Assessing Meaningful Learning

Overall, I believe that replacing the standardize test and quizzes with assignments that require applying what you have learned is better for this class. Looking back, normal test only see what a student has learned from watching a video, reading a book or paying attention. Getting them to actually explain how they feel about an assignment or express their own opinion on a tool, gives more thought to it instead of simple memorization.  As for using a rubric on a project, it gives students a actual guide as to what is needed. They interpret what is being asked of them and then they make the effort into create the proper needed result. Over the course of the class, when there is a rubric for the project I normally refer back to it to make absolutely sure that I have covered the needed material to receive the most credit possible. Another way to say “I’m getting what I have put work into”; getting credit where credit is due so to speak. With just working with these types of assessment tools, I believe that students need to find the answers themselves in a way of self awareness.


The classroom is a place to learn, it is where trial and error are okay, and expected even, technology and tools like that of the Web 2.0 tools we have discussed throughout the course are excellent ways of teaching students to communicate and express ideas and opinions. Web 2.0 tools also allow students to present questions and answers in different forums. Tools such as Prezi can be used to in many ways such as demonstrate different methods for solving a specific type of mathematical problem, or present a timeline of mathematical history. Podcasting a lecture can allow students to review specific lessons that provides material that they need to focus and improve on. Blogging is excellent for sharing ideas and opinions and the responses one gets from these opinions.

Graphing Calculus starting from Point 0

§111.35. Precalculus, Grade 11

(b)  Introduction.

(1)  In Precalculus, students continue to build on the K-8, Algebra I, Algebra II, and Geometry foundations as they expand their understanding through other mathematical experiences. Students use symbolic reasoning and analytical methods to represent mathematical situations, to express generalizations, and to study mathematical concepts and the relationships among them. Students use functions, equations, and limits as useful tools for expressing generalizations and as means for analyzing and understanding a broad variety of mathematical relationships. Students also use functions as well as symbolic reasoning to represent and connect ideas in geometry, probability, statistics, trigonometry, and calculus and to model physical situations. Students use a variety of representations (concrete, pictorial, numerical, symbolic, graphical, and verbal), tools, and technology (including, but not limited to, calculators with graphing capabilities, data collection devices, and computers) to model functions and equations and solve real-life problems.

(2)  As students do mathematics, they continually use problem-solving, language and communication, connections within and outside mathematics, and reasoning (justification and proof). Students also use multiple representations, technology, applications and modeling, and numerical fluency in problem-solving contexts.

With teaching what would be junior level students in High School, it would be best to keep in mind that they need to develop assessment skills for this course. From the TEKS, I understand that the students need to be able to look at graphs, functions, and diagrams to understand what the question is asking. They need to be able to explain what is going on in the problem. Overall they will need to be taught skills that allow them to analyze the problem and solve thru definition, decryption, calculating domain and range, finding symmetry, and looking for behaviors, continuity, asymptotes, etc. Students would also be required to memorize formulas or recognize which are to be used in a certain cases. Another requirement would be to calculate different equations without the usage of a calculator,  going back to the age of basic math.

In Precalculus, there really isn’t a single concept that is more important than any other. Each concept has be already taught or is being taught for the sake of expanding the knowledge. They will come to understand an variety of representations, tools, and technology to model functions and to solve equations. As the students are exposed to the numerous examples, they will develop small tricks of the trade to solve their problem and develop into problem solvers. They then create a language and forming communication skills to make connections and deduce reasoning. Students can also develop a sense of independence as they learn traits to solve problems without the use of calculators and to simple apply simple math to their work and finding the answer where it is.