Jesuit Education and Science in the Spanish Imperial Context, 1859-1898: a talk by Dr. Aitor Anduaga of University of the Basque Country

The Institute of Philippine Culture (IPC)
School of Social Sciences
cordially invites you to a lecture on

Jesuit Education and Science in the Spanish Imperial Context, 1859-1898

by

Dr. Aitor Anduaga
University of the Basque Country Leioa, Spain
Visiting Research Associate, IPC

on

February 13, 2012 (Monday)
4:30 to 6:00pm
IPC Conference Room
Rm 203, Frank Lynch Hall
Social Development Complex

*Please call local 4651 or e-mail ipc@admu.edu.ph for inquiries.

Abstract

Although the Royal Decree of 1852 by the Spanish Queen Isabel II  assigned to the Jesuits a strictly missionary function (i.e., to  evangelize the pagan tribes of Mindanao and Jolo), activities soon  extended to education and science. The history of this development is  well known. In 1859, Jesuits took charge of the ?Escuela Municipal.  In 1865, they extended primary education to the secondary one, and  turned the Escuela into a private school, the Ateneo Municipal de  Manila?. That year, they found the Meteorological Observatory as an  auxiliary centre for teaching. Twenty years later, it became the most   important geophysical Observatory in the Far East.

Many historians have placed those achievements within the framework of apostolic spirituality. The ideological structure of the Society of  Jesus would house a spirituality at its core whose values of  diligence, learning, etc. would explain the legitimacy of this study  of empirical sciences. Reality, however, is much more complex. In this  lecture, we shall examine the institutional (not the ideological)  structure of the Society in the educational field, and the influence  that it exerted on the promotion of science. We shall also see that
there was strong interaction between religious and socioeconomic  factors that help to understand those achievements. Last but not  least, the Jesuit experiences in the Spanish dominions of Cuba and  Puerto Rico will help us to better understand the Philippine reality.

Understanding by design 3: Designing Physics Instruction

Mariett L. Bergantin

Understanding by Design Part 1
Understanding by Design Part 2

After deciding on the desired results and identifying the student’s preconceptions through the different types of assessment, the next challenge is to design and implement appropriate instruction modes. This is the third stage of the backward design process and involves planning learning activities and experiences. Traditionally, teachers consider this stage first when designing the course work. The UBD framework however, considers this the last stage after the desired results have been known and acceptable evidence was determined on how well the results have been achieved.

The acronym WHERE suggests guidelines that can be used in planning instruction that would match the desired results (Wiggins and McTighe 1998)

• W- Where is the unit headed and what is the purpose of day to day work?
• H- Hook the students through engaging work that makes them more eager to explore key Ideas
• E- Explore the subject in depth, equip students with required knowledge and skill to perform successfully on final tasks, and help students experience key ideas
• R- Rethink with students the big ideas; students rehearse and revise their work
• E- Evaluate results and develop action plans through self- assessment of results

Applying WHERE criteria in physics classroom, the lesson usually starts on posting the essential questions. This will guide students on what they are expected to answer at the end of the lesson. The teacher also focuses on the BIG ideas to which instruction and experiences are based. Physics teachers are then encouraged to move away from the “recipe style” experiment to semi structured lab and interactive demonstration activities. Experiments in traditional physics instruction are done through observation of the prepared set-up and students answer the question. In the new framework, experiments are carried out in a way that students framed the procedures by giving them materials and objectives and identifying the concepts/ideas underlying the experiments. Student then present the lesson at hand. This is discovery learning. Several approaches have been found to have a positive impact on physics instruction. Among these are : ICT integration, problem-based learning, project-based learning, and differentiated instruction. More on these approaches will be discussed in subsequent articles The different learning experiences can increase student’s participation and interest. Providing enrichment activities could help students to explore the subject in depth and thus encourage then to engage in research. This is usually part of their assignment or homework. Ongoing assessment on student’s performance through different modes of assessment could help the teachers differentiate instruction..

