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Showing posts with label Job Interview Questions. Show all posts
Showing posts with label Job Interview Questions. Show all posts

Thursday, August 15, 2019

Tech Job Brain Teasers

Tech engineers are some of the smartest people in the world.
But even they have a hard time answering the brain teaser questions a lot of tech companies like to ask during job interviews.
We went through Glassdoor to find some of the trickiest brain teaser questions they get asked, and the best way to answer them.

Systems engineer at Google: "How many trailing zeros are in the number 5! (5 factorial)?"

Business Insider / Jillian D'Onfro
Suggested answers:
"5!=120. So there is 1 trailing zero."
"This sounds like one geared not so much towards getting the right answer, but getting to it the right way. If you think a bit and say "one", the interviewer will know you did it the brute-force way, doing the math. You'd get at the answer faster, and probably impress them more, if you think instead how many times a ten will be produced in doing that math, rather than what the actual result of the math will be."

Answer like a real Silicon Valley Engineer!!! Most engineers and tech leaders who now shape the way we use our technology can be found in the Silicon Valley. They are in Apple, Facebook, and Google, to mention a few of the many startups and global tech companies located in the southern San Francisco Bay Area of California. But before people get to be hired as part of these tech think tanks, they undergo a rigorous process to prove themselves worthy of a Silicon Valley job. 
Part of that process is to answer bizarre brain teasers to test the thinking abilities of prospective hires. They range from basic, tricky, to difficult which measure the logic of engineers. Listed below from MyCareerStacks are 5 of such brain teasers coming from multiple companies, and 9 others complete with answers. If you plan to be part of any of the Silicon Valley companies, these are worth a mental exercise. 

Company: Adobe Can you answer like a real Silicon Valley engineer… an Adobe engineer? There are 50 bikes with a tank that has the capacity to go 100 kms. Using these 50 bikes, what is the maximum distance that you can go? 
Answer: Source: Giphy The most naive solution would be to just make all the bikes go together, but sadly you cannot go further than 100kms using that approach. There is another solution to this that can cover 350kms. Move the bikes 50kms so that each bike has half-tank empty. Now pour the fuel from half the bikes to the other half so that they are all full. Now you have 25 bikes with full tanks and then you again repeat the trick. This way you can go 50, 25, 12, 6, 3, and 1 to cover 5*50 = 250kms. That’s 350kms in total. 

Company: Microsoft Can you answer like a real Silicon Valley engineer… a Microsoft engineer? If you had an infinite supply of water and a 5-liter and 3-liter bucket, how would you measure exactly 4 liters? The buckets do not have any intermediate scales. 
Answer: It is a classic puzzle with a simple answer. Fill the 5-liter bucket and empty it in the 3-liter bucket. Now you have 2 liters in the bigger bucket and 3 in the other. Empty the 3-liter bucket and pour the 2 liters from the bigger bucket into it. Now fill the 5-litre bucket completely, and pour water from it to the smaller bucket. Since the smaller bucket already has 2 liters, it can only take 1 more. This leaves us with 4 liters in the 5-liter bucket. 

Company: Google Can you answer like a real Silicon Valley engineer… a Google engineer? The probability of finding the parking slot occupied is 1/3. You find it empty for 9 consecutive days. Find the probability that it will be empty on the 10th day. 
Answer: Sometimes, there is trick with probability questions; but more often, there is none. Always go for the logical answer to questions like this one. The answer to this is 2/3, because it says about the probability of finding it empty on the 10th day. In probability, if an event has already happened, it cannot have an effect on the probability of an event to occur in the future. So the parking slot has been empty for 9 days but that does not affect the 10th day. 

Company: Amazon Can you answer like a real Silicon Valley engineer… an Amazon engineer? Read more  Scientists Turn Soybean Oil Into a Material 200 Times Stronger Than Steel You toss two coins. If you get heads with the first coin, you stop. If you get tails, you toss it again. The second coin is tossed regardless. What is the ratio of heads to tails? Answer: Since you’re only expected to toss the first coin twice — given a 50/50 chance of getting heads — the ratio is 1 to 1. The second coin is also continuously tossed, and has a ratio of 1 to 1. So, the whole ratio is still 1 to 1. Company: Microsoft Can you answer like a real Silicon Valley engineer… a Microsoft engineer? You’re given a pair of tic-tac-toe boards. Find a way to determine, when rotated, that they are the same board. Answer: With your tic-tac-toe boards, you can rotate them left or right four times, and then mirror it and do the same again. So, the way to do this is to reduce it down to a matrix and then rotate it, one step at a time, to check if it matches another board. Mathematically, the way to do this is to turn it into a three-by-three matrix, and then flip the rows and columns. If you want to rotate it to the right, switch the columns, and to rotate it left, switch the rows.

