Teaching Math - Pt. 4

Having a math degree is pretty worthless for teaching math - in fact, most college degrees are pretty insignificant if you want to teach math. I have two degrees, neither of them in math, both of them in the humanities, and they may be more valuable than a degree in education or a degree in math. Having taught for several years now, I believe that the most important skill is not mastery of any content area, but rather, a teacher's most valuable asset is classroom management.

Classroom management is the both the most important skill and the most difficult skill. Not having it means that even if you have a PhD in mathematics and even if you can somehow teach the content to a college level, you will still be less of a teacher than some guy who barely has mastery of high school algebra, but knows how to keep students quiet and in their seats. To put not to fine of a point on it, classroom management is what it means be a teacher. Nothing else is important - curriculum, assessment, instructional strategies - these are professional skubalon until you learn classroom management.

I write this as someone scarred by my own misfortunes. My first year of teaching was very rough. I had students fighting in my classroom, kids dancing around, and other such nonsense. Multiple days I would go hoarse from screaming, and some days I was honestly holding back tears of frustration. I was sick constantly, both from the intensity of workload and from the stress and fatigue that came from actually trying to teach. Ours is no easy job, not least because of the fact that we are not handed self-motivated, highly mature learners - rather we receive a population of people quite disinterested in the knowledge we would like to share, and our job, part of what makes us uniquely skilled, is that we work to transform what is given to us into what we would like given to us. Being a teacher is not about conveying knowledge of content from one mind to others. Teaching is turning non-learners into learners.

The vessel through which this transformation takes place is the classroom. The captain of that vessel is me, and to ensure that I successfully navigate my students through the year, I set some rules. In the education field we refer to these rules as our "rituals and routines." When I was first told about this idea of creating highly structured sets of expectations for my children, I resented it because my natural mode of engagement with people is not highly structured. I suffered for my foolishness. It is oft stated, but too seldom actually believed and practiced that "children want structure." This has proved to be absolutely true. With each year, I set higher and higher amounts of preset rules and expectations for my students and in doing so they have come to like me more and more each year. The stricter I got the more they enjoyed my class. This, of course, flies in the face of modern notions of "freedom," but it is a fact that cannot be ignored.

Another thing that I've learned about classroom management is that not only are rules to be set and regularly communicated, but that they are to be held to with near blind commitment to the coldest of justice. What I mean is that when you tell a student that you expect them to do something, and they do not meet your expectation, then you must either do one of two things: 1) Correct the student, or 2) No longer expect them to follow your expectation. The key here is consistency. If you do not consistently hold students accountable to your expectations, then you cannot justly expect them to live up to your expectations.

Setting multiple clear expectations and then holding students accountable to those expectations is not something I am naturally good at. This is important. Most people are not natural teachers. 90% of the job is acting, performing, putting on a show. If I care about my students and doing my job well, then I cannot be who I naturally am. I have to change who I am and put on a persona that will help them succeed. Often times, peers will see me in "teacher mode" and they will get a mild chuckle watching me interact with the kids because they know how different that is from my normal personality. In most social contexts, I am the classic quiet, passive, reserved introvert. But starting from 9:15 AM until 4:05 PM, I am somebody else. I become an alpha. It's my job to be this other person and I get better at it every year, with improved results year to year.

Teaching Math - Pt. 3

When I began teaching, I had this ambition and eagerness to eventually get my kids to some sort of beatific vision through Neo-Platonic mysteries. I thought that a distinctively Christian approach to math might involve pushing children beyond shapes and equations onward into visions of the beauty of God. I mentioned that to one of my colleagues and he simply shrugged that it might be nice to get there, but honestly, it's hard enough just to teach them the essentials of the curriculum. I believe he was right.

This may sound Lutheran, but I more and more believe that my primary goal as a math teacher - as a Christian math teacher - is simply to teach my students mastery of the content that I am assigned to teach. This is my fourth year teaching basically the same curriculum, and I still have plenty of ways that I could teach it even better. When you really understand and appreciate the responsibilities of this job, there is never any shortage of goals and challenges. One simply needs the will and creativity.

This is not to say that math is separate from the unveiling of the face of God in nature - but only that the process of this unveiling is not as mystical and glamorous as meditating on triangles and the Trinity. Posted above my door is Vern Poythress' comment that mathematics is the rhyme of the universe. I believe that and I occasionally struggle to explain that to my students upon their asking. But much as you learn the Christian life through the drudgery of prayer, so do you learn the glistening harmony of the natural order through the monotony of solving linear equations.

Staring me in the face, from the back of the classroom, is Wittgenstein, firmly declaring to me over and over that there is nothing so difficult as not deceiving oneself. This is no less true in the field of secondary public education. We must be very clear about what our job is and do it very well. It is a hard job as much as it is an important job. Much more, it is a job that we can do unto the glory and honor of God, but as the cross reminds us, the shape of glory is not always identical to the honor of men.

Teaching Math - Pt. 2

The point, of course, of the baseline tests (mentioned here) is to assess specific needs of students and then adjust instruction accordingly. If, for example, I see that a high percentage of students score well on questions about the volume of rectangular prisms, then I know that I can compound a lesson on rectangular prisms with triangular prisms and right square pyramids. This year we found that, because students did not have the formula for the volume of triangular prisms given to them, it was missed more than any other shape, even shapes with more complex formulas, such as cylinders. This indicated that many students already had mastery of using formulas, but were less skilled in deducing formulas or understanding the logic that underwrites the formulas. (Understanding the logic of the formulas is part of the state standards. We have traditionally bypassed this, to our students peril, but because we yearly work to teach to the test, we are raising the quality of their education.)

