What do a great math class and a daffodil have in common?
I am always excited to see daffodils! Not only are they beautiful, but they are one of the first signs of spring! A few are blooming in my yard, and I think of each one as an exciting ‘first impression’ of spring. A great math class also has a powerful and exciting ‘first impression’! How you introduce a concept sets the tone for the learning and conceptual understanding of that concept!
Have you ever met someone for the first time and felt you did not make a good impression? Can you try again? Is, “You never get a second chance to make a first impression!” an expression you have heard many times? Does this expression apply to math classes?
The way a concept is introduced, or the ‘first impression’ is critical to students’ understanding! (I’m not referring to your activating strategy, although that is important.) You see this in your classroom, and research supports this, too. In a letter to parents, NCTM states that research shows students who discover mathematical truths have a better understanding of those concepts and remember them longer than students who are told how to do something, even when those who are told are later given the opportunity to see how and why it works! What experiences do we provide that allow students to discover and derive in mathematics?
What is a good ‘first impression’?
Do you expect the best from your students? What is their best? As a math coach, I work with teachers who have a variety of viewpoints. From my discussions with others, my guess is this is true in every school. Recently, I was working with a team and shared a question/task I would use to introduce a concept. From their faces, I could read their thoughts. I asked, “Do you think your students can do this?” The answer was no. One of them asked if the lesson could begin with a much easier task/question. This is a great teacher who wants the best for her students. My guess is she wanted to start with a task/question that would be accessible to almost everyone so that all students would feel immediate success. Is that helpful? Why or why not?
When we, as teachers, show our students instead of giving them the chance to discover and derive, or teach procedures and rules instead of letting students develop an understanding, we are taking away their best opportunity for discovery and deep conceptual understanding! Even letting them see it later does not make up the difference! Much like first impressions, you do not get a second chance on that concept!
So, then, what should we do?
Plan your questions in advance, and scaffold! Allow all students to think about the concept at the most challenging level without giving ‘hints’. Give students time to think independently before collaborating. Then, as needed, ask scaffolding questions to guide students in discovering concepts for themselves. Some will need more questions than others, but by allowing students to have a productive struggle, you are also promoting perseverance!
We might never have a second chance to make a first impression, but just as daffodils bloom each year, we, as math teachers, have another chance every time we introduce a new concept to students! It is never too late to start; we have many second chances! I don’t know about you, but I am very thankful for that! I love learning and applying new strategies!
The rest of the story…
The story above has a happy ending, and I’ll share more with you as we continue to explore this topic. What is a practical application of this? How would it look in a 3rd grade classroom vs. a 7th grade classroom? What about more challenging topics, such as quadratic equations? Do you agree you should begin with a challenging question/task? What types of task/question promote student discovery of mathematical concepts?
What are your thoughts? How do you promote perseverance? How do you introduce new concepts?
I look forward to exploring this together and hearing your thoughts!