The conventional way of teaching is to put across the content of textbooks, make quarterly exams after instruction in accordance to the Learning Competencies of DepEd and come up with a yearly evaluation of the targets/learning outcomes. This is in contrast with the principles suggested by UbD framework. According to Wiggins and McTighe, textbook-based instruction focuses too much on facts accumulation and knowledge taught—sacrificing understanding and learning in the process.

While UBD emphasized the backward design it doesn’t mean that process should always starts from results going to activities. The three stages enumerated in this section can be used interchangeably provided the activities should match the identified learning goals. After all, the whole design of the curriculum is accentuated by a comprehensive and unified plan that emphasized on the Big idea.

The most important part of the backward process is the first stage where one decides on the desired learning outcome. This is the essence of the backward design; to start with the end.

The success of the UBD framework does not lie solely on the teacher’s choice of instruction and assessment but also on the administrators as well. Time and facilitation are some of the major issues encountered in UBD implementation which started two years ago. In 2013, the UBD framework will be implemented in the fourth year level secondary physics courses.

Imperfections in image formation: astigmatism, coma, and distortion

by Quirino Sugon Jr.

There are several imperfections or aberrations if you use lenses to form images:

1.  Astigmatism

An optical system with astigmatism is one where rays that propagate in two perpendicular planes have different foci. If an optical system with astigmatism is used to form an image of a cross, the vertical and horizontal lines will be in sharp focus at two different distances. The term comes from the Greek α- (a-) meaning “without” and στίγμα (stigma), “a mark, spot, puncture”. (Read more in Wikipedia)

2.  Coma

Coma is an inherent property of telescopes using parabolic mirrors. Light from a point source (such as a star) in the center of the field is perfectly focused at the focal point of the mirror (unlike a spherical mirror, where light from the outer part of the mirror focuses closer to the mirror than light from the center–spherical aberration). However, when the light source is off-center (off-axis), the different parts of the mirror do not reflect the light to the same point. This results in a point of light that is not in the center of the field looking wedge-shaped. The further off-axis, the worse this effect is. This causes stars to appear to have a cometary coma, hence the name. (Read more in Wikipedia)

3.  Distortion

Distortion can be thought of as stretching the image non-uniformly, or, equivalently, as a variation in magnification across the field. While “distortion” can include arbitrary deformation of an image, the most pronounced modes of distortion produced by conventional imaging optics is “barrel distortion”, in which the center of the image is magnified more than the perimeter (figure 7a). The reverse, in which the perimeter is magnified more than the center, is known as “pincushion distortion” (figure 7b). (Read more in Wikipedia)

Essay questions on light scattering

by Quirino Sugon Jr.

1.  Why is the sky blue?  

The atmosphere around the Earth is largely made up of two colorless gases: oxygen and nitrogen. Red and blue light reacts very different from each other to oxygen. Because the wavelength of blue light is roughly the size of an atom of oxygen, blue light interacts with the oxygen and is scattered by it, while red light, with its longer wavelength, goes right pass the oxygen atoms. If the Earth had no atmosphere, the sun’s light would travel directly from the Sun in a straight line towards our eyes and we would see the Sun as a very bright star in sea of blackness. But because the Sun’s blue light is scattered by the oxygen in the atmosphere, blue light from the Sun enters our eyes from all sorts of different angles and we see the entire sky as blue. The atmosphere scatters violet light even more effectively, but our eyes are more sensitive to blue. Wherever we look towards the sky, some light is bouncing off an oxygen atom and entering our eyes, making the sky appear to be blue. (Skywatch)

2.  Why are sunrises and sunsets red?

Read the same article in Question 1.

3.  Why is the sea blue?

Visible white light is made up of a spectrum of all the colors-red, orange, yellow, green, blue, indigo, and violet. When we look at an object and see it as blue, we are seeing the blue light of the spectrum reflected from the object. All other colors are absorbed and cannot be seen. In the case of the sea, red light is absorbed as soon as it breaks through the water’s surface. And by a depth of about 25 feet virtually all the red light discernible to the human eye is gone; a bright red air tank on a diver, for example, would seem a dull dark brown. At a depth of 75 feet a yellow air tank looks more greenish blue, because the discernable yellow light has been absorbed by the water. The still shorter rays of light are almost all absorbed by 100 feet. All that remains are the shortest rays: blue, indigo, and violet. Below 100 feet or so, all light appears a monochromatic blue. So, when the sea is pure and clear, as often is the case in the open ocean, the least-absorbed shade of the spectrum blue, is reflected to our eyes. (marine-surveyor)

4.  Why is the sea sometimes bluish green or brown or even red?

Read the same reference in Question 3.

