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| This is my presentation entitled Mathematics Seminar & Formative Assessment, Message to Teachers: <i>Dialogue required when instructing students in mathematics</i>. I really connected with some people at this training, but I also found I planned a little too much and subsequently I was rushed towards the end. Being rushed caused me to do a poor job of explaining that Teacher-Presenter-Scribe, Delegate-Teams, and Practice-Create-Reflect are all scaffolded graphic organizers that assist in the implementation of seminar. More information on those techniques can be found on an earlier post: <a href="http://oemb1905.livejournal.com/8183.html">Paideia Strategies</a>. Additionally, through the approach of seminar educators are able to gather valuable formative assessment information about their students. Thanks to everyone who provided feedback both positive and negative; I am indebted to you for your insight. | |
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| I came across the country today to speak to you about Seminar. No, not Socratic Seminar like even Stringfellow Barr would admit, but to me just seminar. Forgive me for not wanting to use Socrates’ name as an adjective, but that has never been comfortable for me. At any rate, seminar is an approach to learning and instruction. It is an approach that is sorely missing from our secondary schools today but is actually one of the most ancient methods of instruction available. In short, it is where the old school meets the new. It is both surprisingly ancient and yet nascent and state of the art. In light of budget constraints and economic depravity that many schools find themselves, seminar stands out as a solution freely available to all. Seminar is an equalizer of sorts, in which every student is on the same footing as another; indeed, students are on the same footing as the instructor. | |
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| Formative assessment, on the other hand, is a buzzword in today’s educational system. On the one hand it is commonplace and obvious, and yet on the other so basic that the minutiae of its system are often overlooked or botched. In distinction to summative assessment, a distinction put in place in 1967 by an evaluation specialist Michael Scrivens, formative assessment is an assessment aimed at evaluating how one’s formative experiences, the one’s that “shape who one is and becomes through learning”, are evaluated or assessed by the educator (Scrivens 1967). Scrivens, it should be noted, was an Australian with a mathematics background, favored the summative assessment, because it provided, he believed a picture of the total body of work, or the completed product of learning that a student acquired within a scope of learning. And perhaps that is still accurate today, at least for the student. But educators should really not be concerned with a final benchmark or measure alone, but with more ‘on-the-fly’ measures, the ‘in the process’ measure, those tools that enable an educator to focus on refining the product; shaping the young man or woman. | |
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| Remember, in the case of boys and girls, the product is the person, and the value, the character, is still developing. Summative assessment, or perhaps it would be better called static assessment, will no doubt have its place later in life for every student. There is no need to bring it in quite so early. Indeed, it has its place right now as you measure the efficacy of this speech, later today when you fill out my evaluation, and throughout this conference when you hear different educators, and most recently right now as you ponder Ms. Gates’ opening address. But I challenge the premise that students should be concerned with this measure at the outset of their development as a young citizen. In the secondary environment and perhaps even up through the first two stages of college, the goal should be maturation and growth. The very notion of applying a summative assessment to an unfinished product is inherently contradictory. How can one evaluate the sum of something’s parts before its parts are developed fully? | |
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| Moreover, there is a sense in which even summative assessment itself is a premise that deserves to be challenged. I proposed above that it be called static assessment but even that is lacking. Can something ever be assessed in sum total? Is anything ever done growing? Are young men and young women finished growing when they complete secondary? Complete college? A thesis? A dissertation? If that were so, then why are we here today as educators? Our very presence here indicates our commitment to self-growth, our commitment to developing despite our stage in life and despite however far we have come this far. Summative assessment thus becomes an almost antiquated misnomer when it is subjected to careful scrutiny. I realize that some of you are thinking “wait a second, what kind of math teacher are you?” Are you saying that tests like the SAT and ACT are not valuable? Is there no purpose to our local and state mandated tests? Are you one of these anti-assessment crusaders? I thought you were a math teacher … maybe I should leave!” | |
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| But hold on. Bear in mind, I am an A.P. Calculus teacher and this year 10 of my sixteen students had 5s on the exam, including 3 5s for my BC students. And the A.P. Calculus Exam is a good exam. I am not advocating the abolition of all tests; rather, I am supporting fixing how educators have used tests. I think that somewhere along the line many of us must have forgotten how to use tests. To think that there was ever a day when a test was given, scored, and then the class moved on? Wait; was there ever a day like this? Maybe there was or maybe we just have said that there was for so long that we have forgotten that there never were days like this. Perhaps these were just bad teachers. Nevertheless, I digress from the question at hand. Are the SAT and ACT exams really summative? Is the A.P. Calculus Exam summative? Or the PARCC? I challenge the premise that they ever were or are summative. Of course, I realize what Scrivens had in mind, I realize what his intent was in evaluating the complete product and distinguishing that from the growth of the product, but I would argue that summative assessment is best understood as a subset of formative assessment. | |
