Pruebas de cumplimiento con los errores máximos permitidos

“T

oday, I am to announce the Top 10 achievers in this class,” says Mrs. Francia. Low

murmurs can be heard until a name is called. “Nenita,” Mrs. Francia reads from her class record. Crisp rounds of applause filled the room until nine other students are called.

“Congratulations to our top ten!” Mrs. Francia smiles, beaming with pride for her students. “Now, for those whose grades are below 82, I’ll give you more drills, so we’ll

have more than just top 10 achievers next quarter.” The students look relieved.

“Let’s put the top ten aside and open your workbook on page 37,” Mrs. Francia instructs the class. Noticing that Mrs. Francia is referring to a lesson they already discussed, Pipay informs her teacher, “Ma’am, we’re done with that already.”

“I know,” replied Mrs. Francia, “but we have to review it because Mabel was absent when we discussed this. She represented our school in a regional competition, so we just need go back a little for her. Is that okay, class?”

“Yes, ma’am!” The boys at the back exclaim, “It’s definitely okay, we sure need a review!” The girls in the middle row agree, “A review is just what we for our

summative test this Friday.”

In her thanks, Mabel tells the class, “It’s nice to be back, classmates!” “We missed you, Mabel,” her classmates exclaim. The entire class congratulates Mabel for the silver medal she got from a news writing regional contest. The class is in a great mood.

The class discussion continues until finally, when the board is filled with

equations and solutions, Mrs. Francia asks the students, “Class, in what ways in your life are these algebraic expressions useful?” The students are silent until a group of boys recite in chorus, “To pass the test!” The students laugh.

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“Well, that’s true,” Mrs. Francia said thoughtfully. “But algebra is not just for tests. Look at this—” Mrs. Francia writes a problem on the board and lets the students solve it on their notebooks. Three minutes later, a couple of students go to the board to write their solutions. A couple more do the same. Without being told, more students come to front to show their answers. When all the seven students are done with their

boardwork, Mrs. Francia examines each of their solution processes, corrects some errors here and there while explaining these to the students, and marks each of the seven answers with a big check.

“Now class,” Mrs. Francia calls the attention of the students. “All these seven solutions are different from each other. But they are all correct. What does this say about Maths in general?” The students seem to be in deep thought.

“That there are many solutions to one problem?” replied Onyok. “Exactly!” Mrs. Francia exclaims. “That’s what we should learn from maths—that we shouldn’t give up because there is always, always not just one but many solutions to a single problem.”

“Ah, just like life then, ma’am?” remarked Kiko. “Yes, just like life. See, class, maths is not just for tests but for life, too,” Mrs. Francia reminds the class. The students smile and take notes as they listen to Mrs. Francia continues her lessons.

Mrs. Francia’s explanations are flawlessly crystal clear even I find myself doing some solving in my notebook and finally understanding algebra like never before. “I like her. She makes maths seem easy and lovable,” whispered Pipay to me as I solve problem set B. Four days later, the class had the summative test which lasted the entire period.

Mrs. Francia: The students’ (life) coach

In observing Mrs. Francia’s class for forty minutes every day, I noted that a large amount of time is allotted for student drills and practice. Assessments of all kinds (e.g. formative and summative tests, from whole class ‘problem-solving’, board work and workbook exercises, quizzes, to graded tests and comprehensive exams) are spread across evenly within the three weeks of my observation in her class. Generally, Mrs. Francia’s approach in teaching appears to provide her students with many examples as possible until they finally ‘master the concept’. Mastery of the concept, as Mrs. Francia later explained to me, is attained when at least 25 of the students (81 percent of the class) get a perfect score in her teacher-made summative exams. For the rest of the 19 percent of the class (around six students) who did not get a perfect score, they are provided with remedial tests and tutorials (referred to as ‘make-up tests’) by Mrs. Francia after school.

