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Bronx Math Middle School tutors

Book Top-Rated Middle School Math Tutors Near Me In Bronx, NY

Our Bronx Math Middle School tutors are top college students and graduates from local area universities. They have an average GPA of 3.5 or higher in their areas of tutoring specialization. At Frog Tutoring, we work with students in all grade levels and our Bronx private Math Middle School tutors provide customized one on one in-home tutoring through our proven three step approach to academic success.

1.Bring student up to speed by reviewing past work to ensure they are not missing any important concepts that might affect their abilities to learn future lessons. 2. Keep student ahead of the class by using the teachers lesson plan, textbook, and online curriculum to cover lessons before it is taught in class. 2. Reinforce key concepts they might have missed. This ensures they will never be behind again. Your tutor will also help with organization, study skills, and note taking strategies.
Your Bronx area Math Middle School tutor will also track student progress through detailed session reports which will be available to you at the end of each tutoring session. If it is okay with you, your tutor will contact your child's teacher, for K-12, to get a more detailed understanding of what they are struggling with and also to make sure that he/she and the teacher are both on the same page in their approach to tackling the problem.

Browse our list of qualified Math Middle School tutors below. If you are in need of an Math Middle School tutor in Bronx, please call us or simply go to the tab above and Request a Tutor and let us help provide the understanding and assistance needed for success.

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List of High-Achieving Middle School Math Tutors Near Me In Bronx, NY For In-Person & Online Tutoring


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Our Students and Parents Love Us
as Much as We Love Them

RG
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Overall, AJ was absolutely amazing. I didn’t understand almost anything in physics and he made it seem like elementary grade stuff, overall was amazing and I will miss him

KB
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Ali is an amazing tutor always willing to help me on my school assignments and is a very down-to-earth person.

JD
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good tutor

KB
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Looking forward to meeting you.

AN
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Joyce has been great in helping me review topics for the NCLEX

SM
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Ryan in very knowledgeable on the topics I was needing help with. He is professional and works around your schedule. The best tutor I have had on frog tutoring.

RW
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Good tutor

RW
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Never partnered so unable to rate accurately but frog tutors are great so why not give a 5

OS
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patient and knowledgeable

Dm
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{not commented yet}Hayeon Lee is fantastic !
Very knowledgeable and wonderful to work with.
She is kind and is very easy to learn from.
Thank you for finding her.
We have another session Tuesday but I have to reschedule
Perhaps Wednesday?

DY
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Very encouraging and funny. He makes learning fun and teaches in a very simple, easy way to understand.

MP
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Pamela is wonderful! She's the perfect fit for my son! She's very engaging and makes tutoring fun for him

HB
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{not commented yet}
Vince is very happy with this tutor.

RF
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{not commented yet}Jaelynn Cafourek's accomplished computer skills and college training make her a very valuable asset to those who need a professional with their studies.I highly recommend her and her excellent attitude, and clear ability to connect with others and their specific learning...

JS
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Carolle is an excellent tutor. She explains things well, sends me frequent reminders of what I learned during the week, and is altogether a pleasure

DR
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Jeff was extremely knowledgeable and helpful. Deep industry knowledge in running in investment firm and very solid resource. Thank you!

MV
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{not commented yet}
Joyce is very knowledgeable and helpful.

TS
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A very smart individual, has great knowledge to cover the stuff needed based off your preference.

RF
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{not commented yet}Craig has been a big help with helping me learn how to use the internet, navigate a job search and I have learned quite a bit in a shot time.

DY
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Makes learing fun!

OT
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Matthew and I concentrated on financial statements in my CFA Level 1 curriculum. He was extremely knowledgeable and, with his own industry experience, he was very effective at providing real-life examples that made it easier to understand the concepts.

Ma
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He is a great tutor. He knows the topics very well and explains them easily. My only complaint is that his handwriting is somewhat messy. All in all, he is a great SAT tutor for English and math.

MB
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Awesome! he and my son work great together! My Son won't work with anyone else.

IB
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Gurleen is AMAZING!!!!!! She is the best tutor you will find on here. She is very knowledgeable on chemistry and will help you work through so many problems despite them being very challenging. Gurleen helps with retaining the knowledge and provides notes and practice problems as well. if you need...

