High School - Gateway 3
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Usability
| Score | |
|---|---|
Gateway 3 - Partially Meets Expectations | 74% |
Criterion 3.1: Teacher Supports | 6 / 9 |
Criterion 3.2: Assessment | 7 / 10 |
Criterion 3.3: Student Supports | 7 / 8 |
Criterion 3.4: Intentional Design |
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for Usability. The materials partially meet expectations for Teacher Supports (Criterion 1), Assessment (Criterion 2), and Student Supports (Criterion 3).
Criterion 3.1: Teacher Supports
The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for Teacher Supports. The materials provide explanations of the instructional approaches of the program and identification of the research-based strategies, and provide a comprehensive list of supplies needed to support instructional activities. The materials partially provide general guidance that will assist teachers in presenting the student and ancillary materials, partially contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject, and partially include standards correlation information that explains the role of the standards in the context of the overall series.
Indicator 3a
Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. The materials do not consistently provide general guidance that will assist teachers in presenting the student and ancillary materials, but they do include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Examples include, but are not limited to:
Within each course a Lesson contains an Introduction, Ideas, Exploration (if applicable), Examples, and an Idea summary sections. The introduction connects prior learning to the current lesson. The ideas section lists concepts addressed within the lesson. The Exploration “provides students an opportunity to discover patterns and algorithms independently and connect them to prior knowledge.” The Examples build on the exploration and provide a worked solution, sometimes accompanied by a video. The Idea summary “consolidates student generated ideas into formal procedures, algorithms, and tools by presenting the key information in a student friendly way.” Although the materials provide a consistent structure in the layout of the lessons there are multiple instances throughout the materials where Examples in the Teacher guide are different from the Student Lesson; no explanation or guidance in using the different examples are provided to the teacher.
Teacher guides are provided with each lesson to assist teachers in preparing for and facilitating student learning. In most lessons, the teacher guide starts with a Suggested review of topics in previous grade levels and/or subtopics. For example: In Algebra 1, Subtopic 4.01, Lesson, Teacher guide, Suggested Review, “Depending on your students’ level of prior knowledge, consider revisiting the following lesson: Algebra 1 - 3.05 Graphing linear functions.” There is no guidance provided to the teacher on how to use the previous lessons with the students.
Evidence for materials including sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives to engage and guide student mathematical learning include:
In Algebra 1, Subtopic 6.01, Lesson, Teacher guide, Misunderstanding the term notation in a recursive rule (Address student misconceptions), provides the following support, “Students may incorrectly write a recursive rule. For example, for the sequence 3, 7, 11, 15,...students may say something like a_n=+4 because they recognize that we are adding 4 between terms. In addition, they may write something like a_n=a_n+4 without realizing that they are using the same variable on both sides of the equation. Support students to overcome this misconception by encouraging them to describe a_n in their own words. Then, help them determine which term is needed to find a_n and how that term relates to a_n. Remind students that a recursive rule should allow us to input the term number and have it output the term value. A table of values or annotated sequence may help students to see this.”
In Geometry, Subtopic 6.02, Lesson, Teacher guide, Exploration, Purposeful questions, “Which angles are considered consecutive angles in the diagram you created in the applet? What do the markings on the diagonals represent? Change the parallelogram’s shape. Are your responses to the questions the same?”
In Algebra 2, Subtopic 8.02, Lesson, Teacher guide, Example 3c, Reflecting with students, “Ask students if they think the situation is realistic and what limitations the real-world scenario might have. Let them know that stocks regularly increase and decrease based on the market, so the price of stocks would not realistically decrease by a simple formula. Also, the price of the stock would have a limitation on how low it can be feasibly traded and the number of stocks available for purchase would also have a limit.”
Indicator 3b
Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
The materials reviewed for Mathspace High School Tradition Series partially meet expectations for containing adult-level explanations and examples of more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.
Materials contain adult-level explanations and examples of the more complex course-level concepts so that teachers can improve their own knowledge of the subject. While adult-level explanations of concepts beyond the course are not present, there are embedded instructional supports designed to help teachers facilitate instruction while improving their knowledge of the subject. Opportunities for teachers to expand their knowledge include:
In Algebra 1, Subtopic 10.05, Lesson, Teacher guide, Lesson supports, List key features of functions and review which are easiest to identify (Targeted instructional strategies), “Provide students with a list of key features they can be asked to compare for different functions. … Some possible answers could be: To identify the domain for linear, quadratic, exponential, or linear absolute value functions we can use ‘all real values of x’, unless otherwise specified or determined by a constraint. It is easiest to see this with the graph and the table of values we can assume continues to follow the pattern unless otherwise stated. To identify the y-intercept, it is easiest from equations in the form y=mx+b, y=ax^2+bx+c, y=ab^x, y=\lvert{x}\rvert+k, versus other forms of these functions, as we can read the y-intercept directly from these forms. We can also see it fairly easily from the table if it is one of the given values, but otherwise we first have to find the equation or extrapolate from the table. From the graph, we need to look where the function crosses the y-axis. All of these functions will have exactly one y-intercept.”
In Geometry, Subtopic 4.03, Lesson, Teacher guide, Lesson supports, Rotate a figure by considering rotated translations (Targeted instructional strategies), “Teach students that we can rotate a figure about one of its vertices by considering the translations from the point of rotation to the other vertices. For example, suppose we want to rotate the line segment \overline{AB} about the point A by 90\degree counterclockwise. We can see that the translations required to get from A to B are 2 units right and 3 units up. Consider that if we rotate 90\degree counterclockwise, the directions of the translations will also rotate. So we get \cdot Right \rarr Up \cdot Up \rarr Left So then we can get from A to B’ by translating 2 units up and 3 units left. This rotates B, about A, to get B’ . We can do this for any pair of points, where one is the point of rotation. This means that we can use this to rotate any shape about one of its corners, rotating each corner with respect to the point of rotation.” An example of the translation from A to B on a coordinate plane is provided.
In Algebra 2, Subtopic 6.05, Lesson, Teacher guide, Examples, Explicit steps and phase shift (Targeted Instructional strategies), “Students may find difficulty with horizontal translations, in particular if the phase shift is not a multiple of \frac{Period}{4}. Using tables or graphs together with a sequence of steps could help students consistently transform the key points of the functions accurately. Explicitly show examples demonstrating phase changes to help students become comfortable with finding the new key points. Have students write a general set of steps for graphing a sine function of the form y=asin[b(x-c)]+d, including an example alongside the steps. In particular, students can use the step-by-step graphic organizer from our lesson support templates to support them in writing their steps…Note: When the phase shift is not a multiple of \frac{Period}{4}, the additional step of further dividing and labeling the x-axis in multiples of the lowest common denominator of the \frac{Period}{4} and the phase shift can assist being able to accurately translate the graph. Alternatively, working from a table and translating the x-values of key points before drawing the graph using an appropriate scale, may be more efficient for more complex transformations.” An example of the possible set of steps students can use to graph transformations of the sine function is provided.