5.  How do rainbows form?

Read the Wikipedia article on rainbow.  What causes the dispersion of light?  What must be the angle formed by the sun, the water droplet, and the eye of the beholder? What is the Alexander’s band?  What does Newton have to do with rainbows? Why do you think rainbows formed after the Great Flood of Noah?

Problems for electricity and magnetism

by Quirino Sugon Jr.

1. An electron is under a 2T magnetic field pointing out of the paper and the electron has a speed of one-tenth the speed of light and is initially moving towards the right.  What is the magnitude and direction of the  magnetic force on the electron?  What will be the orbital radius of the electron?  Is it clockwise or counterclockwise?
2. In a Hydrogen atom, what is the ratio between the electric force and the gravitational force on the electron due to the proton?
3. Prove  the rules for equivalent resistance of two resistors connected in series and parallel using Kirchoff’s voltage law.  Hint: resistors in series requires only a single loop; the resistors in parallel requires two loops.
4. Three charges are connected in 30-60-90 degree triangle with the longest side equal to 1 m.  The charge on the right angle is 1 C, the charge on the 60 deg angle is 2 C, and the charge on the 30 deg angle is 3 C.  What is the net electric force on the 2C charge? Hint: use Coulomb’s law.

Essay questions for electricity and magnetism

by Quirino Sugon Jr.

1. Why do auroras or northern lights occur? Hint: magnetic force on charges
2. Why are the wires of plugs tied together? Hint: Ampere’s law.
3. Why is iron attracted to magnets? Hint: magnetic domains.
4. How does a metal detector work? Hint: magnetic induction and eddy currents.
5. How do some birds and fishes know where the North Pole is?
6. Compare and contrast electric and magnetic forces.
7. State Gauss’s Law
8. State Ampere’s Law
9. State Faraday’s Law

Understanding by Design II: Construction of suitable assessment method

Mariett L. Bergantin

In the first part of this article, we presented the Understanding By Design (UBD) teaching framework. The three steps comprising the framework were enumerated and the first step, dealing with setting learning objectives or outcomes, was discussed.

How does the teacher know if the desired learning outcome in the first step has been met by the students? What are the accepted evidences that these outcomes have indeed been achieved? These questions are addressed in the second part of the UBD backward design process.

The second part of the backward design process is designing the assessment. It is argued that that several types of assessment are essential in proving true understanding [1]. According to learning theories, students learn when they can “apply” their learning to new situation or real life problems. In assessing the performance of students, the teacher has to take this into account as well as the suitability of the chosen assessment to the established learning goal.

There are three methods of assessment associated with the UBD framework: Performance tasks, in which student are given real world challenges or the performance of tasks or activities; criteria referenced assessment such as quizzes, tests and prompts, which provide feedback on how well the material has been assimilated to both teacher and students; and unprompted assessment such as classroom observation and journals.

As an example, let us briefly examine projectile motion in the context of performance tasks. Projectile Motion is commonly demonstrated using an object thrown on a moving carrier or an object projected at an angle with respect to the horizontal. As a basis for understanding, students are expected to solve, for example, the time of flight, horizontal distance, the vertical and horizontal component of the projection velocity. Learning can be extended by using these quantities in describing or explaining real life problems.

Scientific learning in projectile motion is done usually using interactive simulation from Phet [2] or a laboratory experiment. After about a week, an assessment, usually comprised of quizzes long test, is performed. UBD stresses that these are not sufficient for students to achieve the required target. Instead, student centered activities are encouraged rather than teacher initiated activities such as demonstrations. Modifications can be made from the old laboratory experiments to make assessment more successful. An example would be to ask students to assemble a golf ball launcher that will produce maximum range. Aside from the student effort, the teacher can gauge if students have prior knowledge on the project rather than giving them the needed materials and measuring the time of flight and distance traveled by the ball. Knowing something is different from understanding the context. This is the essence of the assessment.