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It is important to note, however, that the majority of tests administered by Mrs. Francia and other urban teachers are ‘teacher-made’ or designed and constructed by the same teacher teaching the subject. Only four of these tests, referred to as ‘quarterly examinations’, are provided by the Division Office (local entity of the Philippine education ministry, the Department of Education). The weight allotment for these quarterly examinations comprises sixty percent of a student’s grade; that is, ten percent for the preliminary and prefinal examinations while twenty percent for the midterm and final examinations. The remaining forty percent is upon the discretion of the teacher, which she could allot for ‘class standing’ which means a student’s participation in class discussions and activities, ‘graded recitation’, group projects, and even leadership efforts in co- and extra-curricular involvements, among others. It is important to mention this here to clarify that the tests I refer to in this urban school are not similarly situated with how tests are designed, constructed, administered, and valued in the contexts of public schools in the United States or in Singapore (see Tan, 2008), Thailand-Myanmar (see Tyrosvoutis (2016), and Hong Kong (see Biggs, 1996; Yeung, 2009). Therefore, it cannot be said that the pressure of tests (particularly high-stakes tests) placed on the students in this urban school in this Philippine context is similar with those in its neighbouring Asian countries.

Explaining well during lectures

There is a general pattern in how Mrs. Francia teaches this junior class. The first fifteen minutes is allotted for a brief review of the previous lesson (this review comes in the form of checking of solved problems given as ‘assignments’ or homework by Mrs. Francia). This is followed by an introduction of the new lesson which is done through workbook exercises or drills as board work. The next thirty minutes is for checking of students’ answers, which also serves as the discussion proper of the lesson. The discussion culminates with some form of assessment, either formative or summative, depending on how prepared the urban students are for a graded test based on their engagement and performance during class discussion.

In my interview with Mrs. Francia, she refers to this way of teaching as ‘lecture- discussion’, a strategy that she refers to as a deductive method of teaching in mathematics, where she starts with a concept or a rule, which she introduces through a lecture. She then gives examples or what she calls, ‘problem sets’ which she also solves to demonstrate various ‘solution processes’ to her students. After which, she provides different ‘problem sets’ for her students to solve on their own. Later, several students volunteer or are nominated by Mrs. Francia to show their solutions to the class through board work. The discussion part comes in when the students, as a class, express their thoughts about their classmates’ solution on the board with Mrs. Francia

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moderating the students’ exchange of ideas. In using this ‘lecture-discussion’, Mrs. Francia describes herself as a ‘traditional teacher’. Interested in what Mrs. Francia means by ‘traditional’, I probed further:

Lucille: Why do you call yourself a traditional teacher? Mrs. Francia: because I give a lot of lectures, I give a lot of drills. Lucille: Why is that?

Mrs. Francia: That’s how students learn best […] My seventeen years of teaching taught me that students still need someone to help them understand how the solutions are made. That’s where the part of the teacher comes in— explain, lecture, so the students understand.

It is important to note in this interchange how Mrs. Francia places emphasis on her ‘seventeen years of teaching experience’ as a reason behind her use of traditional instructional practices like lectures and drills. The use of this ‘long experience’ narrative among teachers is argued by Schweisfurth (2013) as a critical factor to a possible rejection of learner-centered practices in the classroom.

Lineage of ‘long experience’

In developing countries, Schweisfurth (2013) observes that teachers, albeit receiving training are less likely to implement learner-centered practices as issues of quality teaching (i.e. poorly resourced classroom) are rarely addressed, and “therefore they have only their own experiences to draw on to inform their practice” (p. 66). In the same way, teachers’ motivation (or the lack of) to make the ‘paradigm shift’ is further curtailed given their ‘long experience’ of perennial problems in education which seem to perpetuate despite the state’s pressing call for change or the constant promise of innovation. This supports the conclusions in the separate studies of Kaya Yilmaz and Michele Schweisfurth which found that given the compounding issues of challenging classroom realities, working conditions, and the outlook within a school culture may become ‘real’ obstacles for teachers to adopt learner-centered teaching (Yilmaz, 2008), which could explain why they ‘retreat’ to, if not, retain their traditional methods of teaching (Schweisfurth, 2013, p. 67),