Indicator 3c
Materials include standards correlation information that explains the role of the standards in the context of the overall series.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series. The materials do not include explanations of the role of the specific course-level mathematics in the context of the series.
Generalized correlations are present for the mathematics standards and are located in the Materials Guide, Textbook Guides, Correlations and Alignment documents, Topic overviews, and Subtopic overviews. Examples include:
In the Materials Guide, Correlations and Alignment documents are available for each course (Algebra 1, Geometry, and Algebra 2). The “Written Correlations” section provides, Lesson number and name, focus standards), prior connection standards, future connection standards, and mathematical practices for each lesson, if applicable. The “Standard Alignments” section lists the CCSSM and the subtopics where the content is covered.
Each course contains a Topic overview referencing CCSSM standards under the Foundational knowledge and Future connection sections. The Foundational knowledge section can include standards that are on course-level or from prior grades, the Future connection section list standards that students will cover in future lesson within the current course or outside the current course.
Each course subtopic contains a Lesson narrative that explicitly identifies where in the lesson you will engage with a mathematical practice. For example: In Algebra 2, Subtopic 3.05, Subtopic overview, the materials state, “In the Engage portion of this lesson, students will use repeated reasoning and structures to generalize the formula for factoring the difference of cubes (MP7, MP8) by investigating the volume of an actual difference of cubes (MP5). In the student materials, students will examine the structures (MP7) in order to plan a strategy (MP1) for factoring polynomials. Students will apply the remainder theorem to identify whether or not a divisor is a factor of a polynomial, and justify their reasoning (MP3). By the end of the lesson, students will be able to apply various strategies to factor polynomials.”
Each textbook has a Curriculum map; however, a description of how to use the map is not readily available for teachers. The curriculum map does not provide the student learning outcomes and where they are accessed.
Each topic's first subtopic is a Topic Overview which contains a section that lists Big Ideas and essential understandings, this section includes a summary statement about the big idea that connects a group of subtopics and a description of the essential understandings found in each subtopic. However, this section does not include explanations of the role of the specific course-level mathematics in the context of the series. Examples include:
In Algebra 1, Topic 3, Topic Overview, Overview, Big ideas and essential understanding, the first big idea states, “Functions provide a representation for how related quantities vary. This makes functions a good way to represent many real world situations.” The materials identify the essential understanding for the first three subtopics as the following: “(3.01) For a function that represents a real world situation, analyzing the output for a given input can provide valuable information for understanding the situation. (3.02) The domain and range of a function can provide insight into the context it models but a real-world context can also be a limiting factor on the domain and range of a function. (3.03) Rate of change describes how one quantity changes with respect to another. A function’s rate of change determines the function family it belongs to and the real world situation it can model.”
In Geometry, Topic 2, Topic Overview, Overview, Big ideas and essential understanding, “Geometric figures are bound by properties that can be verified.” The materials identify the essential understanding for the subtopics as the following: “(2.01) If two parallel lines have been cut by a transversal, the angle pairs that are formed are congruent, supplementary, or both. (2.02) The relationships between angle pairs created by lines cut by a transversal determine whether or not the lines are parallel. (2.03) Perpendicular lines are characterized by the right angle they make when they intersect.”
In Algebra 2, Topic 3, Topic Overview, Overview, Big ideas and essential understanding, the first big idea states, “The properties of real numbers can be applied to many types of expressions.” The materials identify the essential understanding for two of the subtopics as the following: “(3.01) Operations can be applied to polynomials in much the same way that they can be applied to real numbers. (3.04) Polynomials can be divided using steps similar to those used when dividing real numbers.”
Indicator 3d
Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials reviewed for Mathspace High School Traditional Series provide some strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.
The materials do not contain strategies for informing parents, or caregivers about the mathematics their student is learning. The Mathspace website, under the Solutions tab, does have a section dedicated to parents, but the statements address the overall curriculum and not specifically what students are learning. Examples include, but are not limited to:
“Engaging content in a fun and interactive format Your child can immerse themselves in our library of standards-aligned textbooks. All interactive, with videos and worked examples, this is an easy way to refresh on what they are learning at school.”
“Personalized learning recommendations for your child With regular skills check-ins, our smart learning engine will be able to identify knowledge gaps and make the best recommendations for what to learn next. What’s unique is that these recommendations can be made at every step, every question and at a curriculum level too.”
The materials does provide parents or caregivers with information about the progress of their student(s). In the Help section under Student Settings, it states, “Teachers can enter multiple parent/guardian emails for a student. This enables ‘Receive parent notifications’ which will send them a weekly email with progress updates of the student.”
Indicator 3e
Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.
The materials reviewed for Mathspace High School Traditional Series meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies. Instructional approaches of the program and identification of the research-based strategies can be found within the Materials Guide, General Guides, Research Basis document. Examples where materials explain the instructional approaches of the program and describe research-based strategies include:
Within Research Basis, the 1. Research base and design principles section describes the program instructional approaches and describes research-based strategies. Examples include:
In section 1a. Core Guiding Beliefs states, “We built these materials with four research-based core beliefs at the heart of our approach. They are:
All students must develop a positive mathematical identity that allows them to view themselves as learners and doers of mathematics.^1
Classroom structures should emphasize an inclusive mathematics community in which every student has a voice and teaching practices benefit all students.^2
A personalized learning approach should aim to offer learning experiences that customize education to an individual’s unique needs and interests while fostering connections to a larger community of learners.^3
Technology should support, enhance, and transform the role of the teacher in the classroom.^4
We transformed these beliefs into an educational approach that pairs an inquiry based curriculum with a world-class diagnostic and continuous formative assessment system to build procedural fluency from a strong foundation of conceptual understanding, with application integrated throughout our curriculum. We have created a clear, intentional instructional model with three phases: Engage, Solidify, and Practice – each of which is informed by Mathspace diagnostic and continuous formative assessment data, in order to provide a personalized journey towards mastery for every learner…^1(Boaler J. , 2002); (Boaler J. &., 2008); (Berry III, 2008); (Dweck C. S., 2007); (Martin, 2000) ^2(National Council of Teachers of Mathematics (NCTM), 2000); (National Research Council, 2001); (National Council of Teachers of Mathematics (NCTM), 2008); (Strutchens, 2011), (Gutiérrez, 2012) ^3(Surr, 2018) (Sandler, 2012) (Tomlinson, 1995) (DuFour, 2002) ^4(Surr, 2018) (Marzano R. W., 2005) (Hayes-Jacobs, 2018)”
In section 1b. Educational Approach states, “Mathspace offers an interactive digital program for high school mathematics that balances a student-centered, inquiry based instructional approach with a continuous formative assessment tool. This provides a truly personalized experience for all students as they develop a deep understanding of mathematics, as called for in the Common Core State Standards for Mathematics. Teacher resources provide a research-based rationale for instructional strategies to support the development of student identity as learners and doers of mathematics through a three-step process which includes elements of both student-centered and explicit instruction…”
In section 1c. How research informs our Curriculum and Lesson Structure states, “A typical Mathspace instructional module Mathspace subtopics follows a clear, intentional lesson structure with three phases 1 Engage \rarr 2 Solidify (please note at the time of this review Solidify has been changed to Lesson)\rarr 3 Practice Engage The Engage phase serves to develop student understanding by activating prior knowledge, intuition, and insights in order to make sense of a problem; which optimally prepares the student to acquire new learning.^{15} An Engage activity contains two parts: an agency opener followed by the launch-explore-discuss lesson framework… ^{15}(Kapur, 2018), (Hattie, 2008), (Boaler J. , 2002), (National Council of Teachers of Mathematics, 2014), (National Research Council, 2001)”
Throughout the document references to research-based strategies are cited and the document includes references pages at the end.
