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MATH TEACHING
A- Strategies for Motivating Students in
Mathematics
B- Math Teaching Strategies
A- Strategies for Motivating Students in
Mathematics
Motivating students to be enthusiastically receptive is one of
the most important aspects of mathematics instruction and a
critical aspect of any curriculum. Effective teachers focus
attention on the less interested students as well as the
motivated ones. Here are nine techniques—based on intrinsic and
extrinsic motivation—that can be used to motivate secondary
school students in mathematics

EXTRINSIC AND INTRINSIC MOTIVATION
Extrinsic motivation involves rewards that occur outside the
learner’s control. These may include token economic rewards for
good performance, peer acceptance of good performance,
avoidance of “punishment” by performing well, praise for good
work, and so on.
However, many students demonstrate intrinsic motivation in their
desire to understand a topic or concept (task-related), to
outperform others (ego-related), or to impress others (socialrelated).
The last goal straddles the fence between intrinsic and
extrinsic.
With these basic concepts in mind, there are specific techniques
that might be expanded, embellished, and adapted to the
teacher’s personality and, above all, made appropriate for the
learner’s level of ability and environment. The strategies are the
important parts to remember—examples are provided merely to
help understand the techniques.

STRATEGIES FOR INCREASING STUDENT MOTIVATION IN
MATH
1. Call attention to a void in students’ knowledge: Revealing to
students a gap in their understanding capitalizes on their desire to learn
more. For instance, you may present a few simple exercises involving
familiar situations, followed by exercises involving unfamiliar situations
on the same topic. The more dramatically you reveal the gap in
understanding, the more effective the motivation.

2. Show a sequential achievement: Closely related to the preceding technique
is having students appreciate a logical sequence of concepts. This differs from
the previous method in that it depends on students’ desire to increase, not
complete, their knowledge. One example of a sequential process is how special
quadrilaterals lead from one to another, from the point of view of their
properties
3. Discover a pattern: Setting up a contrived situation that leads students to
discover a pattern can often be quite motivating, as they take pleasure in
finding and then owning an idea. An example could be adding the numbers from 1
to 100. Rather than adding the numbers in sequence, students add the first and
last (1 + 100 = 101), and then the second and next-to-last (2 + 99 = 101), and so
on. Then all they have to do to get the required sum is solve 50 × 101 = 5,050.
The exercise will give students an enlightening experience with a truly lasting
effect. There are patterns that can be motivating, especially if they are
discovered by the student—of course, being guided by the teacher.

4. Present a challenge: When students are challenged intellectually, they react with
enthusiasm. Great care must be taken in selecting the challenge. The problem (if
that is the type of challenge) must definitely lead into the lesson and be within
reach of the students’ abilities. Care should be taken so that the challenge does
not detract from the lesson but in fact leads to it.
5. Entice the class with a “gee whiz” mathematical result: There are many
examples in the mathematics realm that are often counterintuitive. These ideas by
their very nature can be motivating. For example, to motivate basic belief in
probability, a very effective motivation is a class discussion of the famous birthday
problem, which gives the unexpectedly high probability of birthday matches in
relatively small groups. Its amazing—even unbelievable—result will leave the class in
awe.

6. Indicate the usefulness of a topic: Introduce a practical application of genuine
interest to the class at the beginning of a lesson. For example, in high school
geometry, a student could be asked to find the diameter of a plate where all the
information he or she has is a section of the plate that is smaller than a semicircle.
The applications chosen should be brief and uncomplicated to motivate the lesson
rather than detract from it.
7. Use recreational mathematics: Recreational motivation involves puzzles,
games, paradoxes, or the school building or other nearby structures. In addition to
being selected for their specific motivational gain, these devices must be brief and
simple. An effective execution of this technique will allow students to complete the
recreation without much effort. Once again, the fun that these recreational
examples generate should be carefully handled, so as not to detract from the
ensuing lesson.

8. Tell a pertinent story: A story of a historical event (for example, the story of
how Carl Friedrich Gauss added the numbers from 1 to 100 within one minute when
he was a 10-year-old in 1787) or a contrived situation can motivate students.
Teachers should not rush while telling the story—a hurried presentation minimizes
the potential motivation of the strategy.
9. Get students actively involved in justifying mathematical curiosities: One of the
more effective techniques for motivating students is to ask them to justify one of
many pertinent mathematical curiosities, like the fact that when the sum of the
digits of a number is divisible by 9, the original number is also divisible by 9. The
students should be familiar and comfortable with the mathematical curiosity
before you challenge them to defend it.
Teachers of mathematics must understand the basic motives already present in
their learners. The teacher can then play on these motivations to maximize
engagement and enhance the effectiveness of the teaching process. Exploiting
student motivations and affinities can lead to the development of artificial
mathematical problems and situations. But if such methods generate genuine
interest in a topic, the techniques are eminently fair and desirable.

Math Teaching Strategies
1-Interacting with Peers
Peer interactions can greatly benefit a student's understanding of mathematical
concepts. To facilitate peer collaboration based on differentiated needs, teachers
should pair students carefully, model effective ways to interact, provide students
with relevant tools, and offer specific advice. Struggling students may find it
especially helpful to interact with peers who can provide explanations, clarify a
process, and ask and answer questions. This give and take involves listening,
speaking, writing, creating visual representations, and using virtual and physical
manipulatives.
Interactıng Wıth Peers - Teach Wıth Tech Exploring math together -
discussing, reading, and writing about concepts - can build your students’
mathematical understanding. However, your students need your help to learn how to
use their peers as resources, as well as how to be a useful resource for their peers.
The strategies given here provide a strong starting point for differentiating
instruction. Consider using digital communication methods such as blogs, emails, and
text messages.

