## 8 strategies for developing student motivation in mathematics

Student motivation is one of the most important aspects of mathematics instruction and an important aspect of any curriculum. The eight motivational strategies discussed below have repeatedly proven their effectiveness, and I can honestly recommend them to my colleagues.

Extrinsic and intrinsic motivation including addition sentences for word problems
Extrinsic motivation is always based on the benefits that teachers or parents promise the student. Intrinsic motivation is always based on the student’s own desire to achieve some goal.

Strategy 1. Demonstrate failure in student knowledge Give several assignments, among which will be very simple, simple and difficult. On very simple and easy assignments, students will get a taste for the process of doing, but will stumble on the difficult ones. There may be a desire for the new knowledge needed to complete difficult assignments.

Strategy 2. Show a sequence of knowledge.
This strategy is related to the previous one. It is important to prove to students that they have the necessary basic knowledge set to easily grasp the new topic including pennies, nickels, and dimes.

Strategy 3. Suggest little tricks.
For example, if your students need to learn the multiplication table, prompt them with the following patterns:
1. When multiplied by 1, any number remains the same.
2. All examples for 5 end in 5 or 0: if the number is even, assign 0 to half the number; if it is odd, assign 5.
3. All examples for 10 end in 0 and start with the number we are multiplying by.
4. Examples by 5 are half as many as examples by 10 (10 × 5 = 50, and 5 × 5 = 25).
5. To multiply by 4, we can simply double the number twice. For example, to multiply 6 × 4, you have to double 6 twice: 6 + 6 = 12, 12 + 12 = 24.
6. To memorize multiplication by 9, write down a series of answers in a column: 09, 18, 27, 36, 45, 54, 63, 72, 81, 90. Remember the first and the last number. All the others can be reproduced by the rule: the first digit in a two-digit number increases by 1, and the second decreases by 1.

Strategy 4. Challenge the students for example about telling the time – whole hours
When children are challenged, even taken “for granted,” they light up. Just choose the task for this challenge carefully; it should be challenging, but within the students’ abilities.

Strategy 5. Offer a paradoxical challenge.
For example, when studying probability theory, talk about a paradoxical problem with birthdays. In a group of 23 or more people, the probability of at least two people’s birthdays (number and month) being the same is greater than 50%. For example, if there are 23 or more students in a class, it is more likely that some of the classmates’ birthdays will fall on the same day than that everyone will have their own unique birthday.
For 60 or more people, the probability of this coincidence exceeds 99%, although it reaches 100%, according to the Dirichlet principle, only when there are at least 367 people (exactly 1 more than the number of days in a leap year; taking into account leap years).
This statement may not seem obvious, because the probability of coincidence of birthdays of two people with any day of the year (1/365 = 0.27%), multiplied by the number of people in the group (23), gives only (1/365)×23 = 6.3%. This reasoning is incorrect because the number of possible pairs (( 23 × 22 )/2 = 253) far exceeds the number of people in the group (253 > 23). Thus, the statement is not a paradox in the strict scientific sense: there is no logical contradiction in it, and the paradox lies only in the differences between the intuitive perception of the situation by a person and the results of mathematical calculation.

Strategy 6. State the practical usefulness of the topic.
When studying interest, make up a problem about bank loans. Draw on material that the children will be familiar with: for example, a situation in which they take out an educational loan.

Strategy 7. Tell a relevant and interesting story. For example, about how Carl Friedrich Haass solved complex math problems in 1 minute when he was 10 years old.

Strategy 8. Discuss mathematical curiosities with your children.
For example, that the number 37 has many curious properties. For example, multiplied by 3 and by numbers divisible by 3 (up to and including 27), it gives products represented by a single digit:
37 × 3 = 111;
37 × 6 = 222;
37 × 9 = 333;
37 × 12 = 444;
37 × 15 = 555;
37 × 18 = 666;
37 × 21 = 777;
37 × 24 = 888;
37 × 27 = 999.

Math teachers need to understand the underlying motivations already present in students. The teacher can then play on these motivations to maximize interaction and enhance learning.