Teachers – Summative and Formative Assessment in Mathematics – What Are the Differences?

I’m a big fan of using definitions as a starting point for thinking about a topic…so let’s look at a definition of assessment from the National Council of Teachers of Mathematics (1995):

Assessment is…the process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward, mathematics and of making inferences from that evidence for a variety of purposes (p. 3).  

Depending on your age, this definition may describe the experience you had with assessment in mathematics during your school career, but for most readers, “testing” was really the only kind of “assessment” we knew. Like clockwork, at the end of every few sections of the math book, there would be a quiz (for a GRADE) and at the end of every chapter, there would be a TEST (for a MAJOR GRADE). Then, no matter what grades any of us received, we would go off to the next chapter, where the cycle began again.This type of testing (of which there are many varieties) is known in today’s parlance as “summative assessment,” defined as

“a culminating assessment, which gives information on student’s mastery of content” (Association for Supervision and Curriculum Development, 1996, p. 60).

The principal characteristics of summative assessment are that it:

1) occurs at the conclusion of a learning activity,

2) is to make a final judgment,

3) may compare students to other students, and

4) often results in a grade or some other ‘mark.’

In contrast, the principal characteristics of formative assessment include that it

  • occurs during learning activities/experiences,
  • is for the purpose of improving the learning, and
  • will inform the teacher so that s/he can make adjustments if needed.

A useful definition of formative assessment is

“assessment which provides feedback to the teacher for the purpose of improving instruction” (ASCD, 1996, p. 59).

This concept of assessment meshes nicely with the NCTM definition shown above (i.e., “the process of gathering evidence about a student’s knowledge of, ability to use, and disposition toward, mathematics and of making inferences from that evidence for a variety of purposes”). Formative assessment – with or without that name – has always been around – depending on individual teacher’s attitudes towards this.  For the teacher who believes, as Grant Wiggins does, that “Good teaching is inseparable from good assessing,” there has always been an ongoing cycle of teaching, assessment, of the teaching, reteaching (as necessary), assessment, teaching, and so on. “Assessment should serve as the essential link among curriculum, teaching, and learning” (Wilcox & Zielinkski, 1997, p. 223).

So, the next time you hear others talking about assessment, ask if they are referring to formative or summative assessment. That will help you know what questions to ask next.

A Young Teacher’s Guide To Homework In Mathematics In High School

Most of what appears below was the advice that I wrote for teachers who taught Mathematics in my department when I was its head. It appeared in my department’s handbook.

Homework was an accepted part of what we did as Mathematics teachers for all classes except those with special needs students.

How And When To Set Homework

• It should be set daily or after each lesson.

• Write the assigned homework on the board.

• Ensure the students write it in their school diaries at the end of the lesson. In junior classes, you may stand at the door checking the homework is written in their diary as they leave.

• Discuss how long the work should take and any necessary advice.

• Lastly, early in the school year, teach your students how to use their textbook to help them do their homework.

What Homework Should You Set?

For students to achieve their full potential in Mathematics at high school, homework must be done on a regular basis. Homework, based on current class work, is meant to be an extension of the lesson and is needed for the re-enforcement of concepts.

In high schools, homework in Mathematics may consist of:

• Written exercises set for practice of skills and concepts. These are based on classwork.

• Learning work, e.g. rules, vocabulary and theorems.

• Assessment tasks – these usually count towards Semester reports.

What About Students Who Don’t Do Their Homework?

Teachers should record in their diaries the names of defaulters. Parents must be advised when a pattern of missing homework becomes evident.

Teachers should develop a process for dealing with homework defaulters.

What If Students Can’t Do Their Homework?

As most homework is based on the work done in class that day, this is not usually a problem for most students. However, if a student has difficulty in beginning homework, teach these strategies:

• The student should look for a similar problem in the work done in class. This is usually all that is needed to jog the memory.

• The student should look for an example in the textbook prior to the exercise. Each different type is usually done in full with an explanation.

• If students still have difficulty, they should see their teacher the next day BEFORE CLASS and arrange a time for individual help. Most teachers are available for a “homework help” time at lunch time or before and after school. Your teacher will tell you when he/she is available.

What If A Student Tells His/Her Parents That They Never Have Homework?

Often, there are complaints from parents who tell us that their students never have homework. This is clearly not the case! If a student has no written homework, (which is unlikely) then we would suggest that the parents set one of the following to be done:

• Ask the student to write a summary of the rules for the current unit and to work an example of each type of problem. The textbook will be useful here. Look for chapter summaries.

• Look at the student’s exercise book and find an exercise that caused difficulty. Set this exercise to be done.

• In each textbook, there are chapters on basic skills. Students can do any of the exercises from this chapter.

• Often there are chapter reviews and practice tests. These can be done.

The Review Process

Homework should, wherever possible, be reviewed during the next lesson for the greatest impact on learning to occur. This learning may, in fact, be the basis of the next lesson. A full description of a review practice can be found in the Article “Reviewing Homework in High School Classes” to be found on this website.

Even though there is a continuing debate as to the merits of homework, the advice here will help the young Mathematics teacher deal with homework successfully.

