High School - Gateway 3

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the underlying design of the materials distinguish between problems and exercises.

Problems within the Mathematics Vision Project materials are designated as “tasks.” Every task included attends to specific standard(s) or aspect of a standard(s) and builds upon prior knowledge. There are three different kinds of tasks: Develop Understanding, Solidify Understanding, and Practice Understanding tasks. The Develop Understanding tasks introduce concepts and build on previous knowledge by providing discovery problems. The Solidify Understanding tasks focus on the concepts being developed in the unit. They provide students opportunities to practice what they learned so far in the unit. The Practice Understanding problems extend the learning by adding small extensions to the concepts covered in the unit. The Ready, Set, Go exercises within the Mathematics Vision Project are designated as “homework.” The Ready exercises are intended to prepare students for the upcoming work in class, the Set exercises reinforce the work done in class that day, and the Go exercises review concepts and skills that students learned previously.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the design of the assignments is not haphazard, and they are given in intentional sequences. The materials include connections as the tasks are reexamined so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the materials is designed to spiral concepts throughout the entire series. The Ready, Set, Go exercises are designated as “homework.” The Ready exercises prepare students for the upcoming work in class, the Set exercises reinforce the work done in class that day, and the Go exercises review concepts and skills that students learned previously.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that there is variety in how students are asked to present the mathematics. For example, the series asks students to provide numerical answers, produce graphs, compile charts, draw pictures, find equations and functions, create models, describe patterns, articulate arguments, write critiques, and analyze work and possible solutions. In almost every task, students present the mathematics in multiple ways. For example, in Secondary Math One, Module 8, Task 5 students complete tables, write equations, and draw graphs, and in Secondary Math Two, Module 5, Task 1 students draw a sequence of rotated triangles and then use their drawings to write a mathematical proof.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that manipulatives, both virtual and physical, are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods. The materials do occasionally instruct students to use manipulatives within the materials (for example: Secondary Math 2, Module 8, Task 1, Unit Circle Task). The materials do not provide directions for the use of virtual manipulatives. On the main webpage, under the Resources header, there are links that connect to a set of ten GeoGebra Interactive Applets (i.e., Leaping Lizards, Triangle Dilation). A few examples of suggested physical manipulatives include dice to model a data set and an area model for multiplying binomials, completing the square, and factoring.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that teachers are provided quality questions to guide students’ mathematical development.

The Teacher’s Notes provide suggested questions to use during the Teaching Cycle (see #6 under indicator 3g); these aid in students’ development of the concepts. The following example is found within the Secondary Math One, Module 1, Task 6, Launch section: “Then, wonder out loud whether or not it would be an arithmetic sequence if a number is subtracted to get the next term. Don’t answer the question or solicit responses.” There is also an Essential Question provided as part of the enhanced teacher notes for each task. The tasks themselves contain questions designed to elicit discovery and exploration.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the teacher edition contains ample and useful annotations. The materials provide documents for each module under the Teacher’s Notes. These notes contain structured guidance on how the lessons should proceed. The notes may be included in some or all of the sections. For example:

• Special Note to Teachers: highlights an aspect of the task and how it fits in the overall sequence of the three-course materials.
• Purpose: describes the previous development of concepts needed for the lesson and where to place emphasis for the lesson.
• New Vocabulary: lists new vocabulary introduced in the lesson.
• CCSSM Standards focus and related standards: lists those standards addressed in the lesson.
• Standards for Mathematical Practice: lists those standards in the lesson.
• The Teaching Cycle: Launch, Explore, Discuss: provides a detailed discussion on lesson delivery.

There is also reference made to the use of technology within the teaching cycle, but there is no discussion of how to use the technology. For example: Secondary Math Two, Module 4, Task 1, page 4 states, “If this is the first time they are using CBR’s, you may wish to model how to use this before sending them out in groups. If you are not using a CBR for Ball Bounce 2, you will want to find a way to model quadratic data using a different method.” Secondary Math One, Module 9, Task 5, page 37 states, “Most graphing calculators will work well. Free computer apps would be very helpful and easy to use on this task, as well (GeoGebra and Desmos, etc.).”

The MVP Enhanced Teacher Notes include the basic Teacher Notes, Essential Questions for each task, articulation of Standards of Math Practices of Focus, exit ticket ideas, instructional supports, instructional adaptations, intervention ideas, challenge activities, answer keys to in-class tasks, and answer keys to the Ready, Set, Go!

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that support is provided for teachers to identify and address common student errors and misconceptions.

The materials often include a comment related to common errors or misconceptions, but they do not always identify what these might be. For example, in Secondary Math Two, Module 4, page 13, the teacher notes state, “As you monitor, look for common student misconceptions to discuss during the whole group discussion. For example, some students may not realize….” The notes go on to explain a misconception. In the same module, page 51 states, “Look for common errors among students so that you can discuss these more thoroughly during the whole group discussion,” but no indication is included of what these might be or how to address them in the whole group discussion.

The instructional materials reviewed for Mathematics Vision Project Integrated series meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The Enhanced Teacher Notes offer “Challenge Activities” as resources for advanced students. For example, in Secondary Math One, Module 9, Task 5 the teacher is told to “have students find data in two-way tables on the internet, then have them write a story, using relative frequency statements.”