CoverAbout This BookPrefaceAcknowledgementsResearch1. Introduction to K-12 Blended Teaching2. K-12 Blended Teaching Competencies3. Evaluating Blended Teaching with the 4Es and PICRAT4. Elementary Education: Intro to Blended Teaching4-1. ElEd: Why Blend?4-2. ElEd: Online Integration & Management4-3. ElEd: Online Interaction4-4. ElEd: Data Practices4-5. ElEd: Personalization 5. English Language Arts (ELA): Intro to Blended Teaching5-1. ELA: Why Blend?5-2. ELA: Online Integration & Management5-3. ELA: Online Interaction5-4. ELA: Data Practices5-5. ELA: Personalization6. Social Science (SS): Intro to Blended Teaching6-1. SS: Why Blend?6-2. SS: Online Integration & Management6-3. SS: Online Interaction6-4. SS: Data Practices6-5. SS: Personalization 7. Math: Intro to Blended Teaching7-1. Math: Why Blend?7-2. Math: Online Integration & Management7-3. Math: Online Interaction7-4. Math: Data Practices7-5. Math: Personalization8. Science: Intro to Blended Teaching8-1. Science: Why Blend?8-2. Science: Online Integration & Management8-3. Science: Online Interaction8-4. Science: Data Practices8-5. Science: Personalization
7-5

Math: Personalization

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Review foundational knowledge about Personalized Learning in K-12 Blended Teaching (Volume 1).

7-5.1 The Importance of Personalization in a Secondary Math Classroom

Teachers Talk: Knowing Your Students Better

PP7_Schlink.jpeg

Dawn Schlink

I feel closer to my students. I feel like I know kids more on an individual basis because I've been able to work with them more individually. The thing about blended learning is that there's always a portion of my time during the day that is set aside for students to work at their own pace. And when they're working at their own pace, that means I can call students up or I can let students come up, to meet with me. I can work with them, and really get to hear their concerns, their misunderstandings, and that brings me closer to the student, and not just where math is concerned.

Within a blended learning environment, personalized learning is one of many instructional strategies. When we personalize learning for our students, we allow the instruction to be adaptable to individual students' abilities, interests, and needs. When we describe personalized learning it is important to consider what part of our instruction is being adapted, how it is being adapted, who or what is doing the adapting, the data that the adaptations are based on, and to what extent students are able to take ownership of the adaptations.

In a math classroom, personalization can take many forms and use a variety of strategies. When you allow students to have a choice in the pace and path of their learning by using instructional tools such as playlists, they are personalizing instruction. Allowing students to use inquiry skills to find their own path or method of solving a complex problem is also personalizing. You can personalize learning objectives by allowing students some choice in the research they do for a project or the way they choose to approach a problem. You can also personalize learning by using problem-based learning when introducing new mathematical concepts.

Activities and assessments can also be personalized when students decide how to meet the course's learning objectives and how they will demonstrate their mastery of mathematical concepts. If a student is allowed to show their understanding via a test or a presentation, etc. their learning has been personalized. Notice that in all of these examples, students take some degree of control over their learning.

Teachers Talk: Importance of Differentiation in Math

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Dawn Schlink

Differentiation plays a big part in how I blend, because the blended learning allows kids to move at their own pace. And so some kids will be working on higher depth of knowledge level things online because that's what they're able to do. Some kids won't because some kids just don't get it.

Definitions: Differentiation vs Personalization

Differentiation and personalization are similar but not the same. As you think about the activities and ideas in this chapter, decide if the activity is differentiated or personalized. Both have an important place in classrooms, but personalization with its extra emphasis on student (not teacher) choice tends to foster greater growth in areas such as student ownership and self-regulation.

Differentiation: The teacher tailors instructional materials, pacing, and path to address student needs. She makes significant decisions for and about the student.

Personalization: Students make their own decisions about their goals, time, place, pace, and path of learning, giving them increased ownership over their learning. In most cases, these decisions should still be guided by the teacher.

It is helpful to approach personalization and the idea of student control in two different ways: through allowing students to personalize along the dimensions of personalization and through allowing students to personalize the learning objectives, assessments, and activities we use in our teaching. Both of these can be personalized at different levels of student agency.

7-5.2 Personalization Dimensions in a Math classroom

One way to think about personalization is to examine the ways students can personalize their learning. The five dimensions of personalized learning are guidelines for ways we can allow our students to personalize their learning. These dimensions are goals, time, place, pace, and path. In the sections below, we will explore each of these dimensions.