RH
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Dana is very knwoedgable, especially with anatomy. I was a earning around an 80-84 percent(C) in my medical program exams. With Dana's assistance and vast knowledge in this subject I have passed a written exam AND a practical with a 92(A)!!! Dana positively encourages/challenges her students...

LC
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Sunita Woodcheke has not only demonstrated an extraordinary commitment to my child's academic progress but has also exhibited remarkable patience, enthusiasm, and expertise in their teaching approach. Through personalized lessons and tailored guidance Sunita has fostered a supportive learning...

SM
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Kevin is knowledgeable about math, and he knows how to teach. I’m very rusty on my skills, but he’s been nothing but patient with me. He absorbs my weaknesses and focuses on what I need help with. I appreciate all he’s done so far.

TG
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McKenna has done a great job of working with my daughter on geometry.

TM
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school rating and grades improved.

NC
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I am so happy with this tutoring, my son is engaged all the time. He loves to work in the computer and the activities that they do during the tutoring. She used many different way and form in order to keep him engaged.

EC
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Annie is great!!!!

EC
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Madi is fantastic!!

NT
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I don't sit next to my 9yo during sessions, and this is the first time I ever used a tutor. I can tell you that using a tutor eliminates all the fighting and whining from my kid about doing homework which makes me very happy. They get a lot done during an hour. The tutor is focused, prepared,...

PM
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Fabulous. Olivia is engaging, knowledgeable, and a delight to work with. Highly recommend. Always punctual. Always reliable. Always helpful. Competent with both homework help and direct instruction.

CH
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Extremely knowledgeable and gave direct examples of certain concepts I had trouble with. He also helped assess some of the specific terminology that I need to look for on the exam.

TG
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Chigbo explains concepts in a way that makes it easy to understand. My daughter's understanding and confidence had a real boost in just two days.

JE
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Matthew was very knowledgable in the CFP topics and is very flexible with his ability to review materials and go through the questioning.

KK
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Ivan is absolutely amazing with his knowledge, He is my tutor for college level pre-calculus and I can confidently say that I would not be able to get through my class without ivans help with the class material. He has great patience and will explain and walk you through each problem until you need...

AC
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Very encouraging and goes at a good pace which has been immensely beneficial. Very punctual, there's never been any issues with scheduling. Overall, I have been enjoying my sessions and I look forward to more as he helps me prepare for my ACT.

CP
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Taitana Has tutored my daughter in math and english, she has my daughter think differently in problem solving and expanded her vocabulary. She never gives you the answer but helps you solve a problem together for my daughter to understand why the problem or word is not correct. Will request her...

NB
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So far so good

ER
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Very encouraging, and I enjoy working with her

CO
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My son has been with Barjeana for a few sessions now and loves her! She is so knowledgeable and patient. Best of all she makes the sessions fun and interactive. He struggles with focus, but she keeps him engaged in the session and on track. He looks forward to his tutoring with Ms. Barjeana. ...

IB
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He was great and very knowledgeable on the subject of chemistry, however there was a language barrier

GG
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Excellent tutor! He is very knowledgeable of the content! Our son has improved his grades since he started with Mr. Lopez!

KW
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Mario takes his time explaining each concept. I am finally understanding the subject and my test grades have approved drastically.

DY
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Excellent experience. Very good teacher

AJ
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I think Lisa Chaney is a great tutorial but I also think Corwon need a little more practice.

JB
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Hi my name is Jarian Brooks and I would recommend Greg to anyone who needs tutoring. I'm very pleased and very happy with the changes in my daughter with Greg.

DH
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McKenna has a good grasp of the AP pre-calc work that my daughter is work that my daughter is doing. She's able to help explain in a way that makes sense and has resulted in a benefit of my daughter turning her grades around significantly. I would gladly recommend McKenna for tutoring AP...

Qualification and Certification of Middle School Math Tutors Near Me In Bronx, NY


  • Undergraduate
  • Bachelor degree holders
  • Master degree holders
  • Ph.D. holders
  • Teaching Certification
  • Professional Certificate
  • Background checks
  • Tutoring experience
  • Continuous education
  • FrogTutoring verification certification

Bronx, NY Middle School Math Tutoring Rates


  • Price range from $37/hr - $65/hr
  • Rates vary based on the type of tutoring, methods used, and the number of hours required.
  • Contact our enrollment team to receive your personalized rate.