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| For example, administrators and superintendents meet to discuss SAT or ACT results on a district level in order to evaluate the efficacy of instruction. The A.P. leader at a school meets with other A.P. teachers to ensure that the scores are where they should be. And they ensure that those students are learning college level content. And whether PARCC, Smarter Balanced, etc., these tests are going to be used to evaluate the educators’ current efficacy. Indeed, to some extent these scores will drive our evaluations and our pay in some states, and in some districts. These are not ‘summative’ measures. These are formative measures. Of course I am guilty of a bit of a conflation here. After all, these formative assessments are all macrocosmic in scope – much different than when an educator gives an exit slip and determines a student can’t read (that’s microcosmic in scope). But, after all, it is the year after that the Superintendent gets the assessment data, a year after that the A.P. teacher gets the exam data and adjusts instruction. But just being macrocosmic does not mean they are not formative. Rather, they are a subset of formative assessments, a highly specialized usage of formative assessments in which educators measure students in a norm-referenced manner against others. They are a way in which educators measure themselves as districts, or as educators against one another. I challenge the audience to join me in this redefining of terms. Why is it that one mathematician divided assessment up in the 60s and that it has remained unquestioned to this day? Join me in questioning this division. | |
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| Getting more specific now, why are all of us here today? And what are you going to learn at my training today? What am I purporting to show you and what will I not show you? First of all, I am not here to debate semantics or names. Although I must admit I broke this rule twice already with seminar not being called Socratic and again since I told you just now that summative assessment is at best not applicable in secondary and at worst a misnamed subset of formative assessment! But let me be clear, I am not here to talk to you about informal versus formal formative assessment, or the sheltered model versus another model of instruction, etc., or whether formative assessment should be renamed assessment for learning as some argue. Like Reeves and William I choose to keep our terminology in tact (for the most part), and simply discuss what we can immediately bring back to our classrooms. What we can immediately bring back to our communities and fellow educators. And my message is fairly simple and precise. | |
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| … Message to Teachers: Dialogue required when instructing students in mathematics … | |
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| That’s right. Dialogue. Remember, what you will learn today is an instructional “approach,” an approach to learning, and that approach is called seminar. Seminar would thus be in the same category as cooperative learning and direct instruction. Dialogue, moreover, is the technique whereby educators and students engage in the approach we call seminar. Remember, seminar means ‘seminarium’ and is only the place where ideas grow. The ‘dialectic’ technique, or dialogue, is the tool by which we grow those ideas. Ok, so back to today’s training again. Please forgive me, as I yet again wax classical and philological here yet again. | |
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| To be precise and plain, today you are going to learn of three strategies that I use to scaffold seminar with: Teacher-Presenter-Scribe, Delegate-Teams, and Practice-Create-Reflect. Each of these strategies is to be used with students that start and finish in a circular setting. That is, a seminar seating arrangement. And let me be quite plain, it is my contention to you that this will make your math instruction more effective - not less. I am arguing to you today not that you don’t have time to do fancy techniques such as these, but that you don’t have time not to. And of all the things we do today, it is imperative that you leave, whether you agree or not, with the following exhortation in mind: | |
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| … Dialogue required when instructing students in mathematics … | |
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| Now, this dialogue can take different forms. It might be whole group, or in a traditional circular seating arrangement where we all dialogue, or speak across, to one another. After all, etymologically speaking, dialogue means none other that ‘speaking across,’ for dia means across and logos means speech or talking. Dialogue can occur in more than just seminar. After all, dialogue is a technique and seminar is a broad approach. Dialogue can be with our peers, e.g., student to student through cooperative learning, or student to teacher, e.g., think-aloud, seminar, grand conversation, etc., or simply when the teacher comes by to provide corrective feedback or to refine or redirect a student in their quest to answer the focus question. The important part though is that dialogue happen, regardless of pedagogical approach. Please leave here today with that in mind. Instruction is not a monologue or a prologue, and we all certainly hope it is not the epilogue. No, it is a two way street, a street called dialogue. Dialogue requires everyone to be engaged with one another in academic discussion about content. | |
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| Remember those Calculus students I just told you about? The first reading of the year was was from chapter 2 of Freire’s (1970) Pedagogy of the Oppressed. Now, let’s not get carried away, of course I spent most days on Calculus thereafter, and many days using direct instruction. So, I did intensive tutoring with an ELL student in Calculus this year. And yet he does not remember my stunning acumen. What he remembers, rather, and what he wrote in his dialogue journal, was a commentary in his own words on the banking versus problem-posing education conundrum that Freire laid out so eloquently in 1970. Now, clearly the tutoring had its effect as well since this young man got a 4, however, after a full five months of tutoring, he did not remember most that which he was taught, but how he was taught it. He remembered the dialogue we had the first day. He remembered the message about learning and about academic rigor. He remembered Paolo Freire and pedagogical methods. In the end, he thanked me for the calculus too, but before the results came he remembered most the message about how to learn with me, not what we were learning. This was because the first day of calculus was spent conducting a seminar on Freire. And seminars are the vehicle for teaching dialogue at its finest exhibition. | |