This is what it means to "use data to drive instruction" - a catch phrase as of late that few people seem to be able to adequately speak to, though there is a rapidly increasing amount of pressure to do so throughout the district and the state. There are other ways to do this as well. One creative way to practice this is to use "centers."

The centers model, essentially, involves breaking your class into groups and having each group work on distinct tasks (computer activities, vocabulary, independent practice, and small group instruction) for shorter chunks of time (15-20 minutes), with periodic brief rotations to new tasks. This model is highly engaging for students and takes a lot of different forms. One effective use of this model that we have piloted this year is organizing the groups according to pretest scores. Students are broken into four groups, ranked according to how high or low their baseline scores were. Students in the higher groups would be offered more enriching type activities, while students with lower scores were offered much higher levels of direct teacher support and remediation.

The centers model takes a lot of planning and preparation to execute well. In more advanced classes, the process is fairly stress free, but organizing it for standard level students takes excellent classroom management on behalf of the teacher. It's also not always practical. Occasionally, there will be a subject where students will uniformly, across the board do miserably on the baseline test. (This happened recently with Surface Area, to no surprise.) In these cases, the centers model can be impractical. When all students are functioning at an identical level, "whole group" (traditional) instruction is often preferable. Note, of course, that this is still using student data to drive instruction.

Teaching Math

My entire curriculum through the year is shaped by the state of Florida's standardized test, known as the FCAT. I do this for two reasons: 1) Because this is what my school district expects from me. 2) I was on the board that wrote the curriculum for the district.

My year's curriculum is organized into units called "modules." There are about nine modules for the course I teach, a course known simply as "Math 2." Each module contains a different cluster of state standards to be mastered. Yesterday, my students completed a module known as Module G - Data Analysis and Probability. This covers the state standards MA.7.S.6.1, MA.7.S.6.2, MA.7.P.7.1, and MA.7.P.7.2.

Each module begins with a baseline test and ends with a post-test. The baseline test serves to identify to what level have my students mastered the module's content before I teach it to them. The post-test serves to identify to what level have my students mastered the module's content after I teach it to them. Both results are recorded and compared. The higher of the two grades is given to them, and they are awarded bonus points according to the gains they made between the baseline and post-test.

Other than bonus points for making gains, the only grade they receive for each module is their test grade. Homework and classwork count for zero points in my class. I assign it, most students do it, and it counts for nothing. The only thing that factors into their grade is what percent of the standards can students demonstrate that they have mastered.

This is how I run my class. Because of it, I have some of the top scores in the district on standardized tests. This is because I teach to the test - specifically, the state standardized test. I do this without apology, because my state's standardized test is a very difficult test. If my students are well trained to solve every tested topic at high levels of complexity, then my students are well trained in math.

Evie Mae

And then there were three...

Against Privacy?

"Social Welfare is the not the responsibility of the public sector - rather the poor should be cared for by private organizations such as churches, charities, businesses, families, etc."

Anybody ever realized how sneaky comments like this are? Here, "public" is code for "the State," and "private" is code for "not the State." The upshot of this is the idea that the only truly "public" entity is the State, and that anything that is not "the State" is less so. This seems to be the makings of a subtle tyranny. After all, if the Church is simply another organization of individual interests that have no bearing on the public will, then it really, in any meaningful sense, doesn't matter. If the Church is part of the private sector and not, say, a legitimate participant in public life, on the same footing as the State, then nobody has to listen to her. Too take it all the way: If the President can ignore the Pope on matters of legislation, then Christianity doesn't matter. The Church, it seems, has a responsibility to reject the name "private." Is there any non-blasphemous way to say that Christ is a "private" person? I doubt it. If it is to be that "the government will rest on his shoulders" and kings of the world will be casting crowns before his throne, then oughtn't it be essential that Christians cringe at a statement like "Politics is, in some ways, an expression of a culture's religious beliefs"? It is the responsibility, then, for Christians to reconsider those things that are most essential to "being Christian" and reflect that, in every way, those things are overtly public acts.

Q and A

While writing on my blog has dwindled in the past couple years, I haven't altogether stopped writing. Truth be told, in the past six months, most of the writing that I've done has been on my phone actually, via ridiculously long text messages. If there were an easy way to transcribe all of them to here, I would.

Still, difficult as it may be, I thought that the following message was worth placing on the record, so here it is.

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I received the following text message today from a friend of mine from church:

Does baptism forgive sins or does remission come at the moment of faith in christ?

My reply:

Union with Christ through the Spirit is the means of forgiveness, adoption, sanctification. Faith is the instrument of that process. Baptism unto Communion is the shape of that faith.

Faith cannot be reduced to a moment any more than one can be a Christian for a moment. Many people conflate 'faith' with 'intellectual assent.' While the two are related, they are not the same thing. It may be easy to identify a moment that one first 'assented' to the Gospel. It is more challenging to identify a moment of first 'faith' - in oneself or anyone else for that matter.

The best way to answer your question would be, "Remission of sins took place on the cross." In baptism, we are united to Christ's cruciform death. Thus, in baptism we are united with this death which merits remission of sins. It is in this way that it is proper to say that "baptism is the moment of remission of sins."

There ye be.

"We read to know we are not alone."

So then, why do we write?

Nothing Else

What is idolatry but a radical inwardness?

Epiphany

In the Spirit of St. Francis, we routinely catechize our dog in the doctrine of the Trinity every Sunday when we leave for church by giving him three dog treats.