Tutoring Methods of Our Private Tutors In Bronx, NY


  • In-person/in-home tutoring
  • Online tutoring
  • One-on-one tutoring
  • Group lessons tutoring.

Tools We Use For Online Middle School Math Tutoring


  • Zoom
  • FrogTutoring custom online tutoring platform
  • The Lesson space

Our Middle School Math Clientele In Bronx, NY


  • High school students
  • Middle school students
  • College students
  • Adults
  • Special needs students

Tutoring Locations For Middle School Math In Bronx, NY


  • Student homes
  • Public Libraries
  • Bronx neighborhoods and suburbs

Sign up now for our one-on-one private Middle School Math tutoring in Bronx, NY


Bronx, NY Tutoring FAQ

What options are available for tutoring in the Bronx, NY?

In the Bronx, NY, students have various tutoring options, ranging from in-person sessions at local tutoring centers, private one-on-one tutoring, to flexible online tutoring services. FrogTutoring offers personalized online and in-home tutoring for students in the Bronx, tailored to each individual's learning style and academic needs.

How do I find a qualified tutor in the Bronx?

To find a qualified tutor in the Bronx, you can start by searching online tutoring platforms, reading reviews, and asking for recommendations from peers. FrogTutoring ensures that all tutors are thoroughly vetted and have the qualifications and experience necessary to provide quality educational support.

Are there tutoring services for specialized subjects in the Bronx?

Yes, specialized subject tutoring is available in the Bronx for subjects like math, science, languages, and more. FrogTutoring offers a range of subject-specific tutors who are experts in their field and adept at helping students achieve their academic goals.

What are the costs associated with hiring a tutor in the Bronx?

Tutoring costs in the Bronx can vary widely based on the tutor's experience, subject expertise, and the duration of tutoring sessions. At FrogTutoring, we provide competitive pricing and package deals to ensure tutoring is accessible and affordable for families.

How can I ensure that the tutoring sessions are effective for my child?

Ensuring effective tutoring involves consistent communication with the tutor, setting clear goals, and tracking progress. FrogTutoring provides regular updates and progress reports so parents can monitor their child's improvement and the effectiveness of the tutoring sessions.

Can I get tutoring help for test preparation in the Bronx?

Absolutely, the Bronx offers tutoring for test preparation for exams like the SAT, ACT, GRE, and more. At FrogTutoring, experienced tutors provide customized test prep programs and strategies to help students perform at their best on exam day.

Is it possible to find a tutor who can work with my child's learning style?

Yes, it's possible to find tutors who can cater to different learning styles. FrogTutoring's tutors are trained to identify and adapt to each student's unique learning style, ensuring the most effective and personalized tutoring experience.

What should I look for when choosing a tutoring service in the Bronx?

When choosing a tutoring service in the Bronx, look for a reputable provider with qualified tutors, personalized tutoring plans, flexible scheduling, and positive testimonials. FrogTutoring offers all these features to help ensure your tutoring choice is the best fit for your student's needs.

Are Bronx tutoring services available for adult learners and college students?

Yes, tutoring services in the Bronx are available for learners of all ages, including college students and adults. FrogTutoring caters to this demographic with specialized tutors who are knowledgeable in higher education and professional development subjects.

How can I monitor my child's progress with their Bronx tutor?

Monitoring your child's progress can be done by setting benchmarks, having regular discussions with the tutor, and reviewing assessments or homework. FrogTutoring provides detailed progress reports and open communication lines between tutors and parents to keep you informed of your child's achievements.

Middle School Math FAQ

What are the key math topics covered in middle school?

Middle school math typically covers a variety of key topics, including fractions, decimals, percentages, ratios, proportions, pre-algebra, basic geometry, and introductory statistics and probability. Mastery of these subjects creates a solid foundation for high school mathematics.

How can a tutor help a middle school student with math?

A tutor can help a middle school student with math by providing personalized instruction tailored to the student's learning style, filling in knowledge gaps, reinforcing class materials, introducing new concepts at a comfortable pace, and offering practice problems to improve problem-solving skills and confidence.

What should be the focus of math tutoring for a 7th grader?

Math tutoring for a 7th grader should focus on reinforcing arithmetic skills, introducing pre-algebra concepts such as equations and inequalities, tackling geometry basics like angles and the properties of shapes, and developing the ability to approach word problems strategically and critically.

How often should a middle schooler attend math tutoring sessions?