Indicator 3f
Materials provide a comprehensive list of supplies needed to support instructional activities.
The materials reviewed for Mathspace High School Traditional Series meet expectations for providing a comprehensive list of supplies needed to support instructional activities. The supplies are listed throughout the materials in the Subtopic, Lesson, Teacher guide section under Tools.
Examples of the tools listed include:
In Algebra 1, Subtopic 5.01, Lesson, Teacher guide, the supplies are listed in the tools section, “You may find these tools helpful: Graphing calculator, Scientific calculator, Blank coordinate plane, Ruler”
In Geometry, Subtopic 7.02, Lesson, Teacher guide, the supplies are listed in the tools section, “You may find these tools helpful: Protractor, Clear plastic sheets, Tracing paper”
In Algebra 2, Subtopic 1.02, Lesson, Teacher guide, the supplies are listed in the tools section, “You may find these tools helpful: Graphing calculator, Frayer model graphic organizer.”
Indicator 3g
This is not an assessed indicator in Mathematics.
Indicator 3h
This is not an assessed indicator in Mathematics.
Criterion 3.2: Assessment
The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for Assessment. The materials provide assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices. The materials partially include assessment information that indicates which standards and practices are assessed and partially provide multiple opportunities throughout the courses to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3i
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.
The digital side provides continuous formative assessment utilizing adaptive, AI-powered diagnostics, which “efficiently tracks student growth and identifies learning gaps, using formative assessment check-ins that contain five questions designed to last no more than 10-minutes.” The assessment bank contains over 40,000 adaptive questions. The adaptive tasks are organized by subtopic and can be assigned to students at will but do not identify the standard or mathematical practices for the individual task items. The growth and skill check-ins can be assigned to students, but the skill check-in also allow students to pick a standard that they wish to work on independently of the teacher. Both check-ins questions are system-generated and with the overall standard being identified for the results.
“Each topic includes a summative Topic Assessment, which includes items similar to those found on standardized assessments, with questions aimed at evaluating student understanding of the relevant benchmarks for the entire topic. This is combined with a performance task assessment opportunity to more fully assess what mathematical understanding students have gained in various ways. Answer keys provide the correlating benchmarks so that the results of the summative assessments may still be used formatively, to set personalized learning targets.” Although, the standards are identified for all items in every Topic assessment, the mathematical practices are only identified for the performance task item when the Topic assessment has one.
Examples include, but are not limited to:
Weekly check-in. “Select the two correct statements for the following sum: \frac{1}{2}+\frac{3}{2} The numbers add up to 2 which is a rational number. The numbers add up to 2 which is an irrational number. The answer is not a fraction, so the sum must be irrational. Both of the numbers are rational, so the sum must be rational. Both of the numbers are irrational, so the sum must be irrational.” The skill map identifies the standard code N.RN.3 for this weekly check-in. Mathematical practices are not listed for this item.
In Geometry, Topic 5, Topic Overview, Assessment, Performance Task, Question 12, “Stained glass designs often use congruent triangles to create appealing patterns. a Draw a stained glass design that uses at least 3 different pairs of congruent triangles. Use geometric construction to ensure the triangles are congruent. b For each pair of congruent triangles, describe the transformations that map one triangle onto the other. c Label the vertices of each triangle and, for each pair of congruent triangles. Label the vertices of each triangle and, for one pair of congruent triangles, list all of the corresponding parts. d For each pair of congruent triangles, explain the type of congruence you used to construct the triangles.” The answer key shows the aligned standards as G-CO.6, G-CO.7, G-CO.8, G-CO.12, G-SRT.5 and the mathematical practices as MP5.
In Algebra 2, Topic 4, Topic Overview, Assessment, Question 4, “Consider the function y=2(x-5)^2(x+2)(x+1). a Find the zero(s) of the function and their multiplicities. b Determine the end behavior of the function. c Sketch the graph of the function.” The answer key shows the aligned standards as F-IF.4, F-IF.7c and A-APR.3. Mathematical practices are not listed for this item.
Indicator 3j
Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The materials reviewed for Mathspace High School Traditional Series partially meets expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
The assessment system provides multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance and provide suggestions for following-up with students but only for the formative assessments. Summative Topic Assessment answer keys include a digital and paper option. The answer key identifies the correct answer(s) and the standard(s) assessed. Although answer keys are provided there is no guidance provided to teachers for interpreting student performance or suggestions for following-up with students. Examples include, but are not limited to:
In Algebra 1, Topic 3, Topic Overview, Assessment, Answer key, Question 5, “y\geq200 F.IF.A.2”
In Geometry, Topic 11, Topic Overview, Assessment, Answer key, Question 13, “Yes G.GPE.B.4”
In Algebra 2, Topic 5, Topic Overview, Assessment, Answer key, Question 12, “ a -\frac{1}{4}, b \frac{\sqrt{2}}{2}, c \frac{9}{4} F.TF.A.2”
For formative assessments, “The reporting page provides educators with whole-class and individual student reports by standard and benchmark. You can filter reports to see student proficiency across grade level, strands, standards, and benchmarks. Data is summarized to quickly spot trends and identify special areas of concern. With the growth report page, you can see an annual growth rate estimation and real time progress on grade level skills. This gives you an opportunity to intervene if students require additional support.” There are no tools for scoring as all assessments are online and scored by the computer system. Darker shades of purple correspond to higher levels of mastery, and the red exclamation mark on a topic or subtopic indicates a student(s) needs assistance, clicking on it shows you the mastery level of the student, the time spent on the task, and the questions they attempted including the answer and if the student skipped parts or required hints.