To conclude this second part of the UBD framework, we note that a practical advantage of UBD is that tasks are authentic and transparent. In constructing performance tasks scenarios, the GRASPS acronym [3] (goal, role, audience, situation, product or performance, standards for success) can be used in order to maximize the authenticity of assigned tasks. The success of performance tasks is rated through rubrics. Effective rubrics provide criteria that discriminate the different degrees of based on the outcomes differentiating from novice to expert. The big challenge in UBD is the creation of performance tasks that are parallel to the learning objectives. Finally, observations from the application of UBD to Secondary School classes reveal that UBD requires more time compared to traditional chalk-and-talk.

In the next part of this article, we will cover the third part of the UBD framework.

REFERENCES
1. J. Mctighe, R. Thomas, Backward design for forward action. Educational Leadership. 50 (5), (2003).
2. http://phet.colorado.edu/ accessed 19 August 2011.
3. “Performance Tasks,” http://xnet.rrc.mb.ca/glenh/CourseImplementation/grasps.htm accessed 19 August 2011.

Note:
Mariett L. Bergantin obtained a Masters degree in Physics Education from the Ateneo de Manila University in 2010. Her research interests are geared towards curriculum and instruction. She is currently affiliated with the Basic Education Department, Colegio de San Juan de Letran.

Interrelated conceptual questions for electromagnetic induction: How to light a bulb by moving a magnet towards a coil of wire

Choose a word or phrase inside the parenthesis that makes the statement true.  Write your answer on the space provided before each number.

1. Draw a circle on a sheet of paper.  The normal vector to the circular area points (downward, upward),
2. so that the corresponding path direction around the circular area is (clockwise, counterclockwise).
3. Let that circle represent a wire loop.  If you hold a bar magnet vertically above the circle, with the South pole below and the North pole above, then the magnetic field flowing through the circular area points (downward, upward).
4. Since the direction of this magnetic field is (parallel, opposite) to the positive reference sense for the area’s normal vector,
5. then the magnetic field flowing through the circular area is (negative, positive).
6. This means that the flux of the magnetic field through the area, which is the dot product of the magnetic field and the area’s normal vector,  is (negative, positive).
7. If you do not move the magnet, the magnetic flux through the area will (decrease, remain constant, increase) in time,
8. and (a, no) current will be induced in the wire.
9. On the other hand, if you move the magnet upward, the magnitude of the magnetic field flowing through the circular area will (decrease, remain constant, increase) in time,
10. so that the flux of the magnetic field through the area will (decrease, remain constant, increase) in time.
11. Therefore, the change in the magnetic flux per change in time will be (negative, zero, positive).
12. According to (Ampere’s, Faraday’s) law,
13. the electromotive force along the circular wire is (same as, opposite to) the change in the magnetic flux through the circular wire.
14. This electromotive force is equal to the product of the component of the electric field along the circular path and the total length of the path which is the path’s circumference.  By convention, the path length is always (negative, positive ).
15. Thus, by the law stated in (12), the electric field must be (negative, positive) with respect to the circular path,
16. which means that the electric field must be pointing (clockwise, counterclockwise) along the circular path.
17. In the wire the free charges that can move are (electrons, protons).
18. The electric force on the free charges points (clockwise, counterclockwise).
19. By Newton’s (First, Second, Third) Law,
20. the resulting acceleration of the free charges is (clockwise, counterclockwise).
21. Without friction due to collisions with the nuclei in the wire’s molecular structure, the speed of the free charges would be (decreasing, remain constant, increasing) in time.
22. But because of friction, the free charges move at a (decreasing, constant, increasing) speed around the wire.
23. Since current is proportional to the product of the number of free charges, the charge of the free charges, and the drift velocity of the free charges, then the induced current in the wire is (negative, positive).
24. This means that induced current is flowing (clockwise, counterclockwise) around the circular wire.
25. If the wire is connected to a light bulb, the bulb (will, will not) light.
26. The stronger the induced current, the (dimmer, brighter) is the light.
27. One way to make the induced current stronger is to move the magnet (slower, faster).
28.  Now, by (Ampere’s, Faraday’s) law,
29. the induced magnetic field inside the circular loop points (into, out of) the paper,
30. while the induced magnetic field outside the circular loop points (into, out of) the paper.
31. This means that the induced magnetic field has its North pole (below, above) the circular area
32. and its South pole (below, above) the circular area.
33. Thus, since like poles (attract, repel)
34. and unlike poles (attract, repel),
35. then the original magnet and the induced magnet will attract repel.

