We, teachers, experience it almost every week: our kids may "get" the material on a day-to-day basis,when it is taught one idea at a time, but once they are at the point when they have to deal with a mixed bag of questions, some of students have trouble even starting. I believe that it is very important to let our students know of this very well-recognized psychological phenomenon and that it should be expected.
Every learner has experienced it at some point: as beginners, we might know chunks of information, but most likely, we have not, YET, see connections between them or even developed retrieval mechanisms for initiating them. Sometimes getting over this hump takes us longer then other times...but being aware of it, definitely helps students avoid much of the frustration related to the process.
It is very easy for us, teachers (aka masters of the topic at hand) to take for granted our ability to see the whole picture, and underestimate the value (and magnitude) of students' struggle here. Meanwhile, this experience can be transformed into one of those GRAND teachable moments, that, perhaps, explain why we want our children to learn Mathematics...It shows, that mastery starts with learning facts, comparing and contrasting, deciphering through relevant traits, trying them out, and, maybe, identifying illusions of competence, and tuning up the process along the way. Mastery comes with perseverance ...just like in real life...
INTERLEAVING -doing a mixture of different kinds of problems-is what I use to help students to move from a novice to an experienced learner of the topic. Below is a short video of the mind map that my students will have by the end of the Units on Basics of Segment and Angle Relationships. We summarize new material into CHUNKS reflected by this map (same order as in the clip) after learning new terminology, use of symbols and appropriate diagramming. At the end of the unit, we use this map to help with learning how to shift our mental gears from one situation to another. The poster of this map became a very handy reference when we needed to bring back the structure of communicating about geometric relationships throughout the school year.
Usually, these two topics are taught in the beginning of a course, which makes them vital for an easy student transition to the new level of expectations to their work. I find, that students whose attendance was spotty during this time, have a much harder way of finding a good standing with the subject. I can not control their attendance, but at least I can make an attempt to help them catch up. Later on, I will be posting the videos that give a thorough overview of the material in the CHUNKS of this map.
Every learner has experienced it at some point: as beginners, we might know chunks of information, but most likely, we have not, YET, see connections between them or even developed retrieval mechanisms for initiating them. Sometimes getting over this hump takes us longer then other times...but being aware of it, definitely helps students avoid much of the frustration related to the process.
It is very easy for us, teachers (aka masters of the topic at hand) to take for granted our ability to see the whole picture, and underestimate the value (and magnitude) of students' struggle here. Meanwhile, this experience can be transformed into one of those GRAND teachable moments, that, perhaps, explain why we want our children to learn Mathematics...It shows, that mastery starts with learning facts, comparing and contrasting, deciphering through relevant traits, trying them out, and, maybe, identifying illusions of competence, and tuning up the process along the way. Mastery comes with perseverance ...just like in real life...
INTERLEAVING -doing a mixture of different kinds of problems-is what I use to help students to move from a novice to an experienced learner of the topic. Below is a short video of the mind map that my students will have by the end of the Units on Basics of Segment and Angle Relationships. We summarize new material into CHUNKS reflected by this map (same order as in the clip) after learning new terminology, use of symbols and appropriate diagramming. At the end of the unit, we use this map to help with learning how to shift our mental gears from one situation to another. The poster of this map became a very handy reference when we needed to bring back the structure of communicating about geometric relationships throughout the school year.
Usually, these two topics are taught in the beginning of a course, which makes them vital for an easy student transition to the new level of expectations to their work. I find, that students whose attendance was spotty during this time, have a much harder way of finding a good standing with the subject. I can not control their attendance, but at least I can make an attempt to help them catch up. Later on, I will be posting the videos that give a thorough overview of the material in the CHUNKS of this map.