Indicator 3k
Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.
The materials reviewed for Mathspace High School Traditional Series meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of course-level standards and practices across the series.
Each Topic includes a summative Topic assessment, which assesses the full range of standards addressed in the topic using short-answer and constructed response questions. When performance task item(s) are included on the Topic assessment they are usually constructed response question(s) that sometimes have various solutions with the intent of having students assess higher depths of knowledge. Topic assessments are to be downloaded as PDFs and designed to be printed and administered in-classroom.
The formative assessment item types include multiple choice and short-answer. Teachers can assign individual adaptive tasks to students, these assignments are identified by subtopic.
Examples of assessment including opportunities for students to demonstrate the full intent of course-level standards and practices include:
In Algebra 1, Topic 11, Topic Overview, Assessment, Performance Task, Question 15, demonstrates the full intent of the standards A-SSE.3a, A-REI.4, A-REI.4b, MP1 and MP4. “Ursula is launching a pumpkin off the edge of the physics building at her school with a small catapult. a Determine an equation, defining any variables, that models the path of the pumpkin given the following information: The physics building is 24 m high. When the pumpkin is 2 m from the building, it is 44 m high. When the pumpkin is 3 m from the building, it is 30 m high. b Use an efficient method to find how far from the building the pumpkin hits the ground. Explain your method. c Ursula wants to do a demonstration where she launches the pumpkin into a target. If the target is 2 m high, how far from the building does she need to place it so it gets hit by the pumpkin? Explain.”
In Geometry, Topic 4, Topic Overview, Assessment, Question 6, demonstrates the full intent of the standard G-CO.3. “Consider the regular polygon: a Which of the lines shown in the figures are lines of reflection? b Identify the number of lines of reflection the figure has. c Determine if each of the following transformations would map the figure onto itself: i A rotation of 180\degree about the center, point s. ii A reflections across line r through midpoints of opposite sides. iii A reflection across line p through one vertex, the center s. iv A reflection across line q which passes through a vertex and a midpoint of an opposite side.” Students are provided a picture of a regular polygon.
In Algebra 2, Subtopic 8.02, Practice, Adaptive, demonstrates the full intent of the standard F-BF.1b. “Given the following values: f(2)=4, d(7)=14, f(9)=18, f(8)=16, g(2)=8, g(7)=28, g(9)=36, g(8)=32 Find (f+g)(2)”. This task is considered medium difficulty level and is estimated to take approximately 1 minute.
Indicator 3l
Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
The materials reviewed for Mathspace High School Traditional Series do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.
Summative assessments are designed to be downloaded as PDFs and administered in class. There is no modification or guidance given to teachers within the materials on how to administer the assessment with accommodations.
Using the Custom Tasks, advanced options on the task creation panel, teachers have the ability to allow retries of questions for students to improve their scores. Students will see the option "Try again" when they complete a question without full marks. Students are given five attempts to re-try the question, after which the retry button will be disabled and a tooltip will appear saying that they're out of retries.
The materials do provide a screen reader in accessibility modebut is only available within Mathspace Worksheets, and not all assessments.
Criterion 3.3: Student Supports
The program includes materials designed for each student’s regular and active participation in grade-level/grade-band/series content.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations to support their regular and active participation in learning course-level mathematics, strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning course-level mathematics and provide manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. The materials partially provide extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity.
Indicator 3m
Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.
The materials reviewed for Mathspace High School Traditional Series meet expectations for providing strategies and support for students in special populations to support their regular and active participation in learning series mathematics.
An overview of supports within the series can be found in the Materials Guide, General Guides, Supporting EVERY Student with Mathspace document. The Multi-tiered System of Support section highlights the three-tier system that Mathspace uses, Tier 1 focuses on “Elements that create a supportive classroom environment for all students” which includes clear learning targets at the start of each subtopic, and agency openers to provide positive experiences with mathematics, Tier 2 focuses on “Helping teachers provide targeted supports to small groups of students” which includes using data from continuous formative assessment to inform next steps, and differentiated and customizable practice to support all students in grade level work, and Tier 3 focuses on “Intensive intervention for those who need it” which states, “Mathspace makes recommendations from its adaptive formative assessments to ensure that students learn content at the edge of their understanding. By keeping students in their zone of proximal development and using technology to achieve personalization at scale, Mathspace can be used as a highly effective Tier 3 intervention program.” The Supporting Student with Disabilities section states the following: “...Within our teacher resources, adaptations are offered for teacher consideration in supporting a number of learning needs in eight key areas which have been identified to have a strong impact on student success in mathematics: Conceptual processing, Language, Visual-spatial processing, Organization, Memory, Attention, and Fine-motor skills. Mathspace core instructional materials provide interactive virtual manipulative applets which offers visual and kinesthetic opportunities to deepen conceptual understanding. Accessibility Mode is available (WGAG 2.0 AA compliant) – to ensure that student materials are accessible to students with a wide range of visual and/or reading focused disabilities. This includes such supports as text to speech and braille translation through the use of a number of widely used, assistive technology tools. Additional supports embedded in student materials include: a glossary with images to reinforce text-based definitions of mathematical terminology, a suite of virtual calculator tools to reduce cognitive load often required to perform arithmetic calculations when learning new concepts.”
The Teacher guide in each subtopic provides “Lesson Supports” that purpose is to “assist teachers in differentiating instruction for all students.” The Engage task also provides “supports for students with disabilities” in the preparation and materials section. Examples of the materials providing strategies and support for students in special populations include:
In Algebra 1, Subtopic 4.01, Lesson, Teacher guide, Lesson supports, Assist graphing (Students with disabilities support), “Provide students with larger grid paper or provide printed prelabeled axes. Consider allowing students to use a digital tool like GeoGebra or Desmos to graph the lines. Since accuracy is important when identifying the solution from a graph, if technology is not available, consider scribing or pairing students to have one student explain and the other to draw.”
In Geometry, Subtopic 1.01, Engage, Preparation and materials, Support students with disabilities, “Support collaboration - work in groups. Students are contributing equally to create a collaborative piece of artwork which may involve the critique of each other’s ideas and needs to involve the input from every member. Choose groups intentionally to provide support for students who struggle with social interactions and provide the whole group with suggestions for how to support and include each other’s ideas. Prompts groups can use to help with collaboration: What part of the artwork are you taking inspiration from? How do you want to work that part into our artwork? I'm not sure I understand your inspiration, can you explain it to me in another way? I'm not sure how your inspiration fits with my inspiration. Do you have ideas of how we can connect our art together? I think your piece of the artwork would work in this area because...”
