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Secondary One Mathematics:An Integrated Approach

Mathematics Vision Project in partnership with USOE

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Note that this resource was reviewed during the Spring 2013 review period. The resource may or may not have been updated since the review. Check with the content creator to see if there is a more recent version available.

Review

This resource was reviewed by OSPI in Spring 2013. Learn more about the review process and the data analysis approach.

Background from OER Project Review Team
The Mathematics Vision Project has partnered with Utah State Office of Education on this open textbook focused on an integrated model of the Common Core State Standards. The book is designed around the Comprehensive Mathematics Instruction (CMI) model. Professional development with this resource is highly suggested for effective implementation of the teaching strategies. This should factor into the viewer’s analysis of the review results. Both teacher and student versions are available.

Publishers' Criteria (Learn more)

Chart with scale from 0 (Strongly Disagree) to 3 (Strongly Agree). Focus: 2.4, Rigor & Balance: 2.27, Consistent Content: 1.93, Coherent Connections: 2.27, Reasoning: 1.8, Standards for Practice: 1.93.

EQuIP (Learn more)

Needs Revision (1.4)
Chart with scale of 'meets criteria' from 0 (None) to 3 (All). Alignment: 1.8, Key Area of Focus: 2.4, Instructional Supports: 1.8, Assessment: 0.6.
Module 3

Achieve OER (Learn more)

Chart with scale from 0 (Weak) to 3 (Superior). Explanation: 0.8, Interactivity: 0.0, Exercises: 1.4, Deeper Learning: 2.4.
Module 3

See standard error chart for the review scoring

Reviewer Comments (Learn more)

Moderate (1.2)

The Secondary Mathematics One: An Integrated Approach, by the Mathematics Vision Project, consists of eight units, each including from six to eleven tasks. “In the MVP classroom the teacher launches a rich task and then through “teacher moves” encourages students to explore, question, ponder, discuss their ideas and listen to the ideas of their classmates. (For Educators)” The tasks are described as those to Develop Understanding, Solidify Understanding, or Practice Understanding. It is in this manner that the curriculum announces its inclusion of the Standards for Mathematical Practice. While a skilled teacher will automatically include those discussions within the classroom, they should be more explicitly pointed out in the Teacher Notes accompanying each unit.

Each task includes “Teacher Notes” which follow a pattern: Purpose, Core Standards, Launch (whole class), Explore (small groups), Discuss (whole class), and Aligned Ready, Set, Go homework assignments. These notes include information the teacher needs to bring out in classroom discussions. It also suggests how to use guided questioning to bring to the front information students do not readily contribute to the discussions. New vocabulary is pointed out, as are connections to prior learning. The most obvious lack is that of an answer key – both to the task(s) presented and the aligned homework set. Though the web notes that a teacher should work out these problems in collaboration with other teachers when preparing for a lesson, in reality, this does not foster good time management for the teacher. Guidelines for procedure and skill fluency would also be a useful tool. The Student Edition includes hotlinks to informational videos and sample worked out problems to help the struggling student with their homework.

Another area that could use some bolstering is the use of technology, especially interactive online practice. One of the tasks in Unit 3 (page 37) does recommend the use of graphing calculators (or spreadsheets). This is the only such task I observed in the unit (it is possible that more opportunities are included in other units). Application opportunities seem to occur during class with small/whole groups. More applications are needed, especially at an individual level.

Assessment strategies are not explicitly stated in the curriculum. Classroom discussions do not ensure that all students master the material. The "Ready, Set, Go" homework activities could be used to assess students' individual progress. Nowhere in the lesson format, however, is time set aside for struggling students to ask questions or go over homework problems. The first three modules (0, 1, & 2) include unit assessments. These consist of traditional Multiple Choice, Short Answer and two Constructed Response questions (which are scaffolded). It would be nice to see such assessments developed for the remaining five units.

It is relevant to point out that teachers will need quality, ongoing professional development to help their students achieve academic success. With some work, this curriculum is promising.

