point students begin on the MindBender of the day. MindBenders consist of several problems that they may encounter on a standardized test – this is great practice for the SAT! The content of the MindBender is usually related to the content of the unit we are covering, but may occasionally be related to skills that are under-practiced. Every other day, students are in charge of creating the problem for the day’s MindBender, and after solving the problem, other students have a dialogue to understand the problem and critique the question itself. This practice serves to help students understand that all standardized tests are written by human beings with an agenda, and understanding the agenda of a test-creator can help in solving questions on the exam.
Next, the class will break into the activity for the day. Most often, the activities consist of a formal Lesson which occurs in the Presentation Area of the classroom followed by collaborative GroupThink sessions. My expectation is that students are in the Presentation Area during presentations; however, I will only invite them to this area – the choice to engage or not is ultimately theirs (see On Freedom and Discipline below).
The mathematical work you will be producing this year is what is kept track of in the ‘grading system.’ The work is a three-legged stool comprised of:
- Unit Work (Homework)
- Projects / Presentation Grades
Unit Work refers to the practice that you complete inside and outside of the classroom that serves as the necessary prerequisite to be a valuable member of the Community of Inquiry. You can think of this work as ‘Homework;’ however, the focus of the work will also be on quality and craftsmanship rather than just having completed the work ‘just to get it done.’
Therefore, 10% of the unit work grade is composed of completing the work, and additional points will be added to the Academic Content component of the grade based on the quality of the work. Quality is assessed in two ways: through Entrance or Exit Tickets from class that quiz you on a question from the homework, or by turning in a homework assignment for me to review. Upon my review of the assignment, I will return the document to the ‘Graded’ folder by the sink.
During each unit, notebook checks will be conducted and added as a component of the Unit Work grade. Notes are expected to be neat, organized, and complete (everything discussed in class copied to the notebook).
Projects / Presentations are challenging, yet creativity-oriented problems or paradoxes that you work on individually and complete a write up summary to effectively communicate your findings. Presentations are given for each of the projects by students as a modality for communicating our ideas – each student will play a part in giving one presentation per unit.
Check-in’s are a chance for students to be honest with themselves and get a grip on how well they alone understand the content of the unit. Check-in’s may come in both Standardized Practice format or in Creative Depth format. Standardized Practice format is a multiple choice exam that requires both fundamental skills and creative solutions – the purpose of this format is to help students learn how to ‘play the game,’ if you will, on exams like the SAT (whatever your thoughts on the value of the SAT are, learning how to play the game can open more doors for our students’ futures). Creative Depth format is a free-response question that will present students with a problem that needs to be solved with creative use of tools from the Math Toolbelt. Students may or may not have seen similar problems in the past and must take their time to achieve a depth of explanation on these problems.
A comprehensive final check-in is given at the end of the year and counts only as a 3rd trimester grade.
Character Point Average (CPA):
You may have noticed that the mathematical products you will create only comprise 75% of the total grade in the course. The remaining 25% of the grade comes from your Character Point Average, as measured by both you and I according to the rubric developed for the Character Point Average (CPA) as well as your weekly work for tracking your Habits of Scholarship using the provided tracking sheet.
The reason that we use a CPA grade – which some people would think of as a ‘participation’ grade – is because we believe the Character of a co-worker or employee matters in the real-world. If I am hiring employees, who would I choose between two candidates who have the same GPA and SAT scores – the one who shows up on-time to work everyday with a smile and jumps in and engages? Or the one who shows up late and spends the entire day complaining about annoyances that he could easily solve himself with some better habits? We’d like to help our students grow into the former.
There are a few components of the CPA that are so basic as to not be listed in the CPA Rubric, but that I will mention here because they are non-negotiable. The first is simple – professionalism. The rules surrounding professionalism are in service to a greater purpose of creating a classroom like that described in The Primacy of Self Discovery section of this document – a place that is at once a comfortable and uncomfortable, allowing students to face and overcome fears. The teacher of course plays a role in creating this environment, but so does the community (in many ways even more so than the teacher). I have seen entire communities begin using profanity when only a few students used it to begin with! We are social beings, after all.
So, the three rules of professionalism that I enforce strongly are: 1. Don’t use profanity. 2. Don’t criticize another person. 3. Respect and be sensitive to the educational environment (don’t sit on tables, leave trash, not return items to their proper place, etc.). The first two rules result in an immediate NE for the week’s CPA grade upon one offense, and a Zero upon second offense. The third rule results in an NE to the day’s CPA grade upon one offense, and a Zero upon second.
A few other components of the CPA that are specific to the mathematics classroom are listed here:
- The class will start the year practicing the proper response to the chime. After this has been practiced, the class as a whole will be expected to quiet down for an announcement after hearing the chime, with each crew member making sure to be responsible for other members. In the event that this does not happen, the whole crew’s CPA grade will be lowered by one letter grade for the day.