In Algebra 2, Subtopic 7.02, Lesson, Teacher guide, Lesson supports, Break up information and create a visual diagram (Students with disabilities support), “Help students to break up the information into separate sections: key features of the square root function, key features of the cube root function, transformations. It can also help to highlight key information, like the phrase ‘Radical functions can be transformed in a similar way to other functions.’ Further support can be provided by reformatting information into a visual support, such as a diagram of the parent functions with their key features labeled.”
Indicator 3n
Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.
The materials reviewed for Mathspace High School Traditional Series partially meet expectations for providing extensions and/or opportunities for students to engage with course-level mathematics at higher levels of complexity.
The materials provide students with multiple opportunities to extend their thinking with course-level mathematics at higher levels of complexity in the practice worksheets. However, there is no guidance given to the teacher on how to assign these extensions to ensure individual students would not be completing more assignments than their classmates. Examples include but are not limited to the following:
In Algebra 1, Subtopic 3.06, Practice, Worksheet, Let’s extend our thinking, Question 17, “Effie is a entomologist and is currently studying mosquitos and spiders. She knows that mosquitos have six legs and spiders have eight legs. In her lab, she has a mix of mosquitos and spiders. Between all the bugs, there is a total of 240 legs. a Create a model to represent this scenario. Define any variable and include appropriate labels in your model. b State and describe the possible number of mosquitos. c Explain whether or not every point on the line represents a possible solution.”
In Geometry, Subtopic 10.01, Practice, Worksheet, Let’s extend our thinking, Question 20, “The area of a triangle with vertices A(3,0), B(8,2), and C(8,-6), has been calculated. a If the triangle is translated up 3 units, determine if the area will change. Explain your answer. b If only the vertex A(3,0) is translated up 3 units, determine if the area will change. Explain your answer.”
In Algebra 2, Subtopic 4.03, Practice, Worksheet, Let’s extend our thinking, Question 16, “Explain why a real-valued polynomial of odd degree always has at least one real zero.”
Indicator 3o
Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
The materials reviewed for Mathspace High School Traditional Series provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.
Mathspace subtopics follows a clear, intentional lesson structure with three phases including Engage, Lesson, and Practice. The Engage phase, is designed to build conceptual understanding for students through discourse and exploration via rich tasks that are low floor, high ceiling and peak student interest. In the Lesson phase, students deepen their knowledge through student facing lessons that continue to build conceptual understanding while connecting it to procedural knowledge and skills and preparing students to apply their understanding to real-world contexts. In the Practice phase, personalized practice creates unique learning experiences customized to a student’s individual needs, while building personal connections to the larger community of math learners. Examples of where materials provide varied approaches to learning tasks over time and variety of how students are expected to demonstrate their learning include:
In Algebra 1, Subtopic 1.03, Engage, “Which one doesn't belong? Select one option. Explain your choice.” Students are given the four following choices: A) 5 + 18, B) 5\times4+3, C) 28 - 5, and D) 14 + 11.
In Geometry, Subtopic 6.02, Lesson, Exploration, students explore a parallelogram using a GeoGebra applet. They are expected to draw conclusions about congruent sides and angles of a parallelogram. Students complete statements about the consecutive angles and the diagonals of a parallelogram, distinguishing what makes a quadrilateral a parallelogram. “Drag the points to change the quadrilateral and use the checkboxes to explore the applet. Use the applet to complete the following sentences: 1. A quadrilateral is a parallelogram if and only if its opposite sides are . 2. A quadrilateral is a parallelogram if and only if its opposite angles are . 3. In a parallelogram, consecutive angles will be . 4. A quadrilateral is a parallelogram if and only if its diagonals each other.” The applet has a quadrilateral and students are able to manipulate two points on the quadrilateral, they can also toggle whether to “Show side lengths”, “Show diagonals” or “Show angles”.
In Algebra 2, Subtopic 3.01, Practice, Worksheet, Question 12, students find the perimeter of two different figures. “Find a simplified polynomial that represents the perimeter of the following figures:” Figure a is a quadrilateral with two sides labeled, 8x^2+9x+5 and x+4. Figure b is a triangle with all sides labeled, 4x^2+x, 4x^3+2x^2+5, and 2x+3.
Regular diagnostic check-ins allow students to demonstrate understanding and track their growth throughout the lessons. “Skills check-ins are designed to be student-led and teacher-defined…Both teachers and students will see the data immediately as soon as a student completes one check-in.” These check-ins can either by assigned by the teacher or a student can start a check-in on standard when they feel that they are ready.
Students are also able to monitor their learning at the conclusion of the Engage activity. Students are asked to complete a reflection and to indicate their readiness to participate in different types of practice related to the concepts they have explored.” The reflection always features two questions: 1) How do you feel after completing this activity? Students then rate themselves as one of the following choices: Feeling lost, Proud, Confident, Frustrated, Intrigued, or Exhausted and 2) What would help you to understand this topic? Students select one of the following options: Practice questions, Try harder questions, A class discussions, More explanation, or My own revision.
Indicator 3p
Materials provide opportunities for teachers to use a variety of grouping strategies.
The materials reviewed for Mathspace High School Traditional Series provide some opportunities for teachers to use a variety of grouping strategies. “Mathspace has intentionally built slides into our Engage activities to promote the use of our ‘think-pair-share’, ‘numbered heads together’ and ‘team roles’ grouping and thinking routines. These routines create opportunities where students must depend on one another.” The Teacher guide, Exploration section contains three types of suggested grouping options for students during the section, individual, small group, or pairs. Although, the materials provide a detailed description of grouping and thinking routines used for Engage activities and the Exploration section suggests student grouping there is no guidance provided on the composition of the groups.
Examples of the materials providing opportunities for teachers to use a variety of grouping strategies include:
In Algebra 1, Subtopic 2.02, Engage, Launch, “Suggested grouping: Form groups”. Explore, a grouping strategy of “Numbered heads together” is referenced. Discuss, “Have several pairs share their processes for solving the equations. Start with those that solved the problem visually before moving to those that solved the problem algebraically.” The “Finding your group” page of the Engage activity give the following information, “Your teacher will help you form groups in your class. They will also give you a number.” However, there is limited information provided on how to group students based on student needs.
In Geometry, Subtopic 6.01, Lesson, Teacher guide, Exploration, “Suggested student grouping: Small groups Students explore a GeoGebra applet with two triangles that have two pairs of similar side lengths with a congruent included angle. Students change the scale factor and side lengths of the triangles using sliders. Students notice that the side lengths will remain proportional.” However, there is limited information provided on how to group students based on student needs.