Answers:

1. Upward.  It doesn’t matter whether you choose upward or downward because it is simply reference direction for electromagnetic quantities, but all your other answers will depend on this choice.
2. Counterclockwise.  If your answer in no. 1 is upward, put your thumb pointing out of the paper and look at the curl of your right hand fingers.  They should curl counterclockwise.  That is the path direction.  But if your answer in no. 1 is downward, then your answer in no. 2 should be clockwise.
3. Upward.  Magnetic field lines flow from the North pole to the South pole.  Since the South pole is directly above the circle in the paper, then the magnetic field lines are going towards the South pole.  This means that the magnetic field flowing through the circular loop is pointing upward.
4. Positive.  The magnetic field lines flowing through the wire loop are pointing upward according to no. 3.  Since the reference direction for the area vector is also upward by no. 1, then the magnetic field is positive with respect to the area vector.
5. Positive.  Since the magnetic field and the area vector are both pointing upward according to nos. 1 and 3, then the angle between them is 0 degrees, so that the dot product of the two vectors is positive.
6. Positive.  Since flux is defined as the dot product of the magnetic field and the area vector, then whatever your answer in no. 5 should be the same as your answer in no. 6.
7. Remain constant.  Since you do not move the magnet, the magnetic field flowing through the area will be constant, so that the flux will be constant.
8. No.  According to Faraday’s law, the electric field (which will drive the current in the wire) will only be induced in the wire if the magnetic flux is changing in time
9. Decrease.  The further you are from the magnetic pole, the lesser becomes the magnetic field strength.
10. Decrease.  If you move the magnet upward, the angle between the magnetic field and the area vector remain the same, then the magnetic flux will still be positive after moving the magnet upwards, but it is a smaller positive flux compared to what was before in no. 6.  Therefore the flux decreases.
11. Negative.  Since the flux decreases by no. 10, then the change in flux is negative.
12. Faraday’s. No. 13 is a statement of Faraday’s law.
13. Opposite.  The negative sign  in Faraday’s law means opposite.
14. Positive.  This is the convention, but you must note that the positive direction for the path is defined by no.2.
15. Positive.  The change in magnetic flux through the circular area is negative by no. 11.  Opposite or negative of no. 11 is  positive.  Since the path is positive by no. 14, then the electric field must be positive.
16.  Counterclockwise.  By no. 2, the positive direction for the path is counterclockwise.  Since the electric field is positive by no. 15, then the electric field must also point counterclockwise in the wire loop.
17. Electrons.  The electrons are free to move in a metal.  The protons are locked in the metal’s crystal lattice bonds.
18. Clockwise.  The electric field is pointing counterclockwise by no. 16.  Since the charge of electrons is negative, then the magnetic force, which is the product of the charge and electric field, must be negative counterclockwise.  That is, clockwise.
19. Second.  No. 20 is a statement of Newton’s second law of motion.
20. Clockwise.  The electric force points clockwise by no. 18.  Therefore, the charges will accelerate in the direction of the force, and that is clockwise.
21. Increasing.  Without friction in the air, a raindrop will fall faster and faster because the gravitational force is pulling them down.  In the same way, charges will move faster and faster due to the continuous pull of the electric force, as long a friction is not present.
22. Constant.  Friction causes the raindrops to fall at constant velocity called terminal velocity.  In the same way, friction causes charges to move along the wire at constant speed called drift speed (or velocity).  The motion of the charges will be clockwise by no. 20.
23. Counterclockwise.  Number of charges is always positive.  Since the charges that are moving are electrons, then their charge is negative.  Since the motion of the charges is clockwise by no. 20, then the product of these three factors–which is the current–is negative clockwise.  That is, counterclockwise.
24. Counterclockwise.  This is just a restatement of no. 23 just to know if you are awake.
25. Light.  If you connect the wire to a light bulb in such a way that a close loop is preserved, then current will flow in the bulb and it will light.
26. Brighter.  The sentence explains itself.
27. Faster.  Moving the magnet faster means making the change in the magnetic field flowing in the wire loop bigger.  If the change in the magnetic field is bigger, then the change in the magnetic flux will also be bigger, resulting to bigger currents induced in the wire.
28. Ampere’s .  Ampere’s law is for the generation of magnetic fields by currents.
29. Into.  By no. 23 or 24, the current is flowing counterclockwise.  Now, put your right hand thumb along the wire in the direction of the current.  Outside the area inside the wire loop, the curl of your right hand fingers point downward (or into the paper); inside the wire loop, the curl of your right hand fingers point upward (out of the paper).
30. Out of.   See explanation in no. 29.
31. Above.  The magnetic dipole representation of the wire loop will depend only on the magnetic field direction inside the area of the loop.  Since the direction of the magnetic field in this area points out of the paper by no. 29, then the North pole must be above the paper and the South pole below.
32. Below.  See explanation in no. 31.
33. Repel.  Like poles repel.
34. Attract.  Unlike poles attract.
35. Attract.  The original magnet has its South Pole directly above the wire loop.  The induced magnet has its North pole directly above the wire loop.  The two poles will attract.  (You can use similar analysis why a magnet will float in a superconductor, but that is another story.)

