What makes a math class successful? I have developed 10 components of a successful math classroom that are the basis of the Minds on Math model for learning and teaching.
The first five of ten components that maximize math learning and understanding can be classified as Environment. Learning is emotional. Classrooms must have a feeling of acceptance and belonging for students to thrive. The environment itself can motivate or de-motivate students. We – teachers – have the power to create this feeling for students.
Forbes describes 4 factors that affect motivation for students:
1. Students feeling competent enough to complete classroom tasks
2. Students seeing a link between their actions and outcomes in the classroom
3. Students have an interest or see value in the tasks
4. Students feel a sense of belonging through participation in tasks
These conditions are embedded in the first five components of the Minds On Math model for learning and teaching as described below.
Component #1: Culture
What is the culture of my classroom?
Does the culture allow for students to take risks and feel supported?
Is it ok for students to be wrong? How do they know it is ok?
Is there an emphasis on everyone working as a team and operating as a community?
Does the classroom culture make kids thirsty for learning?
Is there a culture that promotes student success and confidence?
Do students know what to do when they don’t know what to do?
*Positive culture should be created throughout the year and not just during the first week of school. Building a strong culture takes time, reflection and feedback from students and teachers. Individuals should feel important and be encouraged. Without a strong culture and environment, student learning can be compromised.
Component #2: Theme
What is the theme of my classroom?
What do we believe in?
What is our motto?
Why are we here (at school or in math class)?
*Classroom themes that encourage learning emphasize thinking, doing, working hard, and being nice. These four actions are simple, yet complicated. These practices need to be taught, repeated and practice in order for students to begin to live them.
Component #3: Structure
What is the typical classroom routine?
Are all students successful in following classroom routine and procedures?
Are the norms and expectations clear, simple and related to the theme?
Does the classroom structure encourage student independence?
Does the structure develop student habits of mind?
Does the classroom structure support small group and individual instruction?
Does the structure define student and teacher roles?
Does the structure allow for student choice?
*Classroom structure combines routine, procedures and norms that build student independence and habits of mind. Students are more engaged in learning when there are also opportunities for them to choose what they will be working on. While students are engaged in learning, the structure should allow for teachers to work with students in small groups to individualize instruction. Tutoring centers and services have an impact on student learning not just because of the strategies and content they teach, but because of the low ratio of student to teacher interaction. Classroom structure should provide for the same opportunities as these successful tutoring centers.
Component #4: Know students
Do I know my students personally and academically?
Do I have a variety of strategies to analyze student understanding?
Are my assessments informal, ongoing and frequent?
Is assessment a part of daily classroom ritual?
What is my observation documentation system?
How does formal and informal data drive my instruction?
Am I teaching lessons or teaching students?
*Assessment is the act of gaining knowledge of student understanding or misunderstanding. Assessment can be formal and summative, but most often should be subtle and formative. Teacher learning is more important than student learning. Without a clear knowledge of what students know and don’t know, teachers cannot maximize student achievement.
Component #5: Face time
How often am I able to instruct and interact with students in small groups and individually?
What is the rest of the class doing while I work with a small group?
*Ultimately students are more accountable for their learning when the teacher to student ratio is as close to 1-to-1 as possible. Student learning and achievement continues to grow when the classroom culture and structure allows for opportunities for small group instruction targeted to individual student needs. When class sizes are 25 – 35 students, it seems nearly impossible to reduce this ratio. With a culture and structure in place that has elements of choice, teachers can lower the ratio at times and increase accountability and achievement.
The next three components can be classified as Experience.
What are the mathematical experiences we provide our students each day?
Do these experiences teach students how to learn and how to think?
Do the experiences develop student habits of mind?
What kind of experiences allow for differentiation and individualized instruction?
How do mathematical experiences create a balance of exploring concepts while becoming fluent with skills?
What experiences provide a depth of content and a focused engagement on learning?
The 3 criteria answer these questions:
Component #6: Big Ideas
What are the overarching concepts of the year?
What is the most important content of my course?
Does each lesson and unit during the year relate to at least one of the major ideas?
What math ideas are not appropriate for “units” but need to thread through the year and taken to a deeper level during each quarter of the year?