The optimal frequency of math tutoring sessions for a middle schooler depends on individual needs. However, a general recommendation is 1 to 3 times per week. This allows enough time for practice and assimilation while preventing overwhelming the student. Regular assessment should guide adjustments to this schedule.

What are effective strategies for middle school math tutoring?

Effective strategies for middle school math tutoring include using visual aids and manipulatives to explain abstract concepts, applying math to real-world scenarios to make it relevant, breaking down complex problems into manageable steps, encouraging question-asking to assess understanding, and providing regular feedback and positive reinforcement.

Common Questions on Middle School Math Tutors

How can a middle school math tutor help improve my child's understanding of math?

A middle school math tutor can provide personalized attention and tailor their teaching methods to your child's learning style. They can help clarify difficult concepts, provide additional practice, and build your child's confidence in math. With one-on-one support, tutors can identify and address specific areas where your child may be struggling, ensuring they grasp foundational math skills essential for future success. To request a tutor or learn more about our services, please click on this link: Request a Tutor.

What topics can a middle school math tutor cover?

Middle school math tutors can cover a wide range of topics including basic arithmetic, fractions, decimals, percentages, pre-algebra, algebra, geometry, and problem-solving skills. They can also support students in preparing for math exams and understanding standardized test formats. Tutors tailor their lessons to meet the curriculum and educational standards of your child’s school. Looking for a comprehensive tutoring program? Click here to Learn More about our services.

How do I know if my child needs a math tutor?

Signs that your child might benefit from a math tutor include a drop in math grades, a lack of enthusiasm for math, frustration with homework, or difficulty understanding classroom material. A math tutor can provide the extra help and guidance your child needs to overcome challenges and improve their math skills. If you're considering additional support for your child's math education, Request a Tutor today.

How often should my child meet with a middle school math tutor?

The frequency of tutoring sessions depends on your child's needs and goals. Some students benefit from meeting 1-2 times per week, while others may require more frequent sessions, especially before exams or when covering challenging topics. A tutor can help design a schedule that works best for your child's pace of learning. To create a customized tutoring plan for your child, Click Here.

Are online middle school math tutoring sessions as effective as in-person sessions?

Online middle school math tutoring can be just as effective as in-person sessions. Online tutoring offers flexibility, access to a wider range of tutors, and the use of interactive tools to enhance learning. Tutors can engage students through a virtual platform conducive to learning math concepts. To explore online tutoring options for your child, feel free to Learn More about our online services.

Bronx, NY Neighborhoods We Service

As one of the five iconic boroughs that make up New York City, The Bronx boasts a vibrant tapestry of neighborhoods, each brimming with its own unique charm and identity. From the rich cultural hubs to the tranquil waterfronts, The Bronx neighborhoods offer an eclectic mix to residents and visitors alike. With an area spanning over 42 square miles and housing an estimated 1.4 million people, The Bronx is a cornucopia of diversity and history.

At the southern tip, Mott Haven invites antiquity buffs and art lovers with its collection of historic brownstones and burgeoning arts scene. Home to artists and musicians, this neighborhood is flowering into a creative enclave. Port Morris, its neighboring district, also emerges as a destination for new businesses and nightlife, while retaining its industrial roots.

Heading slightly north, Morrisania stands proud, imbued with cultural and musical heritage, often associated with hip-hop’s infancy. Just east, Crotona Park East encompasses the beautiful green expanse of Crotona Park, a local favorite for outdoor activities.

To the east, West Farms is anchored by the Bronx Zoo and the New York Botanical Garden, serving not only as a residential area but also a magnet for nature and animal enthusiasts. Tremont, a central Bronx neighborhood, presents an urban atmosphere close to these attractions, whereas Belmont is informally known as the borough's Little Italy, delighting visitors with its authentic restaurants and markets.

Fordham brings a youthful vibe with the presence of Fordham University, studded with college bars, bookstores, and an inexhaustible energy. University Heights nearby holds onto a collegiate atmosphere, centered around the former New York University campus now hosting Bronx Community College.

Highbridge, with its historical and namesake bridge, is a residential neighborhood that has undergone significant development, improving its parks and community resources. Concourse, close to the area, offers architectural zeal largely due to the famous Art Deco buildings and the proximity to Yankee Stadium.

