The Teacher:

Facilitator is the better word in this classroom. The
teacher is simply a bystander who carefully guides the students down a path
that such they continually recognize relationships with past knowledge. The
teacher will strategically intervene at certain points to make something clear
or to try and spark the idea for a relationship. The teacher though is still
extremely knowledgeable at math so that he/she has the knowledge and
understanding to answer any and all questions thrown their way.

The Homework:

The homework for this math class is for the most part done
out of a set of three workbooks. Usually two assignments from this workbook are
assigned each night for homework. Each assignment consists of 8-12 multistep
questions that rarely repeat format more than 3 questions in a row, reducing repetition.
The questions in the homework aren’t typical math questions and the work book
as a whole teaches wholesome understanding not how to plug numbers into a formula.
The questions also will require using knowledge learned earlier in the year to
keep the old concepts fresh. Almost all new learning is linked to and built
upon previous understanding so that in order to learn the new concepts, the
students have to remember the old ones. This ensures that students don’t forget
old concepts and constantly build upon what they have learned. However, due to
the unique nature of the learning style, some state mandated standards aren’t
taught directly through the workbook. They are taught in two ways. One is teaching
skills and knowledge that can be directly translated to the standard or brief standards
review worksheets, consisting of 6 questions that cover standards not talked
about in class. Although many standards aren’t directly addressed, the skills conveyed
address a multitude of standards.

The grading for homework is also different from standard
homework grading. In my class, homework and other formative assignments account
for 10% of the grade. Each homework assignment is worth 10 points, 2 points for
participation in the classroom discussions and 8 points for completing the homework.
This means that one has to participate in the class discussions and
presentation of answers in order to get full credit on homework. The first week
my teacher was lenient of the participation part as all of the students haven’t
been in that sort of environment. By the end of the first week though, all of
us had grasped the concept and since participation in the class hasn’t felt
like a bullet point to cross off but something that furthers our learning.

The Learning Format:

Almost the entirety of class is spent on going over homework
in depth. The homework usually consists of two assignments out of a workbook. The
following class, each 2 person pair in the class becomes an expert on 2-4
problems and presents their problems, the solution, and how that solution was
achieved. The pair then opens up questions to the class and after clearing up
any confusion and discussing the answers and process thoroughly, the teacher
will then sometimes ask a question. This question will usually question the
authenticity of the answer and the student(s) will have to defend their answer
and thoroughly explain. The other common question usually asks the students to
link what they are learning now and either how it will develop future learning
or how the current learning was developed from past learning. Often as a result
of these questions, an open class discussion can occur which can result in the
class working cooperatively to figure out why something works or can result in
a debate on a problem, theory, etc. These discussions will be cut out by the
teacher if time is of a concern.

Tests:

In my math class there are neither units nor big unit tests.
There are simply weekly quizzes that cover around 6 homework assignments. The
way the tests are scheduled however, the class is usually two assignments ahead
of what is covered on the quiz. This means that the material on the quiz has
already been understood in order to act like a foundation for the next
assignments/topics. These quizzes also consist mainly of 3-5 multistep
questions.

This pedagogy is relatable to Solomon Khan’s concept of a
flipped classroom. The material is made for the students to learn at home and
in class, the teacher ensures the students understand the material and
clarifies any questions and misconceptions. The set up also tries to teach
understanding of skills and concepts, not memorization of formulas. In the rare
case we use a formula, we undergo extensive learning in order to prove that
formula and show that it works. As a result of proving everything we use, it
gives us as the students a better understanding of the topic and facilitates
the learning of related topics.

The constant need for participation within the classroom
also drives all of the students to think outside the box and to never take anything
for granted. During discussions, students have to use their knowledge and
combine it with their creative thinking in order to provide a valid solution or
case. This constant creative thinking encourages the students to create a more
whole understanding of the topic as they are explaining the “how” behind
everything they say. While presenting on their assigned homework problems, the students
have to explain not only the answer, but also how they got the answer. This
vocal repetition will help not only the presenters but also the audience
understand and remember how to do something. Also having to explain the process
helps the students know how to do the process better and understand it more.

The format of my math classroom almost creates a completely student
run operation. This is so apparent that when my teacher is absent, the kids
will teach and facilitate the class. My teacher will just pick two kids to lead
the class that day and the sub will be the bystander that makes sure the students
are on task and if carrying background knowledge on the subject, can contribute
to the many discussions that occur. The two kids leading the class will assign
problems to present on and ask thought provoking questions. This give the
students an opportunity to be empowered and take on a leadership position. The
combined effects of this student leadership, creativity provoking discussions,
and teaching of skills not standards contribute to an all-around nurturing learning
environment.

Wow! I think I would like a math class run on these principles. I found many of my math classes to be boring due to the repetitive nature of mindless problems after problems.

ReplyDeleteThis sentence was one of my favorites "We as students are always linking current learning to past learning and are taught to “act like predators, not prey” and to anticipate future learning."

Thanks, Joe, for your clear description of your math class and your explanation of how it works!