Figure 1

Five Dimensions of Personalized Learning

5 DImensions of Personalized Learning

7-5.2.1 Personalizing Goals

Goals are a means of making choices specific and purposeful. Facilitating goal setting increases student ownership of their learning, encourages lifelong learning skills and attitudes, and increases motivation and self-regulation abilities. 

In order for students to personalize their goals, you and they need to understand some of their needs and proficiencies as math learners. This is where you can use the data you have gathered from the strategies mentioned in the Data Practices chapter. 

Information from such sources helps you understand where students are in their mathematical abilities, skills, and aptitudes. Learning outcomes and standards give focus concerning where students are expected to be. The difference between where students are and the course outcomes is the place for student growth—and goals.

Goals are not goals if they are just aspirations. Writing goals and tracking them are important processes for achieving them. Here are a few ideas about goal-setting conferences and how they might be used in a math classroom.

In Class

Conferencing (regular goal-setting meetings)

An important aspect of personalizing learning is helping students to properly increase their agency as learners. In order to facilitate such growth, it is important to allow learners to control as much of the goal-tracking conferences as possible. Consider various ways to provide them with ownership over their own data, how that data is tracked, how it is analyzed, and how that data informs learner's goals.

Monitoring (tracking progress between conferences)

Chapter 2 refers to a taxonomy of learner agency for guiding personalized learning. Level one of the taxonomy represents a one-size-fits-all generalized pedagogy, whereas level two is tailored to fit the interest or needs of each student, and levels three and four represent a more student-centered pedagogy and allow a greater deal of student agency. In Table 1, you will see some examples of what personalizing goals could look like in a math classroom that reaches levels 3 and 4 of the Taxonomy of Learner Agency.

Table 1
Examples of Personalizing Goals in a Math Classroom
 
Learning Objective:
Students will evaluate algebraic expressions for given replacement values of the variables.
Level 3 Personalization Level 4 Personalization
Performance-based goals Students are given choices of what grade they want to earn in this unit. The teacher guides them to help them understand what they are capable of given their past performance and encourages them to challenge themselves but ultimately leaves the goal and strategies up to them. Students are asked to come up with a goal for their grade or level of mastery in the unit and asked to write about strategies they will use to achieve that goal as well as ways they will measure and track their achievement throughout the unit.
Activity-based goals Students are given a list of study strategies that would be helpful in this unit. Students pick one study strategy from this list that they will work on and come up with a goal and strategies for implementing it throughout the unit. Students are given the freedom to identify a learning behavior or habit that they want to focus their efforts on during the unit. The teacher gives them some possible examples of ways to improve their learning behavior or change their habits but ultimately allows them to come up with their goal and strategies on their own.

7-5.2.2 Personalizing Path

When you allow students to personalize their learning path in your classroom, your students are not all doing the same assessments and activities. You may find that you have become a curator of resources and activities that will best help your students. These resources/activities can be compiled in playlists or choiceboards, which give the students choice about the order in which they complete the activities or about which activities they choose to do.

Table 2 describes ways in which the learning path can be personalized in a math classroom at levels 3 and 4 of the Taxonomy of Learner Agency.

Table 2

Examples of Personalizing Path in a Math Classroom

Learning Objective Level 3 Personalization Level 4 Personalization

Students will be able to solve trigonometric equations and inequalities.
Create a menu of learning activities about solving trigonometric equations. Have an appetizer round in which students are introduced to the concepts, an entree round in which students practice the concepts, and a dessert round in which students demonstrate their understanding. Students pick one activity from each round based on their preferred learning methods (reading, hands-on, videos, etc.) and have to check in with the teacher after each round before moving on. The teacher creates a problem-based learning activity in which students are given several scenarios in which they need to determine if the functions are equal or not. The teacher provides access to resources that may help in students' investigation but does not direct the students down any particular path (i.e., to specific resources) that they could use to solve the problem.
 

7-5.2.3 Personalizing Pace

Teachers Talk: Personalizing Pace and Demonstration of Learning (2:37)

Reflection Questions: How does the teacher in this video allow the students to work at their own pace and demonstrate their understanding? What advantages does this have for student learning?

Personalizing pace means allowing students to take more or less time to complete learning tasks based on their own knowledge, skills, and abilities, as well as their personal and family life circumstances. It often includes giving students a window of time on due dates for completing activities, assignments, and assessments. Personalizing pace encourages students to manage their time. They know what they need to do and when it needs to be completed, but they also know the other demands on their time (sports, school, play, family, and work obligations) and learn to plan for these situations. Table 3 provides examples of personalizing pace in a math classroom at levels three and four of the Taxonomy of Learner Agency.