I would use these materials in my classroom: Agree
(On a 4 point scale: Strongly Disagree, Disagree, Agree, or Strongly Agree)

This course contains 8 units each having between 6 and 14 lessons. Each lesson is designed around a rich task with a significant standard at its center. The task serves as the focal point from which the teacher is directed to provide engaging activities addressing this standard as well as several related standards. Each lesson also contains a “Ready, Set, Go Homework” assignment.

The “Ready”, “Set”, and “Go” sections of the assignment respectively serve to provide practice on content that underlies the current standard, connects to the current standard, and underlies an upcoming standard. For example, at the center of Lesson 3 in Module 3 is the standard F-LE.1: Distinguish between situations that can be modeled with linear functions and with exponential functions. The focus for each section of the homework assignment are as follows.

  • Ready: Recognizing the greater rate of change when comparing 2 linear functions or 2 exponential functions.
  • Set: Representations of linear and exponential functions.
  • Go: Recursive and explicit equations of geometric sequences.

This course was clearly designed with focus through coherence in mind. The rigor in application and concept is robust. For significant content, procedural rigor is accomplished through the classroom experiences and the spiral reviews found in the homework assignments. For the remaining content the practice needed for mastery may not be sufficient. The richness of the tasks provides the teachers with endless opportunities for pre- and formative assessment. Formal assessments are not abundant and need to be created.

Much is required from the teacher to ensure that the attention to focus, coherence, and rigor result in achievement. There is much expected of the learner as well. The learner must internalize and exhibit many of the mathematical practices in order to productively engage in the work. Additionally, the course assumes that students enter the course with necessary prerequisite understanding and skills. Direction is given to teachers throughout the course to support students with conceptual deficits but aside from the first few units (modules) there are few supports provided students with procedural deficits.

Led by a proficient teacher, and with additional assessments and practice exercises, this course could be outstanding. In its current state, in the hands of a basic teacher, it could flop.

I would use these materials in my classroom: Strongly Agree
(On a 4 point scale: Strongly Disagree, Disagree, Agree, or Strongly Agree)

3 Types of Lessons: Develop Understanding, Solidify Understanding, Practice Understanding

Each lesson moves through the phases of a Teaching Cycle:

  1. Launch: Engaging students in a worthwhile mathematical task
  2. Explore: Allowing students time to actively grapple with the mathematics of the task
  3. Discuss: Orchestrating a class discussion in which student thinking is examined and exploited for its potential learning opportunities towards a focused mathematical goal

Though not specifically identified in the unit or lesson notes, the lessons provide guidance for teachers to develop the Standards for Mathematical Practice. Students frequently have structured opportunities to justify their own thinking while clarifying, describing, comparing, and questioning the thinking of others, and develop understanding of the mathematics, not just practice skills and answer questions.

Focus: There are several “Extra” Standards addressed that are not listed on the Integrated I worksheet:

A.REI.1 Construct a viable argument to justify a solution method.

F.BF.3 Build new functions from existing functions

G.CO.12, G.CO.13,--Constructions

G.GPE.4, G.GPE.5, G.GPE.7 –Use coordinates to prove simple geometric theorems algebraically.

One Missing cluster: Prove Geometric Theorems. Instead, there is a unit that makes connections between algebra and geometry and includes the cluster Use coordinates to prove simple geometric theorems algebraically. Coherence: There is explicit effort to draw on students’ prior knowledge. The organization of the modules supports a coherent approach. For example, Module 2 focuses on Arithmetic and Geometric Sequences. Module 3, Linear and Exponential Functions, begins by building upon students’ experiences with arithmetic and geometric sequences to extend to the broader class of linear and exponential functions with continuous domains.

Rigor: All 3 aspects of rigor are developed with tasks and lessons (structured discourse) designed to develop conceptual understanding, procedural fluency, and application.

I would use these materials in my classroom: Agree
(On a 4 point scale: Strongly Disagree, Disagree, Agree, or Strongly Agree)

The course is divided into 7 modules, five of which focus on Algebra 1 content and two on Geometry connections. Each lesson begins with a “launch” question or problem set up by the teacher and then a rigorous group activity. The lesson ends with a “Ready, Set, Go” homework assignment that includes focused problems on the current material, and review of previously learned concepts. At the end of each homework assignment in the student text are links to a variety of online resources that provide homework support, including Kahn Academy.