In Algebra 2, Subtopic 5.02, Lesson, Teacher guide, Exploration, “Suggested student grouping: In Pairs Students rewrite improper fractions as mixed numbers, and try to relate this concept to simplifying a rational expression where there are common factors in the numerator and denominator.” However, there is limited information provided on how to group students based on student needs.
Indicator 3q
Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The materials reviewed for Mathspace High School Traditional Series meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.
The Materials Guide, General Guides, Research Basis document, 3c. Supporting ELLs section highlights how the materials supports students who read, write and/or speak in a language other than English in the following three ways: Digital features, “Visual design features have been utilized to increase readability. For example, clear, concise explanations are offered in student-friendly language. Visual aids are used to present information in an accessible and engaging format within the student materials and teachers are provided with graphic organizers such as Venn Diagrams to help students’ process new content. In addition, a glossary with helpful visualizations of key terms is available to support language acquisition for English Language Learners.” Curriculum design elements, “Key vocabulary for each module of instruction is listed at the beginning of each subtopic. Students will engage in active literacy and note-taking practices while explicit connections are made to the Standards for Mathematical Practice (SMPs) during Solidify [Lesson] instruction via structures that develop meta-cognitive and meta-linguistic awareness. These explicit connections to support English Language Development may be enhanced by: teachers taking opportunities to amplify language during Solidify [Lesson] instruction so that students can make their own meaning; or by providing flexibility for a variety of linguistic output – including opportunities for students to describe their mathematical thinking to others orally, visually and in writing, as well as participating in tasks that cultivate conversation during the Engage phase.” Math language routines, “We have chosen to embed the following mathematical language routines in our curriculum because they are the most effective and practical for simultaneously learning math thinking and reasoning, content, and language. They facilitate attention to student language in ways that support in-the-moment teacher-, peer-, and self- assessment. The feedback enabled by these routines will help students revise and refine not only the way they organize and communicate their own ideas, but also ask questions to clarify their understanding of others’ ideas.”
Examples where the materials provide strategies and supports for students who read, write, and/or speak in a language other than English include:
In Algebra 1, Subtopic 2.03, Lesson, Teacher guide, Lesson supports, Literal equations use letters (but not words) (English language learner support), “English language learners are likely to assume that the term ‘literal equation’ refers to an equation with words, confusing it with ‘word equation’. Explain that a ‘literal equation’ means that there are multiple letters in the equation, while a ‘word equation’ is written entirely in words. It may help to draw a connection between the sound of ‘literal’ and ‘letter’ to aid student memory of this difference.”
In Geometry, Subtopic 10.05, Lesson, Teacher guide, Lesson supports, Literacy exercise: stronger and clearer each time (English language learner support), “Use this routine to help students improve their written proofs. Give students time to meet with two to three partners to share and receive feedback on the flow, validity, and clarity of their proof. Display feedback prompts that will help students strengthen their ideas and clarify their language. For example, ‘How do you know that the diagram you have labeled is indeed an isosceles trapezoid?’ and ‘How can you go from knowing that one line is vertical and the other is horizontal to concluding that they are perpendicular to one another?’ Invite students to go back and revise or refine their written proofs based on the feedback from peers. This will help students justify using sound mathematical reasoning something that might be intuitively true.” (MLR 1)
In Algebra 2, Subtopic 5.02, Lesson, Teacher guide, Lesson supports, Comprehension exercise: collect and display (English language learner support), “As students are working, note how they describe the concepts of ‘rational expression’ and ‘simplifying’. Collect the different ways that students find to understand these concepts and display them in a common place for students to access. If students do not come up with alternative ways to word these concepts and are confused by them, suggest some of your own. For example:
Rational expression
Fraction of polynomials
Fraction of expressions
Fraction with operations in numerator and denominator
Simplifying
Reducing the number of terms in the numerator or denominator
Reducing the degree of the numerator and denominator
Eliminating a common factor from the numerator and denominator
Take care to address any rewordings that contradict or are too similar to other concepts that the student will learn in the future, such as ensuring students know that rational terms are a type of rational expression, although simpler than the ones being looked at in this topic.” (MLR 2)
Indicator 3r
Materials provide a balance of images or information about people, representing various demographic and physical characteristics.
The materials reviewed for Mathspace High School Traditional Series provide a balance of images or information about people, representing various demographic and physical characteristics. The materials do not contain many images depicting people, when images of people are used they do represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Subtopics do include a variety of names in problem contexts that are representative of various demographics.
An overview of supports with the series can be found in the Materials Guide, General Guides, Supporting EVERY Student with Mathspace document. The Supporting Diverse Student Populations section state the following: “A core belief of the Mathspace product, is that attending to the dimension of student identity through a multi-culturally informed approach to content development is critical to student success in mathematics. Engage activities are regularly focused on themes related to diverse students’ pasts including their heritage and the contributions of their ancestors allowing them to make mathematical connections to real-world applications. This multi-cultural balance is also reflected in the diverse cast of animated character illustrations used throughout this series, in order to allow students to have opportunities to see themselves reflected in the curriculum while having a view onto a broader world.” The picture below this statement depicts four individuals of various demographics and physical characteristics.
Examples of the materials providing a balance of images or information about people, representing various demographic and physical characteristics include:
The opening page to the Engage activities features an image of three people of various demographics.
In Algebra 1, Subtopic 11.06, Engage, “Jiang is learning more about skeet shooting and other Olympic shooting events. In skeet shooting a clay target, called the clay pigeon, is launched from a trap house a fixed distance from the shooter. If the height and distance traveled of the clay target along its path is known, how can a shooter plan their aim mathematically?” An image of Jiang wearing glasses and skeet shooting is shown.
In Geometry, Subtopic 8.03, Engage, “Harriet and her dad love to work on cars together. In order to get under the car safely, they use jacks to lift the car. Harriet and her dad want to build a pair of custom ramps that will guide the cars onto a jack so that they can lift a car inside of their garage…”
In Algebra 2, Subtopic 8.01, Practice, Worksheet, Question 22, students are given the following scenario, “When comparing two phone companies, Akeem notices that both offer a $100 monthly contract, but they have different policies on how they charge fees if the bill is overdue…”
Other names that could represent a variety of cultures are represented in the materials, i.e., Lucinda, Neville, Sophia, Jack, Fernando, Rosa, Georgia, Emilio, Athena, and Ursula
Indicator 3s
Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.
The materials reviewed for Mathspace High School Traditional Series do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.
In the Materials Guide, General Guides, Supporting EVERY Student with Mathspace, Supporting Diverse Student Populations section it states the following, “textbooks are printable for students and are offered in English and Spanish.” In the Help menu, the article, “Using Mathspace in Spanish or other languages” provides “step by step instructions on how to translate Mathspace using Google Chrome”. There is no evidence of promoting home language knowledge as an asset to engage students in the content material or purposefully utilizing students' home language in context with the materials.
