How will instruction change as we move toward implementing the Common Core State Standards for math? The emphasis will not be only on
the acquisition of content knowledge but also on the understanding of the underlying mathematical concepts and the fostering of the eight Mathematical Practices:
At the same time, my school is moving from a 50-minute math period to an 70-minute block next year. For these reasons, I know that I will need to make significant changes in the way I organize instruction in my math classes. I realize that I will need to shift from a more procedural approach that loaded students with knowledge of content to a style of instruction that would embed learning more deeply in the child’s thinking.
While attending a California League of Schools conference, I ran across a copy of Teaching with the Brain in Mind, by Eric Jensen[i]. The subject of brain-based learning has always interested me from my teacher education courses in the late 1970’s and I realized that this book might provide some ideas for constructive ways to teach this old dog some new tricks. Here are three key points I’ve gleaned from chapter 3, “Rules We Live By”.
1) Students learn through engagement. Getting students to “pay attention” has always been a primary obstacle in the classroom. In my 70-minute blocks, this task will be even more challenging. I recall a college professor who taught in lecture format. The teacher recited facts about California geography for three hours without a break. We took notes as frantically as possible. (Keep in mind, there were no laptops or tablets when I was in college; we took notes the old fashioned way–with stone and chisel.) Here is all that I remember: “Silver Lake” is the most common name for a lake in California (27 of them).
On the other hand, I remember her diminutive height, hair color, mannerisms, and the fact that during the three hours she sipped a soda that was almost as tall as she.
Jensen shows on page 37 that my middle school students can engage effectively in instruction for only 12 to 15 minutes at a time. After that they need processing time.
What it means for us: For this reason, I plan to divide my instructional block into four micro-sessions of 15 to 20 minutes apiece. In each quarter, I plan to work on one activity at a time. For example, I can use the opening minutes for an exploratory problem that challenges and engages my students. An example is the “Sunshine Citrus” problem featured in my handout “Developing Proportional Reasoning” available on my website.
The second session could involve direct instruction of a mathematical concept. In this case that might involve solving proportions since that relates to the previous task and is a critical domain in the middle grades.
The third quadrant of instructional time could provide students practice time with feedback. On page 48, the author emphasizes that practice is still important in the brain-based classroom.
The final instructional sector could return students to the problem they encountered at the beginning of class or provide exposure to future content. Of course there are many ways I can effectively alter this model.
2) Sometimes, teaching less means learning more. Past standards encouraged us to get as much content in their heads as possible prior to the state test. But often the more we taught, the more they forgot. Then we got trapped in the teach/test/reteach cycle. It turns out that the brain has a built in “surge protector” called the hippocampus that regulates the amount of new learning that is processed. This substantiates what we have long suspected, that “a mile wide and an inch deep” is not as effective as focusing more deeply on more limited content. Jensen adds that in addition to limiting how much content is introduced at one time, students also require time to process this new learning and time to embed it in long-term memory.
What it means for us: That means that I can conclude a 15-minute period of instruction with five minutes of embedding time. This can be accomplished through pair-sharing, written summaries, games, and similar experiences.
Jensen also cites a study that says it takes up to six hours to form the synaptic connections in the learning process.[ii] This means that learning continues after the students leave our classes. Much of this learning in actually finalized during a good night’s sleep. Hopefully our students are getting this needed rest.
What surprised me most of all, though in reflection it should have come as no surprise, was Jensen’s third point:
3) Prior knowledge is highly resistant to change. Jensen states, “It is reasonably easy to learn something that matches or extends an existing mental model, but if it does not match, learning is very difficult.” (page 47) This explains whys bias and prejudice are so difficult to undo in the mind.
The brain has a way of clinging to evidence that supports current models and rejecting those that contradict them. If previous learning was flawed, we clearly have our work cut out for us. Thus we must provide this contradiction.
However, our classroom experience tells us that too much contradiction in a math class results in the outcry, “I don’t get it!” We want a measured amount of anomaly.
Fortunately, Jensen tells us that brains are wonderfully designed to learn from trial and error. If the erroneous thinking of students is challenged, this misguided learning begins to shift.
What it means for us: One of the concepts I teach is linear functions. As students study functions they begin to identify the slope and y-intercept of the graph and how they are represented in the equation of the function. Sometimes, their conclusions are faulted though because they have confused the slope and y-intercept of the function. I can allow them to input different numbers into a function so that they can observe the effect it has on the graph.
Giving them opportunities to test their conjectures will foster the inquiry model of learning I wish to promote. This process will result in greater understanding of concepts and ultimately, in greater learning.
This shift to the CCSS for math will be a good transition in many ways. It encourages a type of thinking for which our brain was designed. Brain-based learning will be a part of this transitional process. As we learn to alter our instruction from the traditional models we may have experienced in our own education, we will help students develop a more complete and viable mathematical understanding that better fits our modern technological society.