Table 3

Examples of Personalizing Pace in a Math Classroom

Learning Objective Level 3 Personalization Level 4 Personalization

The students will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically.
The teacher assigns a checklist of activities the students will use to learn and practice this topic. The unit contains several sections and multiple learning activities in each section. The students can pace themselves within each section but are given checkpoints by which they must complete each section. Using the same checklist explained in the level three example, students are allowed to complete the entire intervention at their own pace, understanding that the course contains additional content that they must master for credit.

Teachers Talk: Individualized Pacing

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Rachel Peterson

I think the most powerful thing that I've been able to use is pacing. If I have kind of a longer activity, maybe 20-30 minutes, that they're doing and working on using their devices at their own pace, not only can they do it at their own pace, but I'm free to go around and help students individually. I can't do this if I'm lecturing. If I'm lecturing, then it's at my pace. Right? And, that's never 100% good for everybody.

Teachers Talk: Videos for Personalizing Pace

Mikki Stuart

Mikki Stuart

I thought, "Okay, what's one way I can do this differently?" I thought maybe they just need to review the content with more self-paced one-on-one instruction. So I created videos. I broke down our unit into three or four sections. I showed an example, and then I had students pause and do a new problem on their own and then come back to another screen where they could check their work.

Students worked individually at their own pace. If they didn't understand, they could rewatch the video. I had students taking notes on what they were doing wrong while other students were working on other things. The next day when they took the test it went from 25% of students not passing to 12% of students not passing. I think that's when I realized, some of these kids just really need that opportunity to go at their own pace. I realized that I was rushing some of these kids, way too fast, because I'm a very fast-paced teacher. I think some of the kids didn’t have the opportunity to internalize everything.

7-5.2.4 Personalizing Time

In a traditional classroom, students may have a class period to finish an assignment. In a blended classroom, this time can be expanded to include time outside the class. Because activities can be accessible outside of the classroom, students can choose times that work well for them. For example, a student may have a difficult time learning in the morning, when he has class. But because he can access his assignment later in the day, he is able to complete it and do a good job. Time is closely related to pace. Because students are not bound to a specific time to do an assignment, they can increase or decrease their pace according to their own preferences, needs, and abilities. Table 4 provides examples of personalizing time in a math class at levels three and four of the Taxonomy of Learner Agency.

Table 4

Examples of Personalizing Time in a Math Classroom

Learning Objective Level 3 Personalization Level 4 Personalization
Students will be able to use the relationships between angles formed by two lines intersected by a transversal.
A teacher does a large group lecture on this topic and then gives the students in-class work to complete. Anything that is not completed in class can be completed at home, after school. The teacher gives students video lectures on the content and a checklist of work to be completed on that topic. Students can work on the videos and checklist at a time of their choosing as long as it is completed by a specific deadline.

7-5.2.5 Personalizing Place

Personalizing place revisits traditional practices about where learning occurs. Because blended courses often include online instruction, students can choose to do activities at home or at school. In addition, they can access instruction when they have to miss activities because of illness, travel, or extra-curricular activities. However, another aspect of place is the configuration of the classroom. Classrooms are often viewed as rows of desks or sometimes desks grouped into tables. But classrooms don’t have to look this way. They can be made more comfortable, inviting, and conducive to the kinds of activities that take place in a blended classroom. Table 5 provides some examples of personalizing the place of learning at levels three and four of the Taxonomy of Learner Agency.

Table 5

Examples of Personalizing Place in a Math Classroom

Learning Objective Level 3 Personalization Level 4 Personalization
Students will be able to communicate mathematical reasoning in oral and written forms. Students are given the assignment to research a mathematician assigned by the teacher. They are given a written research assignment and a recorded video assignment. The teacher provides stations around the room for researching, quiet writing, and recording videos. The students are able to choose where they want to work during class. Students are given the assignment to do an online presentation of a difficult math topic. They are able to work on this assignment from home or at school because the materials are all provided in the online learning management system. Some students choose to work on their own to complete the discussion while others choose to work in groups.

7-5.3 Personalizing Instruction

Approaching personalization through the five dimensions is one way of planning to personalize. Another way is to look directly at what you do in your classroom. Typically teachers plan assessments and activities around learning objectives to make sure they cover the material they are mandated to cover. Finding ways for students to exercise choice in some or all aspects of these activities and assessments is another way to foster personalization in your classroom. 

7-5.3.1 Personalizing Objectives

In Tables 1-5 above, we provided several examples of learning objectives. While many of these learning objectives may not provide us or our students with room to adapt them to individual students' abilities, interests, or needs and are mandated by the states or organizations we teach for, other learning objectives do allow for such customization. For example, the following learning objective can be personalized in several ways:

"The students will use multiple representations of functions for analysis, interpretation, and prediction."