Indicator 3t
Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.
The materials reviewed for Mathspace High School Traditional Series provides guidance to encourage teachers to draw upon student cultural and social background to facilitate learning.
The Mathspace Research Basis document states the following: “A core belief, foundational to the development of Mathspace Common Core materials, is that attending to the dimension of student identity through a multi-culturally informed approach to content development is critical to student success in mathematics. Engage activities are regularly focused on themes related to diverse students’ pasts including their heritage and the contributions of their ancestors to allow them to make connections to real-world applications of the mathematics that they are studying. These activities are designed to strike a balance between developing prior knowledge and having students make connections to ways in which the mathematics is embedded in the experiences of other cultures. This multicultural balance is also reflected in the diverse cast of animated character illustrations used throughout the series, in order to allow students to have opportunities to see themselves reflected in the curriculum while having a view onto a broader world.”
Examples of the Engage activities drawing upon students' cultural and social backgrounds to facilitate learning include:
In Algebra 1, Subtopic 4.01, Engage, students choose from four recipes, arroz con pollo, saag paneer, spaghetti marinara, and egg drop soup. Students are given a price list for ingredients and a budget of fifteen dollars to determine the number of servings. Launch, “Have recipe cards prepared to share with students based on the recipe selected. Provide students with graphing paper or unlabeled graphs to work on. Recommended: Collect grocery ads or provide a way for students to research grocery prices at their local stores as part of the extension of this activity.”
In Geometry, Subtopic 2.01, Engage, students design a multi-cultural weave incorporating parallel lines. Launch, “For contextual background: Ask students what they know about the art of weaving. Allow students to share what they know about weaving within their own culture or other cultures they have learned about. Share that there are many indigenous communities in the Philippines with long histories of weaving, and that many communities have their own particular style or desing of weaving. If time permits, show a short video clip or images of various weaving types found within the Philippines or around the world. If students have a particular context or design to share, encourage students to share with the class and try to use the context for inspiration or design for the activity.”
In Algebra 2, Subtopic 7.02, Engage, students work in groups to investigate the speed of tidal waves and estimate when they will hit various coastlines. Launch, “Use the Launch as an opportunity to discuss what tidal waves are. Invite students to share their experiences living on the coast, if they have, or their experience with tidal waves themselves.”
Indicator 3u
Materials provide supports for different reading levels to ensure accessibility for students.
The materials reviewed for Mathspace High School Traditional Series provide supports for different reading levels to ensure accessibility for students.
The materials state, “Mathspace is committed to making content that is accessible to students with different learning needs. Our new Accessibility mode allows students to use screen readers within Mathspace Worksheets.” Mathspace provides a list of “screen readers that read maths content and work with Mathspace-supported browsers and devices.” When using Accessibility mode you are unable to access practice adaptive problems as the screen reader can only be used within Mathspace Worksheets.
The materials also include embedded instructional strategies, such as the Math Language Routines that are specifically geared directly to different reading levels to ensure accessibility for students. Examples include:
In Algebra 1, Subtopic 11.02, Lesson, Teacher Guide, Lesson supports, Literacy exercise: stronger and clearer each time (English language learner support), “Ask students to write or otherwise communicate an explanation for why the factors of the factored form are related to the solutions of the corresponding equation. Put students into pairs and instruct them to present their explanation to their partner. Give enough time for students to give feedback and discuss an explanation together. After their discussion, give students time to refine their explanation using the results of their discussion and any feedback they received.” (MLR1)
In Geometry, Subtopic 2.01, Lesson, Teacher Guide, Lesson supports, Vocabulary exercise: critique, correct, and clarify (English language learner support), “Before students share their responses, display the following incorrect statement: ‘I know when a transversal intersects two parallel lines, the alternate interior angles are congruent because they are vertically opposite.’ Invite students to identify the error, critique the reasoning, and write a correct explanation. Invite one or two students to share their critiques and corrected explanations with the class. Listen for and amplify the language students use to describe the error and misuse of vocabulary. Elevate explanations such as ‘shared vertex’ versus ‘shared transversal’, ‘using corresponding angles’, or visual diagrams. This will help students better understand why alternate interior angles are congruent.” (MLR3)
In Algebra 2, Subtopic 3.01, Lesson, Teacher Guide, Lesson supports, Comprehension exercise: three reads (English language learner support), “Addition, subtraction, and multiplication of polynomials should all be skills students have encountered previously in Algebra 1, but questions may be worded in unfamiliar ways or presented in a context. Encourage students to read questions multiple times where necessary. On the first read, students can describe the situation by answering questions like, ‘What is this problem about?’ or ‘What type of question is being asked?’ Take time to discuss the meaning of any unfamiliar terms - mathematical or conversational. On the second read, students can identify quantities and relationships by answering questions like ‘What can be measured or counted?’ or ‘What information have we been given?’ or ‘What information are we looking for?’ On the third read, students can brainstorm possible strategies by answering questions like ‘What would an answer look like?’ or ‘What is the key information that we will use?’” (MLR6)
Indicator 3v
Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials reviewed for Mathspace High School Traditional Series meet expectations for providing manipulative, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.
The materials include virtual manipulatives that are presented as applets throughout the series. Examples of how virtual manipulatives are accurate representations of mathematical objects and are connected to written methods, when appropriate include:
In Algebra 1, Subtopic 6.05, Lesson, Exploration, students use an applet to identify the effect on the graph when replacing f(x) with f(x)+k and f(x+k) for positive and negative values of k. “Move the sliders to see how each one affects the graph. Choose different functions to compare the affects across the various graphs.” The applet has a blank Cartesian Plane and the option to produce a linear, exponential, or absolute value function. For each function, students are provided two sliders, one to manipulate the h value from -6 to 6 and one to manipulate the k value from -5 to 5 both sliders can only be decreased or increased by increments of 1. Students can also toggle whether to use an -a or -b value.
In Geometry, Subtopic 1.04, Lesson, Exploration, students use the applet to construct the different types of angles and observe the reflex of each angle. “Check the box to ‘show reflex angle’ and drag point A to change the measure of the angle.” The applet allows students to change a singular angle measure. Students can select “show reflex angle” as they change the angles.
In Algebra 2, Subtopic 6.04, Lesson, Exploration, students use a GeoGebra applet to explore the relationship between a point rotating around the unit circle and the graph of the sine function. “Explore the applet by moving the slider.” The applet has a unit circle and sine function on a Cartesian Plane. Students can manipulate the value of \theta to equal any value from 0\degree to 360\degree by increments of 3\degree. As students choose values of \theta a triangle is placed on the unit circle anchored at the origin and a line is drawn that shows where it corresponds to the sine function. A virtual manipulator shows triangles placed onto the coordinate anchored at the origin.