Read more at: https://gineersnow.com/leadership/can-answer-brain-teasers-prospective-engineers-silicon-valleyese tech think tanks, they undergo a rigorous process to prove themselves worthy of a Silicon Valley job. Part of that process is to answer bizarre brain teasers to test the thinking abilities of prospective hires. They range from basic, tricky, to difficult which measure the logic of engineers. Listed below from MyCareerStacks are 5 of such brain teasers coming from multiple companies, complete with answers. If you plan to be part of any of the Silicon Valley companies, these are worth a mental exercise. Company: Adobe Can you answer like a real Silicon Valley engineer… an Adobe engineer? There are 50 bikes with a tank that has the capacity to go 100 kms. Using these 50 bikes, what is the maximum distance that you can go? Answer: Source: Giphy The most naive solution would be to just make all the bikes go together, but sadly you cannot go further than 100kms using that approach. There is another solution to this that can cover 350kms. Move the bikes 50kms so that each bike has half-tank empty. Now pour the fuel from half the bikes to the other half so that they are all full. Now you have 25 bikes with full tanks and then you again repeat the trick. This way you can go 50, 25, 12, 6, 3, and 1 to cover 5*50 = 250kms. That’s 350kms in total. Read more  This Is The Show Elon Musk Doesn’t Think Portrays Silicon Valley Correctly Company: Microsoft Can you answer like a real Silicon Valley engineer… a Microsoft engineer? If you had an infinite supply of water and a 5-liter and 3-liter bucket, how would you measure exactly 4 liters? The buckets do not have any intermediate scales. Answer: It is a classic puzzle with a simple answer. Fill the 5-liter bucket and empty it in the 3-liter bucket. Now you have 2 liters in the bigger bucket and 3 in the other. Empty the 3-liter bucket and pour the 2 liters from the bigger bucket into it. Now fill the 5-litre bucket completely, and pour water from it to the smaller bucket. Since the smaller bucket already has 2 liters, it can only take 1 more. This leaves us with 4 liters in the 5-liter bucket. Company: Google Can you answer like a real Silicon Valley engineer… a Google engineer? The probability of finding the parking slot occupied is 1/3. You find it empty for 9 consecutive days. Find the probability that it will be empty on the 10th day. Answer: Sometimes, there is trick with probability questions; but more often, there is none. Always go for the logical answer to questions like this one. The answer to this is 2/3, because it says about the probability of finding it empty on the 10th day. In probability, if an event has already happened, it cannot have an effect on the probability of an event to occur in the future. So the parking slot has been empty for 9 days but that does not affect the 10th day. Company: Amazon Can you answer like a real Silicon Valley engineer… an Amazon engineer? Read more  Scientists Turn Soybean Oil Into a Material 200 Times Stronger Than Steel You toss two coins. If you get heads with the first coin, you stop. If you get tails, you toss it again. The second coin is tossed regardless. What is the ratio of heads to tails? Answer: Since you’re only expected to toss the first coin twice — given a 50/50 chance of getting heads — the ratio is 1 to 1. The second coin is also continuously tossed, and has a ratio of 1 to 1. So, the whole ratio is still 1 to 1. Company: Microsoft Can you answer like a real Silicon Valley engineer… a Microsoft engineer? You’re given a pair of tic-tac-toe boards. Find a way to determine, when rotated, that they are the same board. Answer: With your tic-tac-toe boards, you can rotate them left or right four times, and then mirror it and do the same again. So, the way to do this is to reduce it down to a matrix and then rotate it, one step at a time, to check if it matches another board. Mathematically, the way to do this is to turn it into a three-by-three matrix, and then flip the rows and columns. If you want to rotate it to the right, switch the columns, and to rotate it left, switch the rows.

Read more at: https://gineersnow.com/leadership/can-answer-brain-teasers-prospective-engineers-silicon-valley

Software engineer at Facebook: “You have two lightbulbs at a 100-story building. You want to find the floor at which the bulbs will break when dropped. Find the floor using the least number of drops.”

