The messages and words that students hear are what influence how they think they will perform inside the classroom and outside the classroom. Students’ ideas about their ability and potential are extremely important, much more than we think. New studies are always being carried out and it was found in one that the messages students pick up from their parents about math and their parents’ relationships with math can also change how a student believes they will learn and achieve in math.
“The parents’ math knowledge did not turn out to have any impact, only their level of math anxiety.”
In a study including mothers and their daughters when mothers told their daughters they were not good at math in school the daughters grades in math declined almost immediately. Parents’ math anxiety reduced their children’s learning of math through grades 1 and 2, but only if parents helped their children on math homework. If they did not help their children, the parents’ math anxiety did not detract from their children’s learning.
“It is critical that when parents interact with children about math they communicate positive messages, saying that math is exciting and it is an open subject that anyone can learn with hard work, that is not about being smart or not and that math is all around us in the world.”
Teachers need to give positive messages to students at all times. Many elementary teachers feel unsure of mathematics, usually because they have a fixed mindset about their own math achievements. Levels of anxiety held by women elementary teachers also predicted the achievement of the girls in their classes, but not the boys. Girls look up to their female teachers and identify with them.
“Teachers and parents need to replace sympathetic messages such as don’t worry, math isn’t your thing with positive messages such as you can do this, I believe in you, math is an open, beautiful subject that is all about effort and hard work.”
It is widely accepted and known that students often perform better in mathematics when representing their math with visuals. It is often assumed that people will only use visual math as a crutch for more abstract thinking, but it can be used for so much more than that. Visual math is important because it is one more strategy that gets added to a mathematician’s toolbox, and you can never have too many strategies for problem solving. Visual math is an important part of mathematics for its own sake and it is even said that visual math helps students learn numerical mathematics. The most powerful learning occurs when we use different parts of our brains.
“When students work with symbols, such as numbers, they are using a different area of the brain than when they work with visual and spatial information, such as an array of dots.”
Many people get excited and more engaged when dealing with visuals in math because the majority of people would say they do not like math, but the visuals give math a creative and inspiring edge. Pictures help students see mathematical concepts, which aids in understanding. This type of math also connects with higher-level thinking, enables communication and helps people see how creative math can be.
“Mathematics is a subject that allows for precise thinking, but when that precise thinking is combined with creativity, openness, visualization, and flexibility, the mathematics comes alive.”
Teachers can create so much excitement in math classrooms by asking students to solve the problem in different ways. The students can see and solve the problems through encouraged discussion and using different problem solving strategies. When we don’t ask students to think visually, we miss the opportunity to increase students’ understanding.
Intrinsic Motivation: Doing something for personal satisfaction. There is always an internal motivator – students are not looking for anything in return. This kind of motivation makes you feel good, you feel personally challenged, and leads to a sense of accomplishment. Students are doing the assignment “just because”. Extrinsic Motivation: Doing something to earn a reward or avoid a punishment. External motivator – students are expecting to get something in return for completing the task at hand. Students are doing the assignment to get something they like.
Extrinsic motivation only produces short-term effects. Students also learn to compare themselves and their work to that of their peers due to this kind of motivation. There can be room for both intrinsic and extrinsic, especially when there is a task at hand that students do not enjoy. Sometimes the “right incentive” serves as the hook that gets students invested in learning.
The Key is Finding the Right Balance!!
How can teachers spark students’ intrinsic motivation?? We cannot change who a student is, but we can provide an environment that encourages students to develop their own motivation. Here are some examples to get you started!