There are other several layers of tension that can be noted in this interchange with Mrs. Francia. Firstly, her reference to the use of lectures and drills as traditional methods of teaching as a response to how ‘students learn best’ antagonizes some fundamental concepts of learner- centered teaching. The practice of lecture method, categorized as ‘teacher-centered’, alongside the use of student drills, which is associated with the phrase ‘drill and kill’, are criticized for promoting rote learning and failing to develop higher forms of thinking such as critical reasoning and

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creativity (Cuban, 1983; Meece, 2003; McCombs & Miller, 2007). Referring to lecture method, Crumly, Dietz, and d’Angelo (2014) assert:

[A] very traditional approach to teaching and learning, this method does not always meet all the learning styles of students. Truth be told, teacher- centered learning is less a pedagogical method than it is a habit based on suppositions about what’s more difficult or personally convenient” (p. 5, emphasis in original).

Within the context of Mrs. Francia’s use of lectures and drills, it becomes clear to me as the researcher, given the weight of division-based quarterly exams on student grades, that the tensions within and between her ‘very traditional approach to teaching’ are a response to her perceptions of teacher accountability. A closer examination of Mrs. Francia’s practice of lectures and drills tells us that her pedagogical choice could be shaped, first and foremost, by the pressures placed upon her being accountable for her students’ test scores, and her experience which tells her that these methods are more likely to produce strong exam performance.

Teacher accountability

Teacher accountability is a critical issue raised among proponents of learner-centered education (i.e. Weimer, 2002; McCombs & Miller, 2007) and within discussions about democratic education through caring pedagogy (Noddings, 2013). This is because teacher accountability implies strict adherence to content, direct alignment to curriculum goals, and preoccupation with high stakes testing and student outcomes. Issues of mistrust towards teachers are also implied within the discourse of accountability, which might be concealed under a blanket of fixed and prescribed content-driven curriculum that puts premium to standardized testing as the means of validating student learning and holding teachers accountable should students fail. This vicious cycle of teacher blame is argued to only demotivate teachers in delivering the quality of instruction students actually need to learn (Schweisfurth, 2013) and even disempowers teachers in their attempt to care for students (Noddings, 1992; 2013).

As teachers are placed under heavy pressure to achieve the expected student outcomes, their approach in teaching may become focused on teaching to the test. Given the recurrence of tests in Mrs. Francia’s class and her test-preparation teaching strategies, this ‘pedagogical look’ might give an outside observer an impression that her approach resembles teaching to the test. Associated with ‘teacher-centered methods’, teaching to the test is sharply criticized not only by proponents of learner-centered teaching but education reformers, in general. However, W. James Popham (2001), an important figure in the field of student-centered assessments, argues that, based on his decades of research on and practice of assessing students, teaching to the test

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connotes either ‘curriculum-teaching’ or ‘item-teaching’. When teachers direct their instruction towards a specific body of content knowledge or a set of competencies (such as the ability to solve algebraic expressions) represented by a given test, ‘curriculum-teaching’ is taking place (Popham, 2001). For example, if students will be tested on addition, ‘curriculum-teaching’ teachers will cover a range of topics and skills related to addition, so students understand what addition is, know how to manipulate the addends to the find the sum, solve more complex addition, and are able to communicate with and about addition. Popham argues that when practised properly, ‘curriculum-teaching’ will not only improve students’ scores on tests but also “elevate students’ mastery of knowledge and skills” (Popham, 2001, p. 17).

In my observation of her methods, I find Mrs. Francia’s approach in teaching to be similar to this ‘curriculum teaching’ that Popham (2001) describes. In the same way, her practices also resonate the descriptions of ‘whole-class teaching’ as observed by Stevenson and Lee (1995) among Japanese maths teachers who begin instruction by presenting a word problem then ask several students to show their solutions on the board and discuss with the whole class how they solve the problem. Meanwhile, ‘item-teaching’, on the other hand, is an inappropriate form of teaching when teachers use the actual test items in classroom activities or modified versions of test items to improve students’ scores in high-stakes tests. Because it “eviscerates the validity of [tests],” Popham finds “item-teaching…reprehensible [and] should be stopped” as it fundamentally ignores the essential (and ethical) purpose of teaching and testing (Popham, 2001, p. 17). This ‘item-teaching’, which must not be the intention behind the practice of ‘teaching to the tests’ is, as Popham (2001) argues, a consequence of the immense pressure of high-stakes testing in today’s schools, thereby limiting teachers to provide the instruction that really helps students acquire mastery of content and skills. Schweisfurth (2013) also argues that high-stakes tests are a major debilitating factor in implementing learner-centered practices in the classroom. As teachers are held accountable for test scores, they are placed under great pressure to cover as much content as possible.