Flickr / Jackman Chiu
Suggested answers:
"Start moving up in increments of 10 floors and dropping the bulb until it breaks (ie: drop from floor 10, if it doesn't break, drop from floor 20, etc.). Once the bulb breaks, move down to the floor before it broke on and start moving up floors in increments of one until the second bulb breaks. This results in a worst case scenario of 19 drops."
"19 drops is not the best worst case scenario... imagine trying floor 16, if it breaks, you try 1 - 15 and thats 16 tries. If it doesn't break, then try floor 31 and if it breaks, then try 17 - 30 (so 16 tries, including the try on floor 16). And on and on (45, 58, 70, 81, 91, 100). If you reach 91, you'll have tried 7 floors so far and if it doesn't break, then there's 9 more tries to get to 100 (thus 16 in the worst case)."

Manager at Amazon: “If you had 5,623 participants in a tournament, how many games would need to be played to determine the winner?”

John Ferry/Getty Images
Suggested answers:
"The interviewer is not looking for the right answer because there can be many. What he/she is looking for is your logical approach in solving the answer. So you could start by probing more is first I would like to understand if 5,623 participants represent the number of team or individuals. Then ask the next logical question based on the answer."
"5,622. Assuming it is a single elimination tournament. All teams lose one game except the champs. It's always # of teams - 1."

Software Development Engineer in Test at Webtrends: "There are 20 different socks of two types in a drawer in a completely dark room. What is the minimum number of socks you should grab to ensure you have a matching pair?"

Shutterstock
Suggested answer:
"I'm not a mathematician, statistician, or highly analytical but if you pick up 3 socks they could still be all the same type - even if the odds are 50%. Odds do not equal reality. So the only way to 'ensure you have a matching pair' is to pick up 11 of the 20. This is the only fool proof guaranteed way to get a pair (in the real world and not the world of odds)."

Web Technology Intern at Riot Games: “Imagine that you have three boxes, one containing two black marbles, one containing two white marbles, and the third, one black marble and one white marble. The boxes were labeled for their contents - BB, WW, BW - but someone has switched the labels so that every box is now incorrectly labeled. You are allowed to take one marble at a time out of any box, without looking inside, and by this process of sampling you are to determine the contents of all three boxes. What is the smallest number of drawings needed to do this?”

Ilike
Suggested answer:
"The key thing here is that the box does not contain what it says on the label. As such you can guarantee the contents of each box with one draw. Here's how: Draw a marble from the box labeled BW (since it is labeled BW it must be either BB or WW) If you draw a white for example you know 100% that it is the WW box. Then there are only two boxes left labeled WW and BB in this example and the only two things that they can be are BB or BW. The box labeled BB cannot be BB and so hence must be the BW. This leaves the box labeled WW to be BB by elimination. Same thing works if you pick a black marble first. The key is picking from the BW box in the start and confirming what it actually is. One draw is the smallest number needed."

Software Engineer at Cisco: "If you have a square room with no roof, and you had four flagpoles you had to plant on the walls so that each flagpole touched two walls, how would you do it?"

flickr/audio_technica
Suggested answer:
"The answer was that by planting them on the corners, each one is touching two walls because each corner is part of two walls. I wanted to pierce two walls with a pole horizontally too. They said it was an innovative solution."

Software engineer at D. E. Shaw & Co.: "Given 9 balls all of which weigh the same except for one, what is the minimum of weighings necessary to find the ball weighs more (or less)?"

Wikimedia Commons
Suggested answer:
"You could do this with two weighings assuming its a two pan balance - (1) place three balls on each side - if they balance out then its the remaining three that has abnormal ball (2) out of that group, place one ball on each side - if balances it out, the abnormal ball is the remaining one. If the weighing in step (1) does not balance out, grab the group of three balls that is light or heavy and repeat step (2) described above."

ASIC Verification engineer at Zoran: "You have 2 pieces of rope, each of which burns from one end to the other in 30 minutes (no matter which end is lit). If different pieces touch, the flame will transfer from one to the other. You cannot assume any rope properties that were not stated. Given only 1 match, can you time 45 minutes?"