Kingsbridge, hugging the Hudson River's eastern shoreline, is known for its quaint shopping areas and access to scenic views. Riverdale, one of Bronx's wealthier neighborhoods, boasts prestigious homes and private schools, radiating a suburban feel within city limits.

Further north and central to Bronx's geography, Norwood offers a casual respite with its modest homes and diverse community. Nearby, Bronx's Woodlawn Cemetery and Conservancy is a historical landmark and peaceful retreat amidst city bustles.

Pelham Parkway maintains a slice of suburban life featuring spacious apartments and accessibility to the massive Pelham Bay Park, the city's largest park space. Just south of Pelham Bay itself is Country Club, an affluent waterfront neighborhood sporting private homes and manicured lawns.

Van Nest and Morris Park nearby serve as tight-knit communities famously hosting the annual Columbus Day Parade; riddled with local shops and pizzerias, they are home to many city workers.

East Bronx brings us to Throggs Neck and City Island, both set apart by waterways and offering a maritime ambiance, complete with seafood restaurants and nautical activities. Further south, Castle Hill and Soundview beam with evolving landscapes, offering residential living with a rapid approach to the waterfront.

Allerton and Pelham Gardens are predominantly residential districts, where detached houses and garden apartments provide a quieter setting. Baychester and Edenwald in the northeast corner embrace shopping centers and family-friendly venues.

Wakefield, the northernmost neighborhood in the city, offers access to suburban Westchester, while having its own mix of housing and commerce.

And this list would not be complete without mentioning the South Bronx, traditionally referring to neighborhoods south of the Cross Bronx Expressway, including Longwood and Hunts Point, each with its own unique attributes and tight-knit community feel.

Exploring The Bronx is akin to taking a mini world tour, with each neighborhood offering a glimpse into the borough's rich mosaic of culture, history, and renewal. As The Bronx continues to evolve, these neighborhoods stand as a testament to the enduring spirit and diversity that makes New York City truly one-of-a-kind. Whether you're a lifelong resident or a curious traveler, The Bronx’s neighborhoods await to tell their stories and make you part of their ongoing narrative.

About Bronx, NY And It’s Education Institutions

The Bronx, one of the five boroughs of New York City, is a tapestry of cultural and historical landmarks that confer upon it a unique character. Among its notable landmarks is the Bronx Zoo, one of the largest zoos in the United States that captivates visitors with wildlife from around the globe. The borough is also home to Yankee Stadium, the hallowed grounds where the New York Yankees, one of baseball's most storied franchises, play. Another cultural beacon, the New York Botanical Garden, boasts 250 acres of flora in a picturesque setting, offering a peaceful escape from urban life. The Bronx also prides itself on being the birthplace of hip-hop, a legacy that is celebrated at places like the Bronx Walk of Fame.

Founded originally as part of Westchester County in 1639 and later annexed to New York City in 1898, the Bronx has evolved into a densely populated area with a vibrant tapestry of neighborhoods. Home to an estimated population of over 1.4 million people as of 2021, the borough is a melting pot of cultures, which is reflected in its diverse communities, from the historic maritime village of City Island to the bustling commercial hub of Fordham Road. Education in the Bronx is serviced by the New York City Department of Education, with top-ranking K-12 schools including the Bronx High School of Science and the High School of American Studies at Lehman College. Furthermore, education resources like after-school programs, mentoring initiatives, and libraries are readily accessible to students across the borough, ensuring that the youth receive ample support for their academic growth.

Higher education is also a cornerstone of the Bronx's educational landscape. The borough hosts several universities, such as Fordham University, known for its rigorous academics and beautiful Gothic architecture, and Lehman College, part of the City University of New York (CUNY) system, which offers a wide array of undergraduate and graduate programs. Additionally, Albert Einstein College of Medicine is a prominent institution dedicated to medical education and research. The education institutions in the Bronx are not only committed to delivering academic excellence but also to fostering community engagement, making the Bronx not just a place of learning, but also a community that actively shapes the minds of the future.

Students at These Bronx, NY Schools Excel with Our Tutoring

Below is a sample list of top schools in the Bronx, NY area, both private and public. This selection showcases institutions whose students have benefited from our tutoring services. Please note that this list is not exhaustive and represents only a slice of the many schools in the Bronx where we have had the pleasure of enhancing student learning experiences.

  1. Bronx High School of Science A prestigious public high school known for its rigorous STEM curriculum and high achieving students.

