Request Tutoring Info
Please enter name
Please enter email
Please enter phone
Please enter details
Cooper City Geometry tutors

Book Top-Rated Geometry Tutors Near Me In Cooper City, FL

Our Cooper City Geometry 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 Cooper City private Geometry 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 Cooper City area Geometry 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 Geometry tutors below. If you are in need of an Geometry tutor in Cooper City, 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.

Read more... Read less
cnn cbs boston miami fox news

List of High-Achieving Geometry Tutors Near Me In Cooper City, FL For In-Person & Online Tutoring


How it works

tutors, tutoring, tutoring service, tutoring services, homework help, private tutors, home tutors

Request any tutor by submitting a form

tutors, tutoring, tutoring service, tutoring services, homework help, private tutors, home tutors

Speak with our enrollment advisor to get your questions answered

tutors, tutoring, tutoring service, tutoring services, homework help, private tutors, home tutors

Get connected with your private in-person or online tutor

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

">
LC
Knowledge
Presentation

Great tutoring session!

">
JC
Knowledge
Presentation

Sarah is our 5th tutor we have used on Frog tutoring. In just one short month of tutoring my child with ADHD, she has improved his math grade from a C to an A-!! We are so happy for the progress our child has made with Sarah’s help, and we will definitely continue to use her as our child’s...

">
JL
Knowledge
Presentation

{not commented yet}The sessions are going well and I am understanding the material . The information is clear , which I love.

">
RG
Knowledge
Presentation

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
Knowledge
Presentation

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

">
JD
Knowledge
Presentation

good tutor

">
KB
Knowledge
Presentation

Looking forward to meeting you.

">
AN
Knowledge
Presentation

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

">
SM
Knowledge
Presentation

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
Knowledge
Presentation

Good tutor

">
RW
Knowledge
Presentation

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

">
OS
Knowledge
Presentation

patient and knowledgeable

">
Dm
Knowledge
Presentation

{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
Knowledge
Presentation

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

">
MP
Knowledge
Presentation

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

">
HB
Knowledge
Presentation

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

">
RF
Knowledge
Presentation

{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
Knowledge
Presentation

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
Knowledge
Presentation

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

">
MV
Knowledge
Presentation

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

">
TS
Knowledge
Presentation

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

">
RF
Knowledge
Presentation

{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
Knowledge
Presentation

Makes learing fun!

">
OT
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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

">
IB
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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

">
TM
Knowledge
Presentation

school rating and grades improved.

">
NC
Knowledge
Presentation

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
Knowledge
Presentation

Annie is great!!!!

">
EC
Knowledge
Presentation

Madi is fantastic!!

">
NT
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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

">
KK
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

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
Knowledge
Presentation

So far so good

">
ER
Knowledge
Presentation

Very encouraging, and I enjoy working with her

">
CO
Knowledge
Presentation

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
Knowledge
Presentation

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

">
GG
Knowledge
Presentation

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

">
KW
Knowledge
Presentation

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

">
DY
Knowledge
Presentation

Excellent experience. Very good teacher

Qualification and Certification of Geometry Tutors Near Me In Cooper City, FL


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

Cooper City, FL Geometry 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 Cooper City, FL


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

Tools We Use For Online Geometry Tutoring


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

Our Geometry Clientele In Cooper City, FL


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

Tutoring Locations For Geometry In Cooper City, FL


  • Student homes
  • Public Libraries
  • Cooper City neighborhoods and suburbs

Sign up now for our one-on-one private Geometry tutoring in Cooper City, FL


Cooper City, FL Tutoring FAQ

What subjects can I find tutors for in Cooper City, FL?

In Cooper City, FL, you can find tutors for a wide range of subjects including mathematics, science, English, history, and foreign languages. Companies like Frog Tutoring offer personalized tutoring for K-12 and college subjects, test preparation, and skill development.

How do I find a qualified tutor in Cooper City, FL?

To find a qualified tutor in Cooper City, FL, consider using tutoring services that screen and handpick their tutors for quality. Frog Tutoring, for instance, ensures that their tutors not only excel in their respective fields but are also great communicators and mentors.

Are in-person tutoring services available in Cooper City, FL?

Yes, in-person tutoring services are available in Cooper City, FL. Frog Tutoring offers the option to have face-to-face sessions with tutors who can meet at a location convenient for you, ensuring personalized attention and effective learning.

Is online tutoring an option for students in Cooper City, FL?

Absolutely, online tutoring is an option for students in Cooper City, FL. With the flexibility and convenience of remote learning, Frog Tutoring provides online sessions with experienced tutors using interactive tools to facilitate effective online education.

Can I get help with test preparation in Cooper City, FL?

Yes, you can get help with test preparation in Cooper City, FL. Frog Tutoring offers specialized tutoring for a variety of tests, including SAT, ACT, GRE, GMAT, and more, with customized strategies to help improve your scores.

What is the typical cost of tutoring in Cooper City, FL?

The cost of tutoring in Cooper City, FL can vary depending on several factors, including the subject, level of tutoring, and the expertise of the tutor. Frog Tutoring offers competitive pricing and will work with you to find a tutoring solution that fits your budget.