In many ways, personalizing learning objectives creates a guide for personalizing the assessments and activities used to prepare students for and measure their mastery of the objective.

7-5.3.2 Personalized Assessments

Teachers Talk: Showing Mastery

Sandy Chalke

Sandy Chalke

If you don't want to do 20 problems don't do 20 problems. Just do five problems but show me mastery.

What do assessments look like in your classroom: An exam full of equations and math problems? A final project? Word problems requiring brief explanations? A presentation? Do all your students do the same thing? Do all of your students need to do the same thing?

Personalizing assessments means giving students choices in the ways they demonstrate mastery of a learning outcome. Often this means creating a list of ideas that students can choose from, while also allowing them to suggest their own ideas.

This would allow students to personalize the path they take for demonstrating their understanding. Table 6 provides examples of ways to personalize the path of assessments. While you look over these, consider the following questions:

  • What are the different paths that these assessment options create for students?
  • How are these assessments different from traditional assessments?
  • What kinds of growth do these assessments encourage in the students?

Table 6

Assessments

Personalized Assessments
Students choose the media they use for the assessment: PowerPoint, Google Docs, video, etc. 
Students choose the form of the assessment: mindmap, essay, exam, project, presentation, tutorial, guide, etc. 
Students choose the topic of a project or other form of assessment.
Students choose to do the assessment in groups or on their own.

While assessments may most commonly be personalized according to path, they can also be personalized by allowing students to create their own performance or learning habit/behavior goals for the assessment, to choose when they will complete the assessment, to choose where they complete the assessment, or to choose how long they will spend on the assessment or how many attempts they will use on the assessment.

Teachers Talk: Allowing Choice of Products

Rachel Peterson

Rachel Peterson

We did a project recently where they were creating an original work based on a mathematical equation. They have a lot of freedom in the creative aspect of it and the creation of it where they can use a number of different platforms. Maybe they want to create a PowerPoint or maybe they want to make a video or maybe they want to do something else. By giving them that freedom and allowing for creativity, we got much higher quality projects than I have in years past.

In your Blended Teaching Notebook, create a few ideas of personalized assessments that students can choose from in order to show mastery of the content area you choose earlier.

If you haven't already opened and saved your workbook, you can access it here.

7-5.3.2 Personalized Activities

Personalized activities are based on data and goals. Students can choose activities that help them accomplish their specific performance or activity goals from playlists and/or choice boards, giving them choice in the time, place, pace, and path of their learning. Personalized learning activities may include both online interactions as well as online integration activities that are adapted based on individual students' abilities, interests, or needs. The following examples provide some insights into how some teachers personalize the learning activities in their math classes.

Teachers Talk: Allowing Students to Work at Their Own Pace (including ideas for activities) (3:58)

Reflection Questions: How are the activities that this teacher mentions personalized? How are they differentiated? What is one activity or tool that you would like to try in your own classroom?

Teachers Talk: Differenting Activities to Meet the Needs of All Students

Sandy Chalke

Sandy Chalke

I used a storyboard project because I saw that one kid was just drawing in class. They like to draw. They sit and like to draw. So that's why I came up with the storyboard project where they can actually demonstrate how they use math in real life by just drawing and illustrating mathematical principles.

Table 7 provides examples of ways to personalize different learning activities in math.

Table 7

Personalized Learning Activities

Personalized Activities
Create a choice board or playlist of activities for exploring or reviewing a mathematical concept.
Introduce inquiry activities by providing links to simulations and allowing students to investigate a new idea by exploring and answering some guiding questions you have provided.
Have students choose a mathematician and write about the discovery of a theorem or principle from that person's perspective. Share the writings in a discussion board and have the other students ask the mathematician questions about their theory and investigation process.
Allow students to complete the work in a unit in the order they choose and at their own pace. This can be done by assigning the students a checklist and providing them with clear instructions and support via blended teaching strategies.

In your Blended Teaching Notebook create a few ideas of personalized activities that students can choose from in order to show mastery of the content area you chose earlier. 

If you haven't already opened and saved your workbook, you can access it here.

Personalization is a powerful pedagogical tool. It allows students to grow where they need to grow and in a way that is meaningful to them. It combines all of the competencies of blended learning: online integration, online interaction, and data practices to create a unique learning experience for each student. Throughout these chapters, you have learned how to use these competencies in a math context. Now it is up to you! You are ready for your first small step!

Suggested Citation

, , , & (2021). Math: Personalization. In , , , , & (Eds.), K-12 Blended Teaching (Vol 2): A Guide to Practice Within the Disciplines , 2. EdTech Books. https://edtechbooks.org/k12blended2/math_pers

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