WOWZERS EMBEDS THE STANDARDS OF MATHEMATICAL PRACTICE INTO THE WOWZERS ONLINE MATH PROGRAM
Standards for Mathematical Practice
The Standards for Mathematical Practice contain eight types of expertise that students at all levels should strive for. These standards stress the importance of understanding what a problem is asking, creating a solution using tools and models, and communicating this solution with peers. Skills such as problem-solving, reasoning, and using tools and models appropriately are important at all grade levels. Below is a brief explanation and example of how Wowzers addresses each one.
CCSS.Math.Practice.MP1: Make sense of problems and persevere in solving them.
In order to support students in making sense of problems, Wowzers teaches several key skills. Students must understand how to break apart problems into simpler pieces, plan how they intend to solve the problem, and continuously monitor their solution and ask themselves if it makes sense. After providing students with the basic skills to solve a problem, Wowzers builds on this knowledge by asking questions that combine integral concepts in a word problem.
This is an example of one of our blended learning assignments, where students are asked to use the concepts from the day to answer a more complex story problem. With students in younger grades, this process is broken down into several key steps: What do I know? What do I want to know? How do I solve the problem? Why did I solve the problem this way?
Through Wowzers, students learn how to compare ideas written in different ways. For example, through equations, tables, and graphs. By fluidly moving between different forms of the same equation, students can make comparisons and decisions in real-world scenarios.
CCSS.Math.Practice.MP2: Reason abstractly and quantitatively.
When learning to reason effectively, students must learn how to represent a situation symbolically with numbers and symbols, but they also must understand what that equation or process means in context. They must be able to translate a word problem into a mathematical process, then relate their answer back to the original context and include the correct units. Every day in Wowzers, students are given problems in the context of a real-world scenario. Students learn to solve these problems using the math skills they are working on, then relate it back to the original problem.
In this particular quest, the students are asked to find missing cargo from a shipwreck.
To do so, they must learn how to make interpolations on a scatter plot and track down a particular crate. In order to find the correct crate, students must decontextualize the problem and represent it in graphical form in order to answer questions. Then, they must contextualize the situation and go into the Wowzers world and use the information they learned from the graph to find the correct location of the crate. Every problem in Wowzers is given a context, which creates a situation where students are invested in the outcome.
CCSS.Math.Practice.MP3: Construct viable arguments and critique the reasoning of others.
Wowzers incorporates the skills of reasoning and proof into all grade levels. Students learn how to formulate a conjecture and build a series of logical statements to support it. Arguments are constructed logically, using definitions, rules, models, drawings, and diagrams. By comparing their reasoning and proof with peers, and evaluating each others’ arguments, students can decide which methods and solutions make sense, identify flawed logic, and improve their own skills.
In this example from an assessment, students are asked to critique a particular characters’ faulty reasoning. Wowzers shows students how to create a conjecture based on a series of logical statements.
In this example, students work through the method of creating the formula for the area of a trapezoid through previously learned and accepted formulas.
Characters in Wowzers present unique scenarios for students, where the student is put into a position of authority, where they can make conjectures and evaluate the logic of others. In this quest, the student must identify a shoplifter based on mathematical data. However, some characters make this process more difficult by presenting misleading graphs that the student must identify and successfully critique.
CCSS.Math.Practice.MP4: Model with mathematics.
Wowzers incorporates a wide variety of models, such as tables, graphs, diagrams, and an equation-writing tool. The curriculum introduces these models to the student, and allows the student to use each type of model to represent and visualize complicated situations. Students create and analyze these models to understand relationships and draw conclusions.
Through Wowzers, students learn a variety of different types of models that can be used. However, we believe it’s equally as important to understand when to use each type of model, and how to apply them to real situations. For that reason, we teach students how to choose an appropriate model and when one may be more useful than another.
Students also grow accustomed to using models to solve complex problems. In this example, the student is using a simulation to calculate the probability of a virus spreading to several of the characters. Students use these models to gather results and form a conclusion based on the data.
CCSS.Math.Practice.MP5: Use appropriate tools strategically.
Wowzers provides a wide variety of virtual tools for students to use, such as protractors, rulers, scales, graduated cylinders, and guess-and-check problem solvers. Students learn how to choose an appropriate tool, how to read the tools with precision, and what the tools represent. By using tools to solve problems, students gain a deeper understanding of concepts, such as how to convert units from one system of measurement to another.
Students are able to move each manipulative around on screen, rotate it, and use it to find the correct answer for a variety of problems.
Students must also make decisions on the best tool to use in different situations. In this example, students must choose the correct tool to measure the length of different objects.
CCSS.Math.Practice.MP6: Attend to precision.
Students must understand and be able to use precise definitions when describing mathematical concepts and symbols. By carefully specifying unit of measure and labeling graphs appropriately, students can give a more accurate answer to problems, with less chance of misunderstanding. Wowzers enforces this concept by defining new concepts and giving creative methods to remind students of what symbols and words mean.
In this example, young students learn the meaning of the inequality symbols by comparing it to the mouth of a crocodile.
Wowzers uses clear definitions when introducing new words and concepts. New words are underlined when they are defined, and more difficult words are written in blue, which is a sign to the students that the word can be clicked on, and a definition will pop up.
Students are then tested on these definitions and expected to use them in their own writing in the assessments.
CCSS.Math.Practice.MP7: Look for and make use of structure.
Recognizing patterns or structures is an important step in understanding many mathematical concepts. For example, by understanding multiplication as repeated addition, or the fact that 7 × 3 and 3 × 7 is the same answer, students begin to recognize rules and definitions. Wowzers assists students with recognizing patterns and structures by setting problems up in a way where students can recognize patterns on their own, and practice applying this pattern to other situations. By showing things visually and allowing the students to interact with manipulatives, students often have an easier time seeing patterns.
In this example, students learn through modeling that the order of the factors in a multiplication sentence can be switched and the answer remains the same.
In this example, students discover through experimentation that the slope of a perpendicular line has an opposite reciprocal of the original line.
CCSS.Math.Practice.MP8: Look for and express regularity in repeated reasoning.
Students who notice when they are performing a calculation repeatedly have an easier time recognizing general methods and shortcuts. For example, recognizing a repeated calculation is essential when determining whether a decimal is repeated or not. Identifying a function or pattern also relies on students recognizing repeated reasoning. Wowzers supports students in finding these repeated calculations by helping them recognize patterns and giving examples of repeated reasoning and how it can be used.
In this example, students learn how to create a function rule by observing patterns. By using experimentation and looking for repeated calculations, students gather the information necessary to write the function.
Students also discover rules by looking at patterns, such as how to tell whether a number is even or odd by looking at the number in the ones place.