Aly Weisman/Business Insider
Suggested answers:
"Take one rope (Rope A), place it down as a circle. Light match and start burning rope A at the tips that are touching. When the rope completely burns out, 15 minutes will have passed (since both ends are burning and being consumed at once). Hold the second rope (Rope B) straight and place one end so that it will immediately catch fire when the two burning points from (Rope A) finally touch and are just about to burn out. Thus 15 minutes on Rope A + 30 minutes on Rope B gives you 45 mins."
"Make a T. Simple."

Software engineer at Raytheon: "In front of you are three light switches. Only one does anything, and it turns on the light downstairs. From here you can't see the light, and it makes no sound. You must determine which switch operates the light, BUT you can only go check it once. How do you figure out which switch is for the light?"

Flickr / Sputnik Mania
Suggested answer:
"Flip any switch you want. Wait for about 5-10 minutes to let the bulb heat up. Flip that same switch off, and another one on. Go check the light. If it's off and hot, it was the first switch, if it's on it was the second and if it's cold and off, it was the last one."

Saturday, April 16, 2016

Best Interview Questions Answered

Have you attended an interview and not knowing the outcome? Are you scared of attending one? Preparing for an interview is probably the most overlooked phase of securing a new job position. Everyone thinks it is easy until they enter an interview room in front of a panel 
of educators who are judging every move and every word. Then, reality sinks in! The panel might include the superintendent, experienced professionals, recruiters, human resources personnel, making it critical to address your answers to all involved. The more you prepare for an interview, the better your odds of securing a job offer will be. Here are some tips for you on answering some interview questions.

Keep in mind, these are just possibilities and should be used with discretion. Each candidate’s background, teaching style, and experiences are different, and the answers should reflect those differences. There is one thing you must remember that applies to everyone who interviews — don’t lie! Also, keep in mind, that you should tailor your answers to address the specific needs of a job or work specifics in which you 
are interested.

1)  Tell me a little bit about yourself.


Oh, yes, this is the question that is most likely to be asked first. I call it a two minute commercial about yourself. This is a great opportunity to sell yourself. Keep in mind, if it is the first question asked, it will set the stage for the interview, so it needs to be extremely strong. Don’t be too modest. This will provide an overview, an introduction, to you. You might start by stating, “As you can see from my resume….” and then mention your degrees and certifications and give a quick run down of your relevant experience. The last 1 ½ minutes should be used to communicate your strengths and skills and what you can do to enhance education in their district. In other words, they are asking “Why should we hire you?” Practice this carefully. You need a few sentences that answer that question at the end of your response. Also, at the end, you may want to mention why you would enjoy working for the school district in the position for which they are hiring.





2) Let’s pretend it’s almost the first day of school and you are a first grade teacher. How would you prepare your classroom?
This question tests how well you will manage the classroom. The philosophy is that the more organized you are, the more well-run your classroom will be.  Don’t give the panel just a few words… they may be using a checklist to see how many items you mention.  Plus, as a teacher, you should be very excited about this question and be able to speak for a while, but limit the response to two minutes.



Your response must provide them with an idea of how nurturing and inviting your classroom will be to students. Come up with some creative decorating ideas, making sure
they are student-centered.  You could also mention a huge welcome sign, the daily schedule, age-appropriate posters, name tags for students, labeled desks (how will they be
arranged?) and lockers, a list of class rules/consequences/rewards, and other labeled areas (e.g., the classroom library, manipulative storage,  computer area), etc.  Or, mention that you might invite parents and students to visit the classroom the day before school
starts, with the administrator’s permission.  If you have a portfolio with have pictures of other first days of school, this is a great chance to share them with the panel.



Next, make it clear that you will have organized the textbooks, your lesson plan book, your grade book and other materials well before school begins.  Mention several
activities you might include during the first day of school, including an ice-breaker, a trip to the restrooms, and a fun art project.



The real key to this question is to show your enthusiasm, passion, excellent organizational skills, and how you will create a warm and captivating environment in which students will feel safe, where learning will be maximized, so that children will look forward to coming to school each day.





3) As a grade one teacher, how would you motivate parents to become involved in the classroom and in their child’s education?


What is critical to communicate in your response to this question is your understanding of the importance of parental involvement and how you always encourage participation to strengthen student-teacher-parent relationships.  (Grandparents can also be encouraged to
participate.)  Talk about some of the things that parents can volunteer to do in the classroom, such as: reading with students, preparing project materials,  creating bulletin
boards, sorting materials, setting up learning centers, hanging up students’ work, etc. 



