8th Grade - Gateway 2

The materials reviewed for Edgenuity Grade 8 partially meet the expectations for developing conceptual understanding of key mathematical concepts.  The lessons containing standards 8.EE.5, 8.EE.6, 8.EE.8.A, 8.F.1, 8.G.2 and 8.G.6 were of particular focus. All of these standards require students to understand key concepts. 

• In Unit 1, 8.EE.5 is listed as the main standard for lessons one and two in the student course map. However, when looking at the Teacher’s Curriculum Map in the course documents, the standard is not listed for the unit.  The instructional videos for this unit begin with direct procedural instructions on how to create a table. There is not any exploration activity for students to discover the relationship presented in different ways. 
• The documents for Unit 8 correctly identified the standards for 8.G.A. This unit contains some exploratory lessons with transformations. 
• The teacher material, called “Common Core Math 8 Curriculum Guide,” has a section titled Representation, Tools, and Interactive Models. In Unit 1, Lesson 3 on interpreting graphs provides an interactive slide with a Ferris wheel. The students can start and stop the Ferris wheel, and the computer generates the correct graph. This visual will help develop the concept of a function.   
• There are only one or two questions for each assignment where students are asked to explain. Once a student starts typing, they are then given a list of appropriate responses and are to check the ones they have included in their response. A student could type anything and then select a correct response. A student’s thinking is not challenged, but the student is immediately given an answer to the problem.

The materials reviewed partially meet the expectations for giving attention to applications. Overall, the materials reviewed give attention to application, but they lose focus on the major work of the grade.

• In the instructional sequences, the teacher walks students through the applications with a step-by-step process.
• Many of the problems in each of the sections (warm-up, instruction, assignment, summary, quiz and test) are written with a real-world context. However, most problems are multiple choice and do not require that students fully apply the mathematics involved, or students are led to the solution in a step-by-step manner.
• For instance, on slide 11 of the assignment in Linear vs. Nonlinear Functions, students must select all of the situations that depict a linear function. This question does demonstrate mathematics being used in the real world; however, students are not asked to determine how to solve a problem.
• There are also open-ended questions in which students must solve a problem in a real-world context and explain their reasoning. Once they select “done,” a list of possible correct answers appears. A student does not have the opportunity to revise their thinking. They are immediately lead to the correct response.

The instructional materials reviewed partially meet the expectations for identifying the MPs and use them to enrich the content. Overall, the MPs are not always identified correctly and not always used to enrich the mathematics content.

• The eight MPs are defined in the Common Core Math 8 Curriculum Guide. The guide fully explains all eight practices and provides a brief summary of how the practice is to be utilized in the said grade.
• The Common Core Math 8 Alignment document lists the eight MPs and the title of the lesson where the practice is evident in the instruction. Following is a list of the practices and how many lessons in which they are identified: MP.1, 52 lessons; MP.2, 49 lessons; MP.3, 32 lessons; MP.4, 45 lessons; MP.5, 34 lessons; MP.6, 53 lessons; MP.7, 72 lessons; and MP.8, 20 lessons.
• The practices are not mentioned in the instructional video or linked on any slide in the assignment. One would have to determine where each practice is being incorporated into the lesson.
• The Student View has a course map for each unit. Under the course map, there is a tab titled State Standards. This is a long list on content standards and mathematics practices. Again, they are not tied to any specific question or part of the lesson.
• The standards listed under the course map are sometimes identified incorrectly. For example, in Unit 1, the title “Make Sense of Problems and Persevere through Solving Them” is identified as MP.3. In this same unit, MP.4 an MP.5 are also identified incorrectly.

The instructional materials reviewed partially meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials reviewed do not always carefully attend to the full meaning of each practice standard.

• The format of this program makes it very difficult for students to reach the full meaning of MP7 and MP8. The heavily procedural instruction and full explanations given by the teachers prior to the assignments do not allow students to make these connections independently.
• MP4 is listed in every lesson in the first unit with the exception of “Using Technology to Explore Data.” At no point do students choose the representation they will use to model the given situations or produce them independently,
• Multiple lessons have more than one practice referenced, and the practice standards are not linked to a particular question or slide. An instructor is not given any guidance as to how to enhance the lesson with the practices.
• For example, a lesson titled “Graphing on the Coordinate Plane” is referenced in the curriculum alignment document and cites MP4. When looking through the lesson, there was no place for modeling with mathematics. In addition, there were a few places where students had to explain and critique the reasoning of another, so MP3 could’ve been cited as it was fully addressed.

The instructional materials reviewed partially meet the expectations for prompting students to construct viable arguments and analyze the arguments of others. Overall, the materials reviewed rarely prompt students to construct viable arguments and analyze the work of others.

Not many questions ask students to explain or justify their answers. This correlates with indicator 2a in the lack of conceptual development questions.

A few questions ask the student to find an error of a model problem. Most of these problems are in multiple-choice format. This does not allow for independent thinking.

Throughout the units there are questions that require students to type in an explanation. Once they submit their answers, a checklist of possible correct responses appears. They are then asked to check the box(es) that match their response. Students do not have the opportunity to share or receive real feedback about their thinking.

The instructional materials reviewed partially meet the expectations for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others. Overall, the materials reviewed provide some assistance to teachers in engaging the students in constructing viable arguments.

• The Common Core Math 8 Curriculum Guide provides a guide for blended instruction. In this section, teachers could find places that would naturally lend to discussions.
• The Curriculum Guide also has a section titled “Unit by Unit Discussion Questions.” There are two questions per unit listed, as well as instructions, on how to conduct the discussion with multiple students or students who are working individually then interact via a discussion board.
• Since the mathematics practices are not identified specifically in the slides, it is difficult for teachers to determine which ones to highlight or mark for students. For example, MP3 is identified in Modeling Real-World Equations. In the assignment, teachers have to make assumptions about which problems engage in MP.3.

On slide eight of the same lesson, an opportunity is provided for students to find an error in another student’s thinking about the number of solutions for his equation. Once the student submits their answer, a list of possible answers will appear that they are to select.

The instructional materials reviewed partially meet the expectations for attending to the specialized language of mathematics. Overall, the materials reviewed attend to the language of mathematics in a few places.

There is a list of vocabulary needed for the entire course in the curriculum guide.

Many warm-ups introduce the vocabulary for the lesson. They identify green words as academic words that are used in other areas of study. Purple words are identified as domain specific. This color-coding continues throughout the program.

There are few questions in each unit that require written answers due to the format of how students respond. They never have to use precise language. They can type any answer and then select an answer from the provided list that sometimes has the correct usage.

Two examples where the specialized language is not used are slide 6, Assignment, Exploring Systems in the Real World, and slide 10, Assignment, Transformations. This series uses the words “rise over run” repeatedly for a method to find slope (Rate of Change and Introduction to Slope, Exploring Slope, Slope-Intercept Form, Graphing). Systems of Equations, but at no point are students asked to explicitly describe what those terms mean using the number of units between two x or y values.