2-Math Language
In math, students must build a shared understanding of mathematical terms to
successfully share and refine their ideas. This can be challenging, because students
must learn new words and symbols that are unique to math, as well as precise new
meanings for words they are already familiar with. All students can benefit from
differentiated instruction when learning terms and symbols. Struggling students
may need more support and practice to gain confidence in their use of language.
Math Language - Teach With Tech Math requires students to understand new
terminology because common words and phrases can have math-specific meanings.
Many words (such as “plus” and “equals”) are so common and important that we use
symbols rather than words. Teaching precise mathematical language will help your
students to think more carefully about their ideas and the ideas of their peers.
The strategies below provide a strong foundation for differentiating instruction.

3-Modeling
Models help promote mathematical thinking and facilitate an understanding of key
concepts and mathematical structures. By seeing and moving objects, students
engage their senses to better understand and reason with abstract concepts, or to
make sense of and solve problems. Teachers can support students who struggle
with abstraction by differentiating instruction using models. Virtual models provide
a different sensory experience, which can be helpful for students who have
difficulty with physical objects.
Modeling - Teach with Tech Struggling students may miss the important step of
connecting the physical model to the more general, abstract concept. Some
students may also have difficulty translating from the problem to the model and
back again to provide an answer. Implementing the strategies below can help you
differentiate instruction.

4-Organizing
Finding and understanding patterns is crucial to mathematical thinking and problem
solving. It is easier for students to understand patterns when they organize their
information. Struggling students may find it helpful to organize information in a
problem because it requires a student to think more deeply about each piece of
information and how those pieces fit together. Technology can significantly
enhance organizational tools and provide support to students.
Organizing - Teach With Tech Creating an organized list, table, chart, or other
graphic organizer is an important problem-solving strategy Organizing information
will help your students to see patterns and learn mathematical concepts more
easily. Organizing will also give your students a structure to help them think about
what they do and don’t know about a problem. The strategies below provide a
strong starting point for differentiating instruction.

5-Supporting Science
Mathematics helps us to understand science and to design, conduct, and analyze the
results of scientific experiments. Science requires us to collect data, interpret it
for significant patterns, and make conclusions that further our knowledge. To
collect and analyze data, students must be able to apply mathematical content and
practices. This includes selecting appropriate tools, using those tools to model the
data by describing it mathematically, and reasoning both quantitatively (to
understand the data itself) and abstractly (to draw conclusions).
Supporting Science - Teach With Tech Students—especially those who
struggle with mathematics—need varied and ongoing support to develop the ability
to apply their mathematical abilities to science. Here are some ways to provide this
support.

6-Thinking Aloud
When students verbalize what they know, it helps them to reflect upon and clarify
the problem and focus on one step at a time. “Thinking aloud” requires talking
through the details, decisions, and the reasoning behind those decisions. Struggling
students, in particular, can benefit from slowing down the process, because it gives
them time to fully comprehend the problem. Technology can help create problems
with natural stopping points that allow students to practice this “thinking aloud”
strategy—that is, to experiment, consider, and then decide their next steps.
Thinking Aloud - Teach with Tech Thinking aloud helps your students learn how
to reason by focusing on their thinking Most students are not used to answering
questions that require more than a single-word or short-phrase response. Many
don’t know how to talk about mathematics or explain their thinking. These
strategies provide a strong starting point for differentiating instruction.
7-Understanding Problems
For many students, mathematics word problems are just a jumble of words and
numbers. A problem-solving process can help students make sense of problems.
They can do this by reading the problem more than once, annotating words and
numbers, visualizing the situation, converting visualizations into diagrams or
mathematical expressions, and assessing the reasonableness of their solutions. All
students need to apply problem solving to more and more complex situations as
they move forward in their mathematical learning.
Understanding Problems - Teach With Tech Learning how to solve word
problems requires students to understand the context and then develop a strategy
to solve the problem. Students build on their ability to organize, create visual
representations, and use precise language. You can help your students build on
these skills and understand how to use them in specific situations

8-Visual Representations
All students can benefit from using visual representations, although struggling
students may require extra support and practice. Visual representations are a
powerful way for students to access abstract math ideas. Drawing a situation,
graphing lists of data, or placing numbers on a number line all help to make abstract
concepts more concrete, whether done online or offline. Developing this strategy
early will give students tools and ways of thinking that they can use as they
advance in their learning of more abstract concepts.
Visual Representations - Teach With Tech Choosing the “right” visual
representation often depends on content and context. In some contexts, there are
multiple ways to represent the same idea. Your students need to view a variety of
visual representations (see UDL Checkpoint 2.5: Illustrate through multiple media)
in order to learn when and why they should choose each one. As you plan how to
provide differentiated support and practice, consider ways technology tools can
support the development of this critical practice.

Isparta Gazi Social Sciences High School TÜRKİYE
Profılırana Gımnazıa Hrısto Botev
BULGARIA
Zespol Szkol Ogolnoksztalcacych nr 3 w Katowicach POLAND
Lıceul Teoretıc Mırcea Elıade
ROMANIA
Stredna Odborna Skola Polnohospodarstva A Sluzieb Na
Vidieku SLOVAKIA
Centre Educatıu Balaguer
SPAIN