Vector addition and subtraction: component and parallelogram methods

by Quirino Sugon Jr.

The sum and difference of vectors a = (3,4) and b = (6,0)

Suppose we choose two points on the Cartesian coordinate system: and .  If we interpret these points as tips of the rays–which we shall now call as vectors–drawn from the origin at $(0,0)$, then we write down our vectors as

The sum and difference of these two vectors is given by

The parenthesis-and-comma notation for vectors is not amenable to algebraic manipulation. To solve this problem, we introduce two unit vectors (vectors of unit length) and . The unit vector points in the direction of positive axis, while points in the direction of positive axis. Using these two unit vectors, let us rewrite Eqs. (1a) and (1b) as

Hence,

It feels natural, doesn’t it?  You add only like terms: those with are added to those with ; those with are added to those with .  If you have a bag containing 3 apples and 4 oranges and another bag containing 6 apples, then putting all these in a single bag results to 9 apples and 4 oranges.  This is an interpretation of .  What do you think is the corresponding interpretation for ?

The sum and difference of vectors a and b using parallelogram method

The apples-and-oranges interpretation, though helpful, is not really precise.  The proper interpretation is geometrical.  In order to interpret and geometrically, we need to draw them together with and (see Fig. 1).  Notice that if we construct a parallelogram with as two of the parallel sides and as the other two parallel sides, then corresponds to one diagonal and corresponds to the other diagonal.

Let us write down some rules.  To draw , connect the tail of to the tip of , then draw  as the vector  from the tail of vector to the tip of .  On the other hand, to draw , connect the tails of vectors and , then draw as the vector from the tip of to the tip of .

In general, we can let the coefficients of and to be any scalar, and we can even include a new unit vector along the positive axis.  If we do this, then

so that

Equations (6a) and (6b) are the algebraic rules for vector addition and subtraction in three dimensions.  The geometrical interpretation is still the same as that for two dimensions.

10 Rules for Chalk Talks: How to give an effective lecture using chalk and blackboard

by Quirino Sugon Jr.