~ Know your students: Design lessons around likes and interests in the classroom ~ Ownership of the environment: Involve students when creating rules and expectations of your classroom ~ Create a solid foundation: Motivation comes from being able to tackle complex tasks, students need a solid foundation of prior knowledge to carry out this type of task ~ Practice setting goals: Goals improve motivation and achievement as well as encourage a growth mindset ~ Provide specific feedback: Instead of saying “good work” try to tie feedback to a strength of the assignment, “nice work detailing all the steps of your work” ~ Allow Choice: When students are given choice they believe that the assignment is more important because they are more interested in completing it ~ Connect class to the real-world: When a student knows that the work they are completing has ties to their future they will be more motivated and engaged
When interviewing students about their strategies and techniques when it appears they may be struggling, have an open mind. With that be asking questions and trying to find out what exactly is going on through the student’s work and explanations. When you have an open mind you are opening your understand of the student as a mathematical thinker. We should always presume competence. Presuming Competence, what is this exactly?
Presuming Competence means that we should always assume a person has the capacity to think, learn, and understand – even if you don’t see any tangible evidence that such is the case.
It is also very important to connect to the student’s thinking. Connecting with the student will push them toward new directions, and show them that it is okay to try new strategies, as well as how important it is for success to fail. No one ever gets anywhere without failing at least once. This type of understanding is almost like a work of art.
“and the art of working with students should always be centered on building off their own brilliance.”
When teachers are told that students can achieve at a higher level, they believe in the students more. Teachers should always be looking for opportunities to provide feedback, both constructive and positive. When students hear “I believe in you” they achieve more in less time. There is so much unrecognized power in teacher-student relationships! All students deserve to hear positive beliefs from the teacher, especially those who could have underlying struggles in their lives.
“You can be the person who turns things around for students and liberates their learning path. It usually takes just one person – a person whom students will not forget”
There is so much value and importance in connections and relationships built with your students. No significant learning can happen without a significant relationship because kids don’t usually learn from people they do not like. Part of building these relationships is admitting to mistakes and apologizing for things done wrong, this will build trust within the relationship. Something else to keep in mind is to acknowledge all students’ victories, even if they are small. This will connect the student to you more as well as boost their self-esteem and confidence which will help them believe in themselves more. “Every child deserves a champion” in the words of Rita Pierson.
“A champion: Someone who will never give up on them, understands the power of connection and insists they become the best they can possibly be”
Did you know that when you believe in yourself, your brain operates differently than if you did not believe in your abilities. Everyone has a mindset, or a core belief about how they learn and what strategies work best for them.
Growth Mindset ~ You believe that smartness increases with hard work Fixed Mindset ~ You believe you can’t change your basic level of intelligence
When mindsets are changed and you start to believe that you can learn to high levels, you are actually changing your learning pathways and can achieve higher levels of learning. Growth mindset individuals have a greater awareness of errors than those with a fixed mindset. If you believe in yourself, your brain is more likely to spark and grow when mistakes are made. When a mistake is made, synapses fire in our brains.
A synapse is an electrical signal that moves between parts of the brain when learning occurs.
We do not need to be aware of the mistake that was made in order for our brains to spark. Making mistakes is not only a learning opportunity but can also lead to times where your brain can grow.
The first step to growing our brains and having sparks from synapses is to have an open mind and believe in the power of your own thinking!
This is understanding how and why the rules and procedures work. Students who are taught relational understanding usually have an easier time remembering certain procedures because they had a deeper meaning of why they work. These students will also retain all their learned knowledge longer and are also less likely to make common mistakes. Some students will be lacking motivation and determination and others may be too ready to accept your help because they are not used to thinking things through for themselves. Through their growth as learners students will make sense of math and will soon be less worrisome.
“Those with a relational understanding can learn new concepts easier, retain previous concepts, and are able to deviate from formulas/rules given different problems easier because of the connections they have made.”
When a student wants to make sense of learned concepts but are not given the time and conditions to experience math, they will come to believe that they are not good at math or they will say “they are not math people”. There are a few ways to try and remedy this; notice instrumental teaching, learn how to move from one to the other, and align assessment practices to meet with relational understanding. When you are unaware of your teaching style it was believe that you are doing a good job because your students are clearly learning something. By becoming more aware of your teaching style you can stop the behaviors that are like instrumental teaching and start transitioning to relational teaching.