*A continuous focus on the top 3 to 4 big ideas of a grade level or course can create a “snowball” effect of learning. Lea, a teacher from Ohio, uses the phrase and idea of “snowballing” content which means adding to and creating bigger, rather than “spiraling” which can be random and disconnected. Lessons focusing on Big Ideas more often than on skills provide more entry points for all levels of students allowing ease for differentiation. Mathematics learning and teaching is enhanced by balancing a “birds eye view” of the content through themes and concepts, with a “microscopic view” of the course content by drilling down to skills. This zoom-in-and-out approach creates different perspectives and embraces mathematical connections.
**Below are Big Idea lists for each grade band. There is a flow and connection from one set of ideas to the next level. The High School focuses (#2-4) are recommended by the College Board.
1. Number** (this is the major focus of k-5)
2. Algebraic Thinking
3. Shape and Area
1. Number and Operation
2. Rate and Function
3. Space and Dimension
1. Number* (needs to continue in high school in connection with course topics)
Component #7: Embedded Intervention
What are the key concepts struggling students lack?
How do I fill below grade level gaps in understanding while teaching the content of my course?
*There are 3 targeted areas that fill gaps in student math understanding. These targets can be embedded into regular classroom instruction at all levels and connected to any concept. The goal is to be deliberate ad intentional about number selection and problem situation when designing lessons and choosing sample problems. Frequent formal and informal assessment on these three target areas, and intervening during structured small group time, fills gaps in student understanding while connecting ideas to course content.
Three target areas of focus:
1. Understanding representation of number by focusing on tens and parts.
a. Knowing how adding, subtracting, multiplying and dividing by 10 affects numbers.
b. Being able to break apart and put together numbers in different forms to ease computations.
2. Understanding the concepts of subtraction and division.
a. Relating subtraction to take away as well as distance and range.
b. Being able to “see” division in two ways: number of groups and number in each group.
c. Knowing that subtraction and division are less flexible than addition and multiplication because they are not commutative.
d. Seeing fraction as division.
3. Applying tens, parts and operation of number to 3 abstract concepts: Time, Money, Measurement
Component #8: Rich Tasks and Problems
What tasks am I providing that give students experience with the Mathematical Practices?
How do I teach students to embrace their own habits of mind through open ended tasks and problems?
How do I plan and develop questions to extend problems and tasks for a greater depth of content?
Am I balancing the types of questions such that there are many that promote thinking?
How do my tasks and problems stimulate curiousity and make kids thirsty for learning?
What tasks, problems and questions promote student engagement?
Do I allow for a variety of ways for students to show understanding?
*Rich tasks can be found at a variety of websites, some listed below. To make any problem or task “rich,” the first step is to give students the situation and remove the questions. Second, allow students to create the math questions themselves. Finally, create variations to each task or problem (“what ifs”) to provide more depth of content. Try not to move away from tasks and problems too quickly as to force student (and teacher!) persistence and perseverance. After introducing a problem or task, give students plenty of time to just make sense of the information. Solving is not the first step and it’s not the last step.
See Rich Task Ideas Here
The next two components can be classified as Extension.
How do we get the extension and depth of content and move away from the “mile wide, inch deep” trap?
There are 2 answers for this:
Component #9: Questions
How do I design questions that meet individual student needs?
How do my questions promote student curiosity, engagement and thinking?
How do my questions target the Big Ideas?
How can I “stop planning lessons” and “start planning questions”?
How do my questions “make kids thirsty” for learning?
What opportunities do I provide for students to create math questions for tasks and problems?
*The idea of “teaching with questions” connects back to the theme of the newsletters earlier this year. Questions have the power to engage and motivate students as well as scaffold and extend the content. Questions allow for differentiation. Questions can extend tasks and problems allowing for the depth of content. Planning daily questions can be the new way of lesson planning!
Component #10: Connections
What connections are made between units of study throughout the year?
How do I connect content from previous grades to the content in my course?
How do I connect abstract/algebraic content to a concrete and visual representation?
Does each unit of study connect to each of the 3 Big Ideas: Number, Rate and Function, Space and Dimension?
*Students do not naturally make the connections between each concept and skill that is taught. They need to see how each lesson, topic and skill connects to previous learning. Choosing tasks and problems that can be extended and varied allows for opportunities to bring in multiple concepts at the same time. By teaching multiple concepts at the same time, students begin to see how different area of mathematics are related. To make math accessible to all students we must make math visual and make math connect!