Chalk talk is one of the oldest way of giving lectures.   But to use this method well, you need to know ten principles:

Chalk talk: Phase angle in oscillations

1. Begin with the end in mind.  Before starting your lecture, ask yourself what is the ultimate goal of the lecture.  Is it to prove a theorem, to discuss a law, to demonstrate a phenomenon?  Write it down in one sentence.  This is your topic sentence for an hour or an hour and a half of lecture.  But if your students are not adequately prepared to handle your topic, e.g. they don’t know integral calculus but only derivatives, you may backtrack and provide introductory material–just enough for them to understand your lecture.  If your students already know the topic, junk whatever you have prepared and proceed to the next lesson.
2. Divide each 50 minute lecture into at most 5 parts. You have only 5 fingers per hand. The brain can only remember at most 7 new things using short-term memory. So do not rack up your your students’s brains by giving them more things than they can associate with their five fingers. A good exercise is to write a four to five sentence abstract of your lecture: state the problem, state what you assume your students know, explain your method, and outline your expected results, and decide on your evaluation tools.  Your evaluation tool can be as simple as getting half of your students to nod when you make a point or as tough as getting perfect in your 20-point quiz.
3. Plan your teaching strategy. There are many ways to deliver a lesson. You can start from general law or theorem and give specific examples of its applications. This is called the deductive method. Or you can start from specific examples in order to lead to the general law. This is called the inductive method. The most important thing is this: you must always start from what your students know and slowly lead them to new things they do not know.
4. Divide the blackboard into four parts. The blackboard is naturally divided into two. So divide each part further into two to give four sections. I am talking about standard blackboard sizes for a class of 50 students. As a rule of thumb, each blackboard section should be at most as far as your two arms can span and at least as far as your left shoulder to the tip of your right hand outstretched.
5. Do not talk and write at the same time. When you talk, don’t write. When you write, don’t talk. Talking is the time for resting your hands. Writing is the time for resting your throat. If you write and talk at the same time, you’ll easily get tired even after 30 minutes. Besides, you students also needs time to take notes and digest what you have said.
6. Never write with your students looking at your back. As much as possible, write with your shoulder perpendicular to the blackboard.   In this way, you can see what you are writing and you can use your peripheral vision to know what is happening in your class. Some may be raising their hands to ask a question, to request permission to go out, or to throw something at you. If you spend too much time looking at the blackboard, you may end up with half your students gone; the rest may be playing card games or taking videos. And before you know it, you are in You Tube.
7. Write from left to write. Since we read from left-to-write, write also in the blackboard from left-to-write, assuming that you are facing the blackboard. Start with the leftmost section, fill it up from top to bottom, then proceed to the next section until you reach the rightmost section. If you have filled the rightmost section, go back to the leftmost section, erase its contents, and write anew. Repeat the whole process.
8. Remember that teaching is drama.  You are an actor whether you like it or not.  The podium is your stage and your students are your audience.  Make eye contact when speaking, by shifting your gaze from left to right.  Make sure that your voice is heard even by those sitting at the back.  Vary your voice to emphasize your point.  Let your points sink in using long pauses.  Sometimes, it is helpful to ask one of your students to be the actor by asking him to graph an equation or show his solution.  Sit in one of the chairs with your students.  Observe what they are doing.  Check out the blackboard layout if it is pleasing to the eye.  Ask the student volunteer probing questions and correct his answers.  Then take your turn at the podium.
9. Use colored chalks.  A blackboard filled with white chalk is dull.  Underline the section headings with colored chalk.  Use different colors for different graphs.  Practice drawing freehand different shapes: parallel lines, perpendicular lines, rectangles, circles, and ellipses.  Then move to 3D objects like parallelpiped, cubes, pyramids, cones, and spheres.  If possible, use the opportunity to teach your students how to draw, too.  Never label the arrows or lenghts or points in your diagrams without asking your students.  The best way to teach is through dialogue and one of the best way to facilitate this dialogue is the chalk.
10. All’s well that ends well. If you still have few minutes left, give a short summary of what will happen in the next lecture. In this way, you can prevent the bad practice of dismissing the class before the bell rings.  If you are in a Catholic institution, end with a prayer–an Our Father, a Hail Mary, a Glory Be, or Angel of God.  And don’t forget the Sign of the Cross. You are not sure if you will still see your students tomorrow.  Death is always an unexpected thing.  So it is always best to prepare for a good death to go to heaven by praying before and after class.