Fractions: Units and Equivalence by William McCallum is a very good read for 3-5 grade teachers charged with the tricky task of teaching students to recognize equivalence in fractions. The author warns us about trying to use words or phrases to explain what is going on with fractions. Our explanations fall flat and in fact, "get in the way of the truth." The expressions "reduce" and "simplify" suggest that the fraction has changed in terms of quantity. Giving students opportunities to experiment with fraction number lines and tape diagrams will help students to understand equivalence vs. explaining equivalence using language that will, in the end, only "complicate the matter."
This is one of my guilty little problems. Too often, in a misguided attempt to speed through curriculum, I set off to explain what my students need to understand. In the end, I often feel frustrated and the student hasn't learned anything.
Students must be the makers of sense. This is work that we cannot do for them. When we try, we supply reasons and examples from our personal learning. More important is giving the students the opportunity to learn for themselves. Otherwise, the student will seldom be able to grasp the big ideas and understand in a way that is marked by fluency and flexibility.
I also use too much direct instruction. At the very least, the direct instruction portion of my lesson always runs over. I wonder how much time I waste explaining things that should be discovered. I am certain that I should wrap up before I do. Another goal for next year is to truly stick to the ten to fifteen minutes of direct instruction in the plan. If I'm to achieve this goal, I really need to be thoughtful about what is taught. Next year, I will explain less and allow more time for my students to do math. I will continue to meet with the class at the end of the block to solidify the big ideas. This is not to say that I should present them. The opposite is true. Ideally, the students will be able to state what they noticed in the course of their work and also share what they're still wondering about. This goal seems like a small one but I know that if I'm successful it will also contribute to a positive climate where the students are in charge of the learning.
Fractions: Units and Equivalence Illustrative Math by William McCallum
A short piece that is well worth your time.