How to Solve Problems in the Mathematics Education Using Calculators

Mathematics is a very important element in the development of the value and standard of the life of the individual and society. Mathematics enters in everything from science, technology and engineering to arts and social sciences to economics and decision making.

It is very important that society constantly produces new generations of well trained mathematicians. This means that the school should increase the student's interest and develop his skills in the subject. To achieve this goal the school should see the reasons why students fear mathematics and why many students do very poorly in the subject.

The fist reason for the difficulty of the subject for students is that mathematics is abstract. It is not tangible they can not hold it. To make them understand a pure concept at this early stage is very difficult. They need to relate it to real life problems that they face in their daily lives. This way they will be stimulated by its importance for them and will see that it is useful and fun. Moreover, the use laboratory experiments using calculators would make concepts more understandable. There are many new innovative software calculators built just for this purpose.

The conventional system of teaching mathematics contributes significantly to the poor performance of students. This is because many teachers teach students how to implement algorithms without teaching them the idea behind the algorithms and there is no stress on the understanding of the concepts. This causes the interest level in the subject to decline and soon students develop a disassociation with the subject. To solve this problem the schools can create a mathematics society and a forum where students can communicate with each other discussing material and asking each other questions. This kind of social behavior may increase the student's interest in the subject.

Students pass early mathematics classes and they are not really fit in the subject. This is because the exams and grading did not reflect the student's true ability. This causes the students to have very big problems in senior mathematics classes which are dependent on the early classes. For example if we look at the early pupil stage we can imagine a pupil who does not understand the concept of divide and multiply. That is to say when should he divide and when should he multiply. Now can this pupil at a later stage know to solve a word problem? The answer is surely no. He will not know what we are talking about. We can also imagine a student who does not understand the concept of the algebraic equations. This student could not be asked to plot a graph because simply he will not have an idea about what we are speaking about. The teachers can use calculators to teach pupils the concepts of multiply and divide. They can let them experiment on their own with many numbers using the calculators. From the observations the pupils will understand the concepts of multiply and divide. Moreover, teachers could use calculators to teach students the concepts of functions and graphing. It is easy and fun using calculators.

Finally, those who are teaching mathematics may have sufficient knowledge in the subject. They usually have a mathematics degree but this is not enough. To be a teacher you certainly got to be strong in the subject but this is only one major factor in being a successful teacher. The teacher should know about education and student psychology. he should also have a strong personality and be a good leader.

20 Tips And Tricks To Teach Mathematics At The Primary Level

The primary Math education is a key determinant and I must say the very foundation of the computational and analytical abilities a student requires for a strong secondary education. It is the very base on which secondary education is built on. This is why it is mandatory that the teaching techniques and methods we employ as teachers and educators be of such rich quality that the development of a child with respect to his mathematical abilities be wholesome, practical and balanced.

Being a Math teacher is not easy. It is usually the favourite of a few and the nemesis of many. It has been observed that children mostly try to escape doing Math work. While there is a section of students who absolutely love mathematics enough to pursue a career in it, many students live in fear of it. Today we are going to give our teachers some helpful tips and tricks to make teaching math an enjoyable and interesting experience not only for the kids.

20 Tips and Tricks to Teach Mathematics at the Primary Level

  1. Ambience plays a very significant role. It is your responsibility to see that a classroom is properly ventilated with ambient light.
  2. Ensure that Mathematics class is neither before lunch break (when children concentrate more on the Tiffin than studies) nor the last period where students wait more for the bell to ring (not to mention start feeling sleepy!) Keep Math class when the children are active and fresh.
  3. Cultivate the students’ interest in Mathematics by letting them know about the power, structure and scope of the subject.
  4. Hold the students’ attentions from the get go! Introduce the topics with some fun facts, figures or interesting trivia
  5. Chalk out the lesson plan effectively keeping time and content allotment in mind
  6. Use audio and visual aids wherever possible
  7. Draw on the board if required (especially, lessons like geometry, shapes and symmetry)
  8. Call students to work on the blackboard (engagement of every child is necessary and not just a select few!)
  9. Ask for a student’s opinions and thoughts on concepts and mathematical ideas.
  10. Give them time to discuss important concepts and study the text of the chapter too before taking on the problems themselves.
  11. Teach more than one way or approach to solve a problem.
  12. Give regular homework exercises making sure that the questions are a mixed batch of easy, medium and difficult) Children should not feel hopeless. Easy problem questions evoke interest.
  13. Reward them! Whenever students perform well, be generous and offer them an incentive to continue working harder.
  14. Let children enjoy Mathematics and not fear it.
  15. Instill in them the practice to do mental math.
  16. Also, never give a lot of homework. Children are already burdened with assignments to work at home in almost all school subjects, it is thus your duty to make sure that the homework you delegate to them is fair sized or little. (This trick will inculcate in them the motivation to complete math homework first)
  17. Present challenging questions to students so as to develop their analytical and deduction abilities
  18. Keep taking regular tests to cement knowledge.
  19. Teach at a consistent pace. Do not rush with any topic. Before proceeding, be confident that the students are clear with the prior topics.
  20. Play games to create a fun filled classroom teach and learning experience.