Criterion 3.4: Intentional Design
The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.
The materials reviewed for Mathspace High School Traditional Series integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in series standards, have a visual design that supports students in engaging thoughtfully with the subject and is neither distracting nor chaotic and provide teacher guidance for the use of embedded technology to support and enhance student learning. The materials do not include or reference digital technology that provides opportunities for collaboration among teachers and/or students.
Indicator 3w
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.
The materials reviewed for Mathspace High School Traditional Series integrate technology such as interactive tools, virtual manipulative/object, and/or dynamic mathematics software in ways that engage students in the series standards, when applicable. Interactive virtual manipulative applets are embedded throughout the series within the lessons and the Engage activities. Students have access to a Toolbox that includes five GeoGebra calculators (Scientific, Graphing, Geometry, 3d, and Statistics). Additionally, students can create study notes for any lesson, this software allows students to write their notes within the lesson and highlight text in one of four colors and one of three styles.
Examples of how the materials integrate technology such as interactive tools, virtual manipulative/objects, and/or dynamic mathematics software in ways that engage students in the series standard include:
In Algebra 1, Subtopic 3.08, Engage, students use an applet to create a light show by graphing the beam of light and its reflection on the coordinate plane. “Use the applet to create your light show. Create a light show that has \bullet At least four unique laser beams \bullet Some steep and some shallow beams \bullet Only one beam reflecting at the origin …”
In Algebra 1, Subtopic 7.02, Lesson, Exploration, students use an applet to compare how the mean and median of a data set change when an outlier is introduced to a data set. “Explore the applet by dragging Point P and clicking the button for a new set of data.”
In Geometry, Subtopic 2.01, Lesson, Exploration, students drag points along two parallel lines and a transversal to observe relationships of corresponding, alternate interior, consecutive interior, vertically opposite, alternate exterior, and consecutive exterior angles. “Check the parallel lines box, then use the points to drag the transversal and the parallel lines.”
In Geometry, Subtopic 3.01, Lesson, Exploration, students manipulate an applet to investigate the relationship between the interior angles of a triangle. “Drag the vertices of the triangle to change the size of each angle. Check the box to explore.”
In Algebra 2, Subtopic 8.02, Engage, students use an applet to combine functions of their choice in various ways and observe the results. “Use the applet to combine different functions. Describe the results of combining the different function types in each of the three ways: f(x)+g(x), f(x)-g(x), f(x)\times g(x)” Two functions can be manipulated with either of the following four options: Linear, Exponential, Polynomial, and Quadratic. Students can also combine the functions using addition, multiplication, and subtraction.
In Algebra 2, Subtopic 9.02, Lesson, Exploration, students use a digital simulator to randomize 100 science test scores. “The simulation below shows the number of questions guessed correctly if a person was guessing at random. There are 100 trials represented.” A “Rerandomize” button is present for students to re-randomize the data if they choose.
Indicator 3x
Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
The materials reviewed for Mathspace High School Traditional Series do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.
While the materials contain references to group work, the activities are expected to be conducted in the physical classroom with the teacher facilitating instructions without the use of digital technology to collaborate. Within the Engage activities, students can record their answers using digital technology for the teacher to review; however, teachers cannot digitally collaborate with students through an Engage activity.
Indicator 3y
The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
The materials reviewed for Mathspace High School Traditional Series have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.
Teacher and student materials are consistent in layout and structure across the series. The left side bar of each textbook indicates the topic and each topic expands to show subtopics. Subtopics that contain Engage activities are identified by a lightbulb icon. There is also a consistent design within the topics and subtopics to support learning on the digital platform. Each topic contains a Topic overview, (which includes Foundational knowledge, Big ideas and essential understanding, and Future connections) and a summative assessment.
Examples of images that are not distracting and support students in engaging thoughtfully with the subject include:
In Algebra 1, Subtopic 11.02, Lesson, Example 5, students write a quadratic equation in standard form modeling a whale’s jump. A picture of a whale jumping out of the water is provided.
In Geometry, Subtopic 3.03, Lesson, Example 4, students use the triangle inequality theorem to determine if Minerva needs to hike more than 2.5 miles. A map containing a section of the Redwood National Park is provided, with the areas mentioned in the scenario highlighted.
In Algebra 2, Subtopic 5.07, Lesson, Example 2, students use rational functions to find the average speed of a plane. A map of the United States is provided with an arc representing the path of an airplane traveling from New York City, NY to Los Angeles, CA.
While the visual design within the topics and subtopics supports students in engaging thoughtfully with the subjects, there are some images throughout the materials and times during generative adaptive tasks when problems or images that are generated contain errors that are mathematical inaccurate making information communicated unclear.
Indicator 3z
Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.
The materials reviewed for Mathspace High School Traditional Series provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable. Guidance for the use of embedded technology can be found in either the Support or Help sections which can always be accessed on the left side panel.
Examples of resources, articles, and/or videos that provide teacher guidance include:
Using Mathspace as a Teacher
How to create a class
How to add students into your class
Navigating the textbooks
How to set adaptive tasks for your students
Can my students type their answers into Mathspace?
Using Mathspace in your class
In Algebra 1, Subtopic 4.04, Teacher guide, Exploration, students explore the graph of a linear inequality in two variables through an applet. The teacher is provided with Ideal Student responses to the following questions, “What do you notice about the label when the point is in the shaded vs. the unshaded region? Why do you think that happens? What do you notice about the label when the point is on the boundary line? Why do you think that happens? How does the inequality symbol affect the graph and the label on the point? Why do you think that happens?”
In Geometry, Subtopic 8.05, Teacher guide, Explorations, students work in small groups to use an applet to explore the ratios of the sine of an angle and the length of its opposite side as they drag any of the vertices of an oblique triangle. The materials state, “Students use GeoGebra applet to create a triangle and record its side lengths, angle measures, and the sine of each angle measure divided by the length of the opposite side. Students discover that the ratios of the sine of the triangle’s angle measures divided by the length of the opposite side are equivalent.”
In Algebra 2, Subtopic 9.03, Teacher guide, Example 4c, students are encouraged to use GeoGebra’s probability calculator to verify their answer from 4b. Although not embedded in the text, the worked solution provided screenshots from the tool. The materials define the purpose of the task is to, “Demonstrate to students how to use technology to calculate the probability of an outcome from a normal distribution.” It is also suggested to, “Demonstrate finding probabilities over the different types of intervals, as well as using the original mean and standard deviation in the calculation to help students become confident in using technology.”