Parental involvement means much more than just attending parent-teacher interviews.  You must set goals to keep the parents abreast of what is going on in the classroom.  You
can communicate that information and ask for volunteers through weekly or bi-weekly newsletters.  You might inform parents when you are starting a new unit or specific
projects and make sure they clearly understand the homework assignments each week.  Make sure that parents are invited to any momentous or appropriate events. 



You should contact or speak to parents not just when a child is having difficulty, but also when they are doing well.  Tell the hiring panel that you will call parents and send notes home complimenting students on good behavior. Also mention that you try to recruit bilingual parents to help with communication as necessary.  



Let the hiring committee know that you coach parents on how they can help their child succeed academically.  You may have read some resource book(s) to gain ideas that you
could implement.  If so, let the panel know.  Holding a parent appreciation lunch or tea to acknowledge those who have helped in the classroom is a great idea.  Consider
attending some of the PTA meetings.  If your portfolio contains any past newsletters or parental communication letters, make sure you show these to the panel.





4) Are you a flexible teacher? If so, explain how.


Yes I am a flexible teacher. I can deal very effectively with people and students from all backgrounds and socio-economic groups.  In teaching, I am completely aware that students have different learning rates and styles. Some are fast learners and some are slow learners, some learn best in auditory manner, others through actions or visual media. Still others have specific learning disabilities. I am flexible in the sense that I address
these differences and make it a point to respond to their different needs. In my teaching, I make use of different learning strategies so that my instruction will be interesting and motivating to students.  I use lecture, discussion, hands-on activities, cooperative learning, projects, manipulatives, role playing, debates, reports, technology, and others. (Choose the ones appropriate to the subject and/or grade for which you are applying.)




5)  What did you find to be the most difficult aspect of student (intern) teaching?


For me, the most difficult part of student teaching is the limited contact hours with students within one class period (or day). When I teach, I have so much information that I
would like to impart to my students that time flies by too fast.  I always go to my classes full of energy and armed with lessons which I believe will stimulate curiosity and
spark understanding and new insights in my students. There is so much information that I need to present for them to have a comprehensive understanding of a concept. My
challenge is to make sure that I structure my lessons so effectively that learning takes place in one class period (or day).  So I plan ahead to maximize every minute of my
class period (or day).

6) What ways do you assess and evaluate students?


In assessing students, I make use of different methods. I use formal and informal assessment procedures to promote social, academic, and physical development. The usual
assessment that I use is written quizzes (case studies, discussions) and examinations. Throughout the semester, I also grade and assess students on their class participation
such as recitations, reports, group activities, and seat work. I also assess and grade students based on their completion of assignments and timeliness in submission. I
also use authentic/alternative assessments, in which the student shows they can perform a task, such as making a speech or writing a story. I like to use written, oral, and day-to-day assessments

7) What would your master teacher or cooperating teacher say about you?


My master teacher would say that I am incredibly energetic in teaching because I love what I do! She would say that I am the type of person who also goes the extra mile to help my students learn and comprehend their lessons regardless of their abilities. She would say that I also try to teach values that are important in life, including the value of 
discipline.

8) What will you do to modify your teaching to meet the needs of a gifted student?


A gifted student in the midst of the regular students can be a challenge in terms of addressing his or her particular needs and capabilities. What I will do is to modify his
work assignments in expectation or length to fit his abilities. His tasks will require a higher level of understanding compared to the regular students. During class discussions, I can direct questions to him or her that require higher-level thinking skills. I also would
encourage the gifted student to take a leadership role in group work so that his classmates can emulate and be inspired by him.

9) What are some of the trends, issues, and methodologies in education that relate to your specific curriculum area or grade level?


Here are some trends, issues, and methodologies that relate to most subjects and grade levels. You might say:

It seems that increasingly students have more information and knowledge than ever before due to access to the internet. A teacher has to be aware of what the internet
is, how it can be used in positive ways, and how to protect students from negative influences on the internet.

It can be a powerful learning tool for students. In addition,
technology in general has changed education greatly. Using computers, videos, and other kinds of technology makes lessons more interesting and more fun. It also makes it
easier to teach students with varying needs. A computer with internet access can open the world up to the classroom.



An issue that is important is teaching to state standards. School time is limited and we must make the best use of it that we can, so I try to relate every lesson and activity
to a grade level standard.  That keeps me focused on the overarching goal of improving education and helping children do better academically.