  2. Riverdale Country School An independent, day and boarding school offering a progressive education from Pre-K through Grade 12.

  3. Fordham Preparatory School A Jesuit college preparatory school for young men, established as a part of the educational ministry of the New York Province of the Society of Jesus.

  4. Horace Mann School An independent college preparatory school that provides a broad and challenging program from nursery through twelfth grade.

  5. The Spence School A private, all-girls K-12 school with a longstanding commitment to academic excellence and diversity.

  6. P.S. 24 Spuyten Duyvil A public elementary school committed to developing a community of lifelong learners and leaders.

  7. Fieldston Ethical Culture A co-educational, independent school that is part of the Ethical Culture Fieldston School, emphasizing progressive education and academic excellence.

  8. Bard High School Early College Bronx A Bard College operated public school providing students with a high school curriculum as well as the opportunity to earn college credits.

  9. The Ursuline School An independent, college preparatory Catholic school for girls, with a focus on academic innovation.

  10. Bronxville High School Known for its strong academic programs and community-based learning, Bronxville High School offers a comprehensive educational experience.

  11. Preston High School A Catholic college preparatory school for girls, with an emphasis on academic excellence and leadership development.

  12. Bronx Leadership Academy II High School A small public high school dedicated to preparing students for college and careers with a commitment to community service.

  13. The Mount Saint Michael Academy An all-boys Catholic school that provides a holistic education including rigorous academics, competitive athletics, and a strong values-based foundation.

  14. High School of American Studies at Lehman College A specialized public high school that focuses on American history and offers access to Lehman College resources.

  15. Bronx Academy of Letters A public school with the fundamental belief that students who can express themselves clearly in writing will achieve more success in any path they choose.

  16. P.S. 83 Donald Hertz A public elementary school that emphasizes the development of the whole child, including a strong commitment to academic, personal, and social growth.

  17. Academy of Mount St. Ursula The oldest Catholic all-girls high school in New York State, empowering young women with leadership skills and strong academic foundations.

  18. Regis High School A private Jesuit university preparatory school for Roman Catholic young men located on Manhattan's Upper East Side. (While not in the Bronx, it serves students from the Bronx.)

  19. Cardinal Hayes High School A Catholic high school for boys that focuses on the development of Christian values, intellectual growth, and community service.

  20. Saint Barnabas High School A warm and supportive Catholic college preparatory school that promotes academic excellence and personal achievement within the tradition of the Sisters of Charity.

Each of these schools has its own unique culture, approach to education, and community. We are proud to have supported students from these fine institutions in reaching their academic goals through our tutoring services.

About Middle School Math & Middle School Math Tutoring

Math Middle School, typically catering to students aged 11-14, is a critical educational stage where pupils explore and build upon foundational mathematical concepts acquired in elementary education. It is at this level that students transition from basic arithmetic to more advanced topics, setting the groundwork for high school mathematics and beyond.

At the middle school level, mathematics becomes increasingly abstract and concept-based. Students are introduced to various types of math including, but not limited to, algebra, geometry, probability, and statistics. This is a period where the application of mathematical reasoning becomes particularly emphasized, and students are encouraged to understand and manipulate mathematical expressions and equations.

Certain related entities play pivotal roles in the middle school math experience. These include standardized testing, common core state standards (in the United States), mathematics competitions, extracurricular math clubs, and advanced placement opportunities. Each of these components can shape the math curriculum and influence the way math is taught and learned in middle school.

When tutoring a student who struggles with math, the best strategy is to nurture a growth mindset, emphasizing that ability in math can be developed through practice and persistence. A strong understanding of the foundational concepts is crucial, so it's important to ensure that these are solid before moving on to more complex topics. Additionally, utilizing visual aids, practical examples, and relatable scenarios can help demystify abstract concepts.

In middle school math, the most common concepts include fractions, decimals, percentages, ratios, basic algebra (such as solving for x in simple equations), and introductory geometry (including the properties of shapes and calculating area and volume). Students also start learning about integers, exponents, and basic data representation.

Among the most challenging concepts for middle school students are the abstraction of algebraic thinking, the theoretical aspects of geometry, and problem-solving that requires synthesizing multiple math topics. As the math becomes more complex, many students also struggle with understanding and applying the logical reasoning necessary for proofs in geometry, manipulating variables in algebra, and handling multi-step problems that involve higher-order thinking.