[i] Jensen, Eric. (2005) Teaching with the Brain in Mind, 2nd edition, Association for Supervision and Curriculum Development
[ii] Goda, Y., and Davis, G. W. (2003, October 9) Mechanisms of synapse assembly and disassembly. Neuron, 40(2), 243-264
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
At the same time, my school is moving from a 50-minute math period to an 70-minute block next year. For these reasons, I know that I will need to make significant changes in the way I organize instruction in my math classes. I realize that I will need to shift from a more procedural approach that loaded students with knowledge of content to a style of instruction that would embed learning more deeply in the child’s thinking.
While attending a California League of Schools conference, I ran across a copy of Teaching with the Brain in Mind, by Eric Jensen[i]. The subject of brain-based learning has always interested me from my teacher education courses in the late 1970’s and I realized that this book might provide some ideas for constructive ways to teach this old dog some new tricks. Here are three key points I’ve gleaned from chapter 3, “Rules We Live By”.
1) Students learn through engagement. Getting students to “pay attention” has always been a primary obstacle in the classroom. In my 70-minute blocks, this task will be even more challenging. I recall a college professor who taught in lecture format. The teacher recited facts about California geography for three hours without a break. We took notes as frantically as possible. (Keep in mind, there were no laptops or tablets when I was in college; we took notes the old fashioned way–with stone and chisel.) Here is all that I remember: “Silver Lake” is the most common name for a lake in California (27 of them).
On the other hand, I remember her diminutive height, hair color, mannerisms, and the fact that during the three hours she sipped a soda that was almost as tall as she.
Jensen shows on page 37 that my middle school students can engage effectively in instruction for only 12 to 15 minutes at a time. After that they need processing time.
What it means for us: For this reason, I plan to divide my instructional block into four micro-sessions of 15 to 20 minutes apiece. In each quarter, I plan to work on one activity at a time. For example, I can use the opening minutes for an exploratory problem that challenges and engages my students. An example is the “Sunshine Citrus” problem featured in my handout “Developing Proportional Reasoning” available on my website.
The second session could involve direct instruction of a mathematical concept. In this case that might involve solving proportions since that relates to the previous task and is a critical domain in the middle grades.
The third quadrant of instructional time could provide students practice time with feedback. On page 48, the author emphasizes that practice is still important in the brain-based classroom.
The final instructional sector could return students to the problem they encountered at the beginning of class or provide exposure to future content. Of course there are many ways I can effectively alter this model.
2) Sometimes, teaching less means learning more. Past standards encouraged us to get as much content in their heads as possible prior to the state test. But often the more we taught, the more they forgot. Then we got trapped in the teach/test/reteach cycle. It turns out that the brain has a built in “surge protector” called the hippocampus that regulates the amount of new learning that is processed. This substantiates what we have long suspected, that “a mile wide and an inch deep” is not as effective as focusing more deeply on more limited content. Jensen adds that in addition to limiting how much content is introduced at one time, students also require time to process this new learning and time to embed it in long-term memory.
What it means for us: That means that I can conclude a 15-minute period of instruction with five minutes of embedding time. This can be accomplished through pair-sharing, written summaries, games, and similar experiences.
Jensen also cites a study that says it takes up to six hours to form the synaptic connections in the learning process.[ii] This means that learning continues after the students leave our classes. Much of this learning in actually finalized during a good night’s sleep. Hopefully our students are getting this needed rest.
What surprised me most of all, though in reflection it should have come as no surprise, was Jensen’s third point:
3) Prior knowledge is highly resistant to change. Jensen states, “It is reasonably easy to learn something that matches or extends an existing mental model, but if it does not match, learning is very difficult.” (page 47) This explains whys bias and prejudice are so difficult to undo in the mind.
The brain has a way of clinging to evidence that supports current models and rejecting those that contradict them. If previous learning was flawed, we clearly have our work cut out for us. Thus we must provide this contradiction.
However, our classroom experience tells us that too much contradiction in a math class results in the outcry, “I don’t get it!” We want a measured amount of anomaly.
Fortunately, Jensen tells us that brains are wonderfully designed to learn from trial and error. If the erroneous thinking of students is challenged, this misguided learning begins to shift.
What it means for us: One of the concepts I teach is linear functions. As students study functions they begin to identify the slope and y-intercept of the graph and how they are represented in the equation of the function. Sometimes, their conclusions are faulted though because they have confused the slope and y-intercept of the function. I can allow them to input different numbers into a function so that they can observe the effect it has on the graph.
Giving them opportunities to test their conjectures will foster the inquiry model of learning I wish to promote. This process will result in greater understanding of concepts and ultimately, in greater learning.
This shift to the CCSS for math will be a good transition in many ways. It encourages a type of thinking for which our brain was designed. Brain-based learning will be a part of this transitional process. As we learn to alter our instruction from the traditional models we may have experienced in our own education, we will help students develop a more complete and viable mathematical understanding that better fits our modern technological society.
[i] Jensen, Eric. (2005) Teaching with the Brain in Mind, 2nd edition, Association for Supervision and Curriculum Development
[ii] Goda, Y., and Davis, G. W. (2003, October 9) Mechanisms of synapse assembly and disassembly. Neuron, 40(2), 243-264
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