Each lesson has a clearly identified purpose and is aligned to the CCSS. Not all lessons identify the alignment to the Standards for Mathematical Practice. Each lesson includes a “launch” that explains how to introduce the lesson / activity and is followed by an opportunity to “explore” through small group work. The lessons do provide guidance to the teacher regarding common mistakes and assumptions by students. The lesson plans provide advice on how to keep the lesson on track when students are working in groups. Each lesson ends with whole group “discussion” and then independent practice through the “ready, set, go” homework. Some of the units have a unit assessment, but it is not included in all units.

There are no answer keys for the homework or assessments. The lesson plans do not include pacing guides and it would be difficult for students to engage in the level of discussion required by the activities in a 50 minute period.

The student text does not include clear explanations or examples, other than in the first two units. While the activities are really wonderful, the average student would not be able to work through this text and gain a clear understanding of the course. The links to other websites included in each homework assignment do provide explanation, but it would be helpful to see some examples in the text as well as summaries of the mathematical concepts that are addressed in each lesson. The format of the materials almost feels like a “flipped classroom.”

The activities in this text are rigorous and thoughtful. They could easily be used in an algebra 1 or geometry classroom to encourage perseverance and improve understanding.

I would use these materials in my classroom: Disagree
(On a 4 point scale: Strongly Disagree, Disagree, Agree, or Strongly Agree)

The item is a collection of a set of 79 Classroom Tasks Organized into eight Modules consisting of 6-14 tasks per module. While many of the tasks cover some content standards in CCSS they are not organized to align with CCSS and as a result individual CCSS content standards may be touched upon by multiple tasks or not at all. Most tasks that do cover items in the CCSS content standards tend to address multiple content standards though coverage is somewhat random and may touch upon many standards but not fully address any one single standard.

The classroom tasks are accompanied by practice exercises but there are no answer keys or scoring rubrics for the practice materials. In a typical Activity such as the “Connect the Dots” task in Module 7, two pages are devoted to the questions which comprise the task followed by several pages of additional exercises for students to work on. In this particular example the task provides a set of single-variable data points and asks students to create a scatter plot of the data and to calculate the correlation coefficient. Unfortunately no instruction is given to students that would define what a scatter or correlation coefficient is and no instructions are given on how to create or calculate either of these. Presumably this task would need to be preceded by teacher-led instruction to provide foundational information which is not provided.

While the content coverage is weak and very little instructional support is provided many of the tasks do provide real-life contexts in which students are asked to consider open-ended situations and come up with solutions that have the potential to engage students in rich problem solving and help develop thinking skills in alignment with CCSS standards for mathematical practice. In Module 1 on Systems of Equations and Inequalities the first task gives students a real-life context in which they have a fixed amount of money and want to buy cat kennels and dog kennels each of which have a different given unit price. The task asks students to consider different combinations of numbers of dog and cat kennels that would satisfy the constraint of having the given total cost. Students are then asked to graph their proposed solutions and finally to develop an equation to model their proposed solutions. While the task creates opportunities for students to persevere in solving the problem and create their own graphic and mathematical models, use of this task in an actual classroom would require considerable teacher instruction to provide background understanding as well as scaffolding to allow diverse students to meet the objective of ultimately creating a graph and equation to model the situation. This example is typical of other tasks in the collection in that it asks students to engage in problem solving but does not provide instruction to support development of prerequisite skills nor scaffolding for diverse students.

To bring this item into full alignment with CCSS and provide materials that would allow it to be used as a full curriculum would be a major undertaking. Many of the individual tasks, however, have some rich questions and there is potential for teachers to select certain tasks in the collection for use as a supplement to other more complete sets of curriculum materials.

I would use these materials in my classroom: Agree
(On a 4 point scale: Strongly Disagree, Disagree, Agree, or Strongly Agree)

Creative Commons License
This work by the Office of Superintendent of Public Instruction is licensed under a Creative Commons Attribution 4.0 International License.