According to the establishment, students should be “led” to their discovery of the answers. Providing explicit instruction is considered to be “handing it to the student” and prevents them from “constructing their own knowledge.”This style of pedagogy is being foisted upon us under the guise of Common Core.
“Discovery learning” isn’t bad. Most teachers use some discovery learning and group work in their classes. Also, staging problems so that they vary slightly from the worked example—so that the students are essentially applying prior knowledge in a new situation (called scaffolding)—has the “look and feel” of discovery. The problem is that the reigning education theory focuses mostly on discovery, with only a nod to direct instruction. That’s mistaken.
The worst class I took in education school was on “math teaching methods"...
Educators who promote “authentic learning” mistakenly believe that novices learn the same way that experts do. They believe that students construct their own knowledge by being forced to make connections with skills and concepts that they may not have mastered. The theory is that they learn what is needed in a “just in time” manner, thus providing the motivation for learning, which they assume would otherwise be a tedious and soul killing exercise...
The ed school approach to teaching math seeks to minimize “inauthentic” learning by replacing it with so called “authentic” exercises. But presenting students with a steady diet of challenging problems that neither connect immediately with their prior knowledge, lessons and instruction, nor develop any transferrable skills results in poor learning.
It is like children playing “dress up” in their parents’ clothing. The education establishment may believe they are producing “little mathematicians"....
Update: Check out this post of mine from 5 years ago on teaching calculus as described above. The more things change....
In my opinion, what "works" is to directly teach several different approaches and then let the student determine which is the most efficient and straight forward for addressing the problem at hand. In my own learning experience, I have found that when the teacher provided the derivation of a formula or an idea, it helped. I have met too many students who were frustrated with the independent group-discovery kind of exercise that "authentic learning" seems to entail.
ReplyDeleteOh, my, sounds like my school today! First day today, a Friday. Makes no sense.
ReplyDeleteThen we are told we have to start testing MAPs on Monday. Sounds like we had the same training, with no idea what to do with 35 kids in a computer lab the second day of school. Got it postponed a week. Why? Because teachers need that first week to establish procedures and order, to get the relationship going on the right tone, to identify the little stinkers??? Why no, none of that. It's because no one will have their AUPs back by Monday and our tech guy won't let them sign on until they do! And did I mention the kids' schedules are a mess and it won't be straightened out by Monday, so we would have had 35 kids, none of whom could have logged into our school system, and even if they could get past that, wouldn't be on our lists, so wouldn't be able to test anyway.
Train wreck; new principal who has a big learning curve ahead. Needs to ask the teachers who know if what he proposes might have some unintended consequences. Would get more help and do better if he owned up to not knowing what he is doing!
I'm posting this anonymously for obvious reasons!
I'm for direct instruction in math, most of the time ...actually, Socratic, but that's just a difference in style. But ...I have had a number of group learning exercises that always work well ... the key, to me, is don't assume the kids no the math...because they don't. That's the reason that they are in your class. 'Guided instruction' is just that ... a group activity that the teacher leads, maybe expectedly, maybe not, to a conclusion. It usually leads to a better level of understanding, but it's also usually not viable. One must pick one's spots.
ReplyDeleteknow the math. Jeez.
ReplyDeleteOK, I'm depressed now. I"m making a point of not stopping by until after noon! First thing in the morning is NOT OK!
ReplyDeleteSeriously, I appreciate the info. I had a discussion regarding Common Core with a Middle School principal that I highly respect. He was more enthusiastic about Common Core. After reading this and other information on Common Core, at least as far as math goes, I find it very troubling.