One of the most important methodologies in my opinion is teaching through multiple intelligences.  Children learn in so many different ways.  I try to reach everyone by teaching through the senses, using visual, auditory, and sense of touch to impart information.  When possible, I try to include the senses of taste and smell, too!



10) Do you know what is going on in education today?

Do you have a passion for the profession? In other words, do you stay current?
Here is a possible answer for this question.

I love education. I think that it is imperative to be a lifelong learner when one is a teacher. I plan to continue my education by (fill in this blank with your own plans).  

Technology continues to evolve into a strategic part of education. Tablet PCs and hand held devices are the newest gadgets on the market for students to use; the internet is
an incredible resource.  Technology provides interactive, individualized learning experiences, increasing student engagement and efficiency – in safer and more secure
schools.

Multiculturalism and securing equal opportunities for all are important themes in education.

And, of course, teaching to state standards to upgrade student academic progress is very important.



11) Do you enjoy teaching children?  If so, how would I know if I observed your class? 



What I most enjoy in teaching is hearing my students explain, in their own words, what they learned in a particular lesson and watching them enjoy participating in a lesson. When you observe my class, you will see that I get my students engaged in our discussions and activities. You will see that my students actively participate in each lesson. I make sure that all of them have a chance to speak, express their thoughts, and share them with the class. I enjoy how their faces brighten every time I recognize their efforts to learn by saying, “Very good,” “That’s a great idea,” “Good job,” and other encouraging phrases. At the end of the lesson, you will hear the students explain what they learned.  Most of all, you’ll know that I enjoy teaching because the children in my class look happy.

12) What is your classroom management plan?


My general classroom management plan is to make my classroom feel like a home to every student. I want them to feel valued, intelligent, safe, and comfortable. I want
them to respect me, the teacher, and each other and to show that respect by treating everyone with kindness and caring.

The class environment must be conducive to learning so I welcome everyone’s opinions and encourage and respect student differences. I try to understand the expectations
of my students and make them aware of my expectations. I always make it a point to clearly communicate my expectations at the beginning of the school year. In this
way, I ensure that the students and I are moving toward the same goal – learning for all. I establish firm, but fair and consistent discipline. I try to maintain a regular schedule each day.  If the classroom is well-managed and teaching is effective, the participants in this learning environment will learn, grow, and become responsible
citizens.  



13) What do you do to accommodate a student with an IEP?


An Individualized Education Plan will be successful if proper coordination and collaboration are emphasized by the teacher, parents, psychologist, and other school staff.  I accommodate a student with an IEP by planning a series of in-depth discussions with the parents to learn about the student’s diagnosis and needs and later to inform the
parents of his progress. This allows me to design an education program that addresses his specific needs and puts into place special accommodations. I also will document my own observations and evaluations of the student’s academic work and behavior. As I gain knowledge and information about the student with the IEP, it will be easier for me to decide on the lessons and teaching and learning styles I should use to accommodate his needs and maximize his learning. There are many types of accommodations, depending on the student’s diagnosis, for example, instructing a student through the use of
 manipulatives, providing a seat near the front of the room, reinforcing positive behavior every few minutes, providing extra time for assignments, and giving tests orally instead
of in writing.



14) What can you contribute to our school community/teaching team?


I am the type of teacher who shares with my peers the classroom experiences that I have had, whether good or bad. I do this because I believe that this the best way for me
and other teachers to improve our teaching. In this way, I get to share with them the best of my skills and, in return, they share with me the best of their skills. I also find
that this is a very good way to learn how to handle situations that are difficult or unusual. The feeling of not being alone, but being part of a team of teachers, is what I can bring to the school.  This will help build morale and a great working environment.  




15) How do you differentiate your teaching? Please provide a couple of examples. 


My teaching is unique in the sense that while teaching approach is holistic, it is also inclusive and individualized. It is holistic because I not only share knowledge with my students, but I also elicit knowledge from them. For instance, when I was teaching mathematics, I didn’t simply teach formulas and methods of solving mathematical problems. I also explained to my students the value of understanding numbers and the great things we can use math for, such as the ability to think logically. I include all students in my lessons.  For those who have difficulty, I use cooperative learning, peer tutors, and re-teaching techniques. I attend to the individual needs of the students by modifying assignments. For example, when I had a group of gifted children in my class, I
regularly gave them special assignments to work on that would stimulate higher level thinking skills and had them present their work to the class.