- Students are expected to sit or stand in the presentation area during class reviews. Failure to do so without prior permission results in an NE for the day’s CPA grade.
- Every GroupThink begins with a few minutes of Individual Think designed to allow all sorts of thinkers to gather thoughts before discussion begins. A failure to respect the silence of Individual Think time results in an NE for the day (it’s only a few minutes!). Students are reminded of this fact almost every class period.
This course is founded on a community that comes together around the work. The best way to have fun learning a TON is by making the explicit learning become implicit through practice. Creating SMART goals will be useful in this course, as well as critically assessing your work habits – do you do some amount of math work every day? The Power of Habit is an excellent resource (available in the classroom) for designing your work habits such that you enjoy math and stay up-to-date.
On Freedom and Discipline
“The paradox seems to be, as Socrates demonstrated long ago, the truly free individual is free only to the extent of his own self-mastery. While those who will not govern themselves are condemned to find masters to govern over them.” – Steven Pressfield
I would like to address a special consideration for students that attend our school which differentiates it from other schools – the idea of Freedom and Discipline. Allow me to take a moment to get a bit philosophical.
The teacher’s primary task is to help the student overcome fears [see The Primacy of Self-Discovery]. Yet, where do these fears come from? I believe at their roots, they stem from social conditioning. “Wealth, status, and power have become in our culture all too powerful symbols of happiness,” wrote Mihaly Czikszentmihalyi, the neuroscientist in charge of the world’s largest ‘happiness’ study to date. “And we assume that if only we could acquire some of those same symbols, we would be much happier.” But what if we aren’t able to acquire them? And so begins our fear of not being adequate, or having enough ambition – so we work our lives away, comparing ourselves to others around us and the Jones’s, hoping to prove to ourselves our significance, when the truth of the matter is each of us is already significant. That fear blocks intelligence and makes us dependent on social controls, which is the entire purpose of socialization, to have people respond predictably to rewards and punishments. This is precisely what the Titans of Industry wanted when they helped to create modern education during the industrial revolution – they wanted a malleable workforce that was educated in certain skills, but that would not question. “And the most effective form of socialization is achieved when people identify so thoroughly with the social order that they no longer can imagine themselves breaking any of its rules,” writes Czikszentmihalyi, “[we become] dependent on a social system that exploits our energies for its own purposes.” The implications here are massive – they challenge our entire tradition-rooted manner of thinking.
“A free human being can never feel that he belongs to any particular country, class, or type of thinking,” wrote J. Krishnamurti. “Freedom means freedom at every level, right through, and to think only along a particular line is not freedom.” So what can we do? Czikszentmihalyi answers:
To overcome the anxieties and depressions of contemporary life, individuals must become independent of the social environment to the degree that they no longer respond exclusively in terms of rewards and punishments. To achieve such autonomy, a person has to learn to provide rewards to herself. She has to develop the ability to find enjoyment and purpose regardless of external circumstances. If a person learns to enjoy and find meaning in the ongoing stream of experience, in the process of living itself, the burden of social controls automatically falls from one’s shoulders.
Many of the components of my class listed above are scaffolding a path through which students may achieve such autonomy, to be the master of themselves. This is not without difficulty and will certainly require a different social dynamic of Dialogue rather than Discussion; however, I believe that until all people are able to self-govern and unlock their own unique intelligence, and the world ceases to have ambitious people who seek to gain power through stripping others of their power, humanity is faced with great challenge, strife, and potentially a crisis (be it environmental, conflict-based, or other).
There are several structures available to students to help them learn self-discipline and communication. One of them, the DOG (Dimensions of Observable Growth) is a regular component of the class Habits of Scholarship grade. A second structure available is the RMSEL Goals structure, which takes the framework of ‘goals’ so often used in our society, acknowledges them, and then transforms the process of achieving those goals into one that works more harmoniously with human biology and teaches self-autonomy. Finally, for students who have found their freedom within societal structures and are ready to engage in effective communication with others, On Dialogue and the associated resources and rubrics can provide a framework for those ambitions.
During the 9th Grade year, students will explore the concepts of Geometry, Trigonometry, Systems of Linear Equations, and Exponential Functions. The main text that we use is the Interactive Mathematics Program, Year 2; the specific units that we will be covering (in order) are Do Bees Build it Best?, Cookies, and All About Alice. A great resource for parents to refresh themselves on the concepts in order to provide help to students is impmoodle.its-about-time.com. A secondary resource we use is Algebra I from Pearson. Students will receive an online login that allows access to a copy of this text to take home with them.