Teachers: Talk less, question more. Be "less helpful"
Too often we give students too much information and answers to questions they never asked.
In Algebra 1: Predicting Patterns & Examining Experiments
problems are posed and students must decide what information is needed in order to answer those questions. The questions are simple, but require a mathematical framework to solve. The strategy is to present difficult problems first- supplying a need for the algebraic framework. Rather than meaningless skill-building to solve a contrived 'application problem'.
The curriculum presents the D.A.N.G. process
, which represents a full view of the many forms of relationships within mathematics, including tables, graphs, equations, and verbal descriptions. This four-fold approach trains a learner to overcome any hurdle by a manifold response to every problem that consists of asking such questions as “can I draw a picture of this situation”, “what pattern do I see in the numbers”, or “how can I make this into something I already know how to solve.”
Expectations of employees and citizens are changing in the 21st century
. Learners need more skills than just reading, writing, and arithmetic, they must create content with innovation, communicate themselves, and be flexible and adaptive when confronted with problems. This course delivers not only high-level problems and the processes needed to solve them, but also engaging, stunning, and interesting mathematics. The advancements of recent years create an opportunity for a new day within the learning of mathematics and this course challenges teachers to equip students for the world in which they are entering.
The year-long course begins each lesson with a one to two day presentation of rigorous problems that call students to work together to solve the problems using as many methods that they can discover. After the solutions are found, students share and discuss their solutions with each other. At the end of looking at each problem the teacher can summarize the numeric, graphic, and analytic solutions. After multiple high-level problems in one presentation, that may take multiple days, students should practice the skills examined. The best homework is corresponding state and local assessment practice that applies to the skills covered, but worksheets are provided as well.