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| So you will see today that in fact seminar, in its intellectual and ancient grace, is both the superior form of instructional approach, and likewise the most profound type of “informal formative assessment” available to educators. Naturally, you see, students cannot fake it when they are right there with you in the circle, man to man, woman to woman, etc., conducting real talk, about real ideas, using textual support, constructing a mathematical argument and testing its viability. When a student tries to read highly complex academic language, you see them struggle or succeed. You see those who question, those who rest in the land of opinion and rhetoric, and those who can utilize evidence and those who cannot. You see who thrives on what and what who is interested in. Who needs that RtI model that teachers are shamefully griping about, who needs tutoring, who needs Tier 2 and may have something complex going on, who needs to have some data points collected now? Again, today, you will learn of these three tactics, and during the exercise of practicing those tactics, you will learn how seminar allows you to formatively assess your students during natural dialogue. You may be wondering if I am saying what you think I am saying and I probably am. That’s right, “talk to your kids academically and they will talk to you, and when they talk to you, you will know what’s going on and what needs to be done.” It is that simple. The simple message we have forgotten: | |
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| … Message to teachers: Dialogue required when instructing students in mathematics … | |
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| Seminar is difficult though! Talking to your students academically is difficult! How sad that is, but strangely true. I had a fellow teacher come up to me this year after he attempted to read some of Al-Khwarizmi’s work on Algebra with his students as I suggested and he said to me “Haack, how do you do that man, like I don’t even know what he is saying and the kids couldn’t even read like a paragraph man, and everyone was lost.” Well, although he was my boy, I can’t help him understand it and he knows he was being lazy, but as for his kids, no doubt, no doubt, they were struggling. But that is precisely the principle at play in seminar. By engaging in the analysis and discussion of complex texts, students will become better readers and thinkers. It is only by challenging them with the real talk, and the raw message, that any of them will grow. Curriculums cannot be comprised of scripted readings. Its shameful that we try to raise reading scores by teaching Treasures. Consider Plato’s Meno. No, really consider it – I aint playing. | |
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| The difficulty aspect. There is no denying my colleague’s appreciation of the students’ struggles. True. That was real talk and that was dialogue. But the easy fix is what I am here to present today, the scaffolding approach to seminar. Use the graphic organizer to break from large group to small group and then back again. Eventually your students will get better at the large group approach and can immediately start seminar without modification, but at the start, my goodness, by all means mix in the scaffold. I’m sure we have all heard of sheltered instruction. I’m sure we are aware of the large number of ELL students in this district. So, bear in mind, that Teacher-Presenter-Scribe is just that, it is a scaffolded seminar activity where students switch from large group to small and then back again, and it mixes in a student presentation at the end of the seminar; some institutions call these type of seminars tutorials. But bear in mind, they are still seminars as long as you are collectively discussing higher order ideas with the dialectic. I simply propose that as educators we add a scaffold or a shelter. That scaffold takes the form of a graphic organizer in my class and a variety of context and arrangement, wedded together with student ownership of the completed product. Throughout the process, the levels of student learning are paramount in importance but strikingly easy to determine. The result is that you have created a dialogue based environment in which formative data is presented intrinsically and explicitly through real-talk with students. This is not a DEA spreadsheet; this is you watching as your student tries to explain how slope-intercept form works. It can’t be faked. You will see that today in action. And these data are those types of information which you can immediately use to instruct better come the next unit, the next lesson, the next day of instruction. It will shape how you construct the groups, which problems you give which groups. | |
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| Again, I will present to you that seminar is best understood by returning to the classics. Those classics can be ancient or modern, but we know they are classics when they have withstood the test of the ages. Return to Stringfellow Barr and the Johnnies. But don’t fear, seminar can also be used with a newspaper clipping, the math textbook, or in a faculty meeting amongst teachers. After all, we are talking about paideia here, namely, the nurturing of ideas through dialogue, not pedagogical whim and undulating fancy. I do, however, posit that you – whether Math, English, History, Science, etc. – will learn more about effective instruction by re-reading The Republic and Notes on Dialogue than you will from reading the whole gamut of current educational propaganda. I’ll stand by that claim. In fact I challenge you to take some of the readings and thinkers I have presented today and to go home and read them tonight. When you see me next, “say, Haack, I read fill in the blank and you weren’t playing. I’m bringing dialogue to my class tomorrow.” Do it. Real talk right now. Bring the message to your teachers. Have seminar during your staff meetings. Dr. Magrum (2004) recently wrote about the efficacy of this approach. A white Principal in a historically black district conducting seminar for faculty meetings. The response of one educator is enough to reveal the entire dissertation, “I think this is working.” | |
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| I posit additionally that seminar is not an antagonistic perspective. You are not out of touch with anyone. You are in touch with academic rigor and real talk. Don’t denigrate the students and degenerate the content because they are at-risk or wounded. On the contrary, when there is a need, a real need, it is only our duty to meet that with the highest content and most challenging texts, methods, and dynamic instruction. When you do this, when we do this, we listen to our students better, we teach better, and we hone in on the first principles of teaching and assessing. Those same principles never change. It does not matter whether the message of rigor comes from Paideia, from MDC and Bill Gates, from Agile Minds, or from Sal Khan, as long as the message is rigor. As long as the message is consistent with the message we agree to today: | |
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| … Message to Teachers: Dialogue required when instructing students in mathematics … | |
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| <b>Real talk.</b> | |
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