Race to cover content

In my interviews with Mrs. Francia and other urban teachers, it appears that much of their pedagogical decisions gravitate towards a strong orientation to cover content. With such orientation comes the notion that ‘more is better’ given that it is in this wide range of curriculum content that their students are tested. As stakes are high on student exams in this urban school, so too is the pressure placed on its teachers to cover the prescribed content within limited time. Such pressure is evident in this response by Mrs. Francia to my question about her practice of

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learner-centered strategies (e.g. cooperative learning) in her class, “What will happen to us then when the Division Office gives the exams? …The worst thing is having too little time to teach all the maths concepts they need to learn”. This response suggests that Mrs. Francia holds herself accountable for her students’ test scores. Mrs. Francia’s sense of accountability could have been influenced by the Division Office’s expectations from its teachers to deliver the desired student outcomes. The proximity of the Division Office to this urban high school (approximately just two kilometers away) could have placed additional pressure on Mrs. Francia, considering that anytime, a district supervisor or the division schools superintendent may pop-in for an informal observation or a school visit.

As Mrs. Francia upholds her accountability to her students’ test scores, her allegiance to content becomes a priority. Weimer (2002) contends that “a strong allegiance to content blocks the road to more learner-centered teaching” (p. 46). A strong allegiance to content often leads to an intense preoccupation with ‘teaching to the tests’, which then places students at the risk of equating ‘learning’ to mere test scores and grades. This superficial conceptualisation of ‘learning’ occurs within a schooling system where students are trained for rote and surface learning, regurgitating exactly what was given in lectures and practised in drills. Instead of focusing on covering large amount of content material, Weimer (2002) argues that attention must be given to ‘uncovering’ the content material by selecting the most appropriate and relevant topics students actually need for lifelong learning.

Teacher accountability, prompted by this strong allegiance to prescribed curriculum content arguably induces mere compliance to curriculum policies, resulting in the practice of teacher-centered methods that not only curb students’ learning and creativity but also restrict relationships in the classroom (Weimer, 2002). Most importantly, teacher accountability distracts teachers from a true sense of responsibility to care for the best interest of their students (Noddings, 2013). Such notions however are challenged by Mrs. Francia, in the sense that while her teaching practices are mostly ‘teacher-centered’, these are in fact perceived as ‘caring and good teaching practices’ by her students. It is also important to note that Mrs. Francia is also identified by the students as the one whom they have the strongest relationship with among all their teachers in this urban school.

Fostering caring student-teacher relationships in the classroom

A caring relationship between Mrs. Francia and the students is consistently evident throughout my three weeks of observation in this urban school. While I observe Mrs. Francia’s instructional

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methods lean heavily towards teacher-centered teaching, it is difficult to dismiss her strong practice of establishing caring student-teacher relationships. In my interviews with Mrs. Francia there are long narratives on ‘creating positive relationships with students’ and ‘prioritising their needs as learners’, which she perceives as the most important and the main priority in ‘good teaching’. This incident on my second week of observation in Mrs. Francia’s class demonstrates her positive relationship with her students.

On a Friday, when it was the day to check the students’ answers from a drill, Mrs. Francia asks one student, Toto, to show his solution on the board. While Toto is at the board, he gets stuck at one point and looks at Mrs. Francia to signal to her that he is not sure how to proceed. “You can do it,” Mrs. Francia encourages Toto. He continues working on the problem on the board, but his solution gets off track. He looks at Mrs. Francia again. Understanding that Toto needs help, Mrs. Francia came over and gave Toto some pointers to find the correct solution. The class was cheering for Toto while his friends in the back row are calling out, “You can do it, To! We are just

In document OIML R 46-1 / R 46-2:2012 (página 46-50)