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

9.1 The Importance of Personalization in a Secondary Math Classroom

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.

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.

9.2 Dimensions of Personalization 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

9.2.1 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

• Teach and discuss the purpose of setting goals. 
• Help students develop a growth mindset; create a culture of growth.
• Introduce a goal-setting process such as the SMART goal framework (specific, measurable, attainable, relevant, and time-bound).

Conferencing (regular goal-setting meetings)

• Some teachers meet with a few students a day or a week, taking several weeks to meet with every student. 
• Others plan a station or lab rotation, where students are working independently, then pull students out individually or in groups for a short consultation.
• Use these conferences to review current data and areas of growth.
• Discuss growth in content areas.
• You may also want to allow students to practice making goals outside the scope of your learning outcomes, such as personal health goals, interpersonal goals, behavioral goals, or self-regulation goals.  
• Goals can be based on performance data, activity data, or learner profile data. The most important thing to remember is that the goals should be measurable. An example of a performance-based goal would be "I will get an 80% on this unit," while an activity-based goal may be more like "I will study 30 minutes per night during this unit." A goal based on learner profile data may focus on pursuing a student's particular interests.
• Invite the student to evaluate where new growth can take place in your content area and make goals for that growth. 
• Record progress toward previous goals and new goals. Include a chart to help students visualize progress. 

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)

• Pair and share—place students in pairs (which either you or the students choose). The students share their goals with each other weekly and help their partners revise the goals if necessary. They also report their progress.
• Journal reflections—Students can keep an online daily or weekly journal in which they reflect on and record their progress toward their goals and/or the challenges they are facing. Teachers check in weekly and address individual student needs.
• Exit tickets—Students turn in an exit ticket daily, reporting that day’s progress, struggles, need for help, and/or next steps. These exit tickets can be completed either online or physically. Either way, they should be easy for both you and the students to track and organize.
• Data trackers—Create charts to record student and/or class progress during the year. 

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.

9.2.2 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.

9.2.3 Personalizing Pace

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.

9.2.4 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.

9.3 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. 

9.3.1 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."

• Goals—Students can determine what analyses and interpretations to prepare for based on their own interests or college and career goals.
• Time—Students can determine when to work on this learning objective, whether it will be during the regular class period and school day or before or after school.
• Place—Students can determine whether or not to work with others on meeting the learning objective or whether they will complete their projects at home, or in a specified area of the school or classroom.
• Pace—Students can choose how quickly they meet the learning objective by choosing the pace at which they complete activities and assessments.
• Path—Students can be given a certain level of flexibility concerning when they will work on this learning objective in relation to other parts of the curriculum, whether the learning objective will occur according to a teacher-provided scope and sequence or outside of that order.

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.

9.3.2 Personalized Assessments

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:

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.

9.3.2 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.

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.

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!