High School - Gateway 3

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet expectations that the design of the assignments is not haphazard and are given in intentional sequences. The materials create connections as tasks begin by re-examining mathematical content so that familiar mathematical situations are viewed with a new level of sophistication. The sequence of the material is designed to spiral concepts throughout the entire series.

Structure of the Materials states that Ready and Go exercises provide a spiraling sequence of content to help maintain skills. However, these spiraled exercises often contain concepts that are unrelated to the content of the new lesson and/or have not yet been learned in the sequence of the course or series. Examples of these exercises affecting the overall sequence of the materials include:

• In Algebra I, Module 5, Ready, Set, Go! Problem 8, students identify transformations in Ready, but this concept is not addressed until Geometry even though the concept is addressed in Grade 8 standards. The main topic of the module is systems of equations, and this practice does not provide practice that connects to the work being done in the Module or the course. 
• In Algebra 1, Module 9, Ready, Set, Go! Problem 8, students create geometric constructions after learning about residuals. These topics are not related, and the materials do not address constructions until Geometry.
• In Geometry, Module 2 addresses geometric constructions and connects those to congruence of figures. In Go for Task 1, students solve systems of equations. In Go for Task 2, students write recursive and explicit formulas for sequences. While this is connected to content from Algebra I, it is not connected to new content in Module 2.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that the Teacher edition addresses the standards in the context of the overall series. An overview of each module and associated tasks is provided in the Introduction to the Materials document on the course page. An overview of each task is also provided in the Teacher Notes. The materials make occasional references to previous and future standards related to the current task. Also, occasional references are made to a course, but rarely to the module or the task. For example, in Geometry, Module 6, Task 2 states, “The purpose of this task is to prove that parallel lines have equal slopes and that the slopes of perpendicular lines are negative reciprocals. Students have used these theorems previously.” No precise reference about how current content fits into the vertical progression of learning is provided.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing materials for gathering information about student’s prior knowledge within and across grade levels/courses. The Ready exercises within a task are intended to help students review and prepare for the skills and concepts that will be needed for the task. However, there is no guidance for the teacher as to how to interpret these exercises, nor is there any discussion of possible strategies for remediation.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing opportunities for ongoing review and practice of both skills and concepts. The structure of the tasks within a module, and across modules, provides for review of concepts. However, besides the Ready, Set, Go! exercises within each task, there is no ongoing practice of skills, and there is no discussion of how to provide feedback. The Ready, Set, Go! exercises do provide students the opportunity to show proficiency on certain topics, but few resources are provided for teachers to provide feedback. 

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that standards are clearly denoted for assessments. Assessments do indicate course, module, and task, but specific standards are not identified on the assessments. Algebra II, Module 2 Quiz, states, “Logarithmic Functions 2.1-2.4”, but it does not indicate for each question which standards are addressed. Assessments are based on modules, which include the standards of focus. Although quizzes and tests do not specifically provide standards, performance-based assessments include the standards.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation that assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

Assessments typically have multiple parts including a mixture of the following types of problems: Multiple Choice, Matching, Building Tables, Short Answer, and Short Essay. Occasionally students are asked to demonstrate different methods to solve similar problems. There were few of the short answer and short essay problems, and the majority of the assessments were comprised of multiple choice/matching type problems.  

Scoring rubrics for the short answer and short essay questions were not available, and grading expectations for weighted value of the assessments. Sample assessments include rubrics for the performance-based assessments which offer limited guidance, but do not provide guided feedback.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. Teacher materials provide a prescribed Teaching Cycle. Each task has an Explore (Small Group) component for developing student understanding. If the students do not meet the expectations in small group, strategies are not consistently provided for how the teacher can scaffold the content of the task. An example: Algebra I, Module 5, under Explore Small Group, “watch and listen and encourage connections.”

The Enhanced Teacher Notes offer “Instructional Supports” that sometimes contain a scaffolding/intervention section, such as in Algebra I, Module 2, Task 10 which provides a graphic organizer to help students classify forms of linear equations. 

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for providing teachers with strategies for meeting the needs of a range of learners. Enhanced Teacher Notes offer “Instructional Supports”, “Instructional Adaptations”, and “Challenge Activities” as resources to differentiate instruction. These, however, are not comprehensive. The note in Geometry, Module 1, Task 5, under Instructional Adaptations states, “The use of the cutouts described in the Instructional Supports section should be sufficient intervention for this task, and provide adequate support for all students.” However, no other strategies or suggestions were given.

The Enhanced Teacher Notes list “Instructional Supports” and “Instructional Adaptations” at the end of each task. For example, Geometry, Module 1, Task 3, has these instructional supports listed:

• Relatable Context - summarizes why this context will engage students.
• Visualization - addresses the misconception that could result if students mistakenly think of this as a three-dimensional action instead of a two-dimensional action of reflecting.

And these Instructional Adaptations:

• Intervention Activity - use of tracing paper.
• Challenge Activity - “Ask students to consider this question: Is it possible to find a sequence of transformations that will carry every image to every other image in the diagram if the first transformation in the sequence is always to translate the tip of the middle fingers of the left hand of the first image to the corresponding point on the second image? What are the implications of this?”.

The instructional materials reviewed for Mathematics Vision Project Traditional series partially meet the expectation for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. Most tasks do not provide multiple entry-points. 

Some tasks do provide multiple entry points. For example, in Geometry, Module 7, Task 1, students explore two-dimensional cross sections of three-dimensional objects. The materials offer many different ways for students to engage in this visualization - drawing “slices” of a cube on a two-dimensional drawing, partially filling a cylinder with water and tilting and turning it different ways while watching what the surface of the water does, and finally, observing the possible shapes of shadows that can be cast by different objects.

The tasks set for the students can often be approached from many perspectives, using different strategies and representations. In some cases this is encouraged; however, in most cases the teacher is instructed to guide the students to the “desired” method of solution so as to address the standard in question.