How do I select the right tutor for my child in Cooper City, FL?

To select the right tutor for your child in Cooper City, FL, identify your child's specific needs and learning style, and seek a tutor who's a good match. Frog Tutoring matches students with tutors based on learning preferences and goals for a customized educational experience.

What are the benefits of one-on-one tutoring in Cooper City, FL?

One-on-one tutoring in Cooper City, FL offers personalized attention, tailored lesson plans, flexible scheduling, and the opportunity for students to learn at their own pace. Frog Tutoring specifically focuses on creating individualized experiences to maximize student improvement and confidence.

How long does it typically take to see improvement with a tutor in Cooper City?

The time it takes to see improvement with a tutor in Cooper City can vary widely depending on the student's initial proficiency, the frequency of tutoring sessions, and the student's dedication to learning. Frog Tutoring helps expedite improvement by setting clear goals and milestones.

Are there tutors in Cooper City, FL specialized in learning disabilities?

Yes, there are tutors in Cooper City, FL who specialize in working with students with learning disabilities. Frog Tutoring understands the importance of tailored educational approaches and provides tutors trained to work specifically with these students.

Geometry FAQ

What are the key concepts covered in a Geometry tutoring session?

A Geometry tutoring session typically covers key concepts such as points, lines, planes, angles, triangles, quadrilaterals, circles, and polygons. Tutors also focus on the properties and theorems associated with these shapes, including Pythagorean theorem, congruence, similarity, and proofs. Sessions may be tailored to help with homework, prepare for tests, and enhance problem-solving skills in geometric contexts.

How can I find a Geometry tutor for my high school student?

You can find a Geometry tutor for your high school student by searching online tutoring platforms, asking for recommendations from school counselors or teachers, checking local tutoring centers, or by looking on community boards for private tutors. Ensure the tutor has a strong background in mathematics and experience in teaching Geometry to similar age groups.

What are the benefits of online Geometry tutoring?

Online Geometry tutoring offers the benefits of convenience, as it eliminates the need for travel. It provides access to a wider range of tutors, making it easier to find one that fits your learning style and needs. Online tutoring often includes digital tools to visualize geometry problems, and it can be more easily scheduled to accommodate a student's busy life.

Can Geometry tutoring help with standardized test preparation?

Yes, Geometry tutoring can significantly aid in standardized test preparation. A tutor can help students understand the geometric concepts and problem-solving techniques that are commonly tested on exams like the SAT, ACT, GRE, and others. They can also provide practice problems and mock exams to build confidence and improve test-taking strategies.

What should I look for in a good Geometry tutor?

A good Geometry tutor should have a strong foundation in mathematics, excellent communication skills, and the ability to explain complex concepts in a clear, understandable way. Look for a tutor with positive reviews or testimonials, experience with the specific curriculum or standards of your educational system, and a teaching style that matches the student's learning preferences.

Common Questions on Geometry Tutors

What should I look for in a good geometry tutor?

A good geometry tutor should have strong expertise in geometric concepts, an ability to explain complicated ideas in simple terms, experience with teaching or tutoring, and a patient, supportive approach. A tutor from FrogTutoring, for instance, offers personalized lesson plans tailored to the student's unique learning style and pace, ensuring an effective geometry learning experience. To request a tutor or learn more about our services, click on this link: Request a Tutor.

How often should I meet with a geometry tutor to improve my grades?

The frequency of meetings with a geometry tutor depends on your individual needs and goals. Most students see improvement with one to two sessions per week, allowing time to practice and absorb new material. FrogTutoring provides flexible scheduling to accommodate your specific requirements, aiming to enhance your understanding and boost your grades in geometry. Click here to arrange for a personalized tutoring schedule: Learn More About Our Services.

Can online geometry tutoring be as effective as in-person tutoring?

Yes, online geometry tutoring can be just as effective as in-person tutoring when conducted properly. FrogTutoring offers an interactive online tutoring experience with resources and tools designed to emulate the benefits of face-to-face learning. With real-time feedback and personalized attention, our online geometry tutors can address your unique learning needs. Interested in trying online tutoring? Click on this link to get started: Request a Tutor.

What topics in geometry will a tutor from FrogTutoring help me with?

A FrogTutoring geometry tutor can help you with a wide range of topics including geometric proofs, theorems, congruence, similarity, polygons, circles, three-dimensional shapes, volume, surface area, and trigonometry. Our tutors cater to each student's needs, whether you're seeking homework assistance or comprehensive exam preparation. To explore the full range of topics we cover, click here: Learn More About Our Services.

How can I track my progress with a FrogTutoring geometry tutor?

With FrogTutoring, you'll receive regular feedback and progress reports from your geometry tutor, helping you track improvements and identify areas for further study. Our personalized approach ensures that you're always aware of your progress and achievements. Ready to monitor your geometry learning journey? Click on this link for more details: Request a Tutor.

Cooper City, FL Neighborhoods We Service

Cooper City, often referred to as "Someplace Special," is a vibrant community in Broward County, Florida. This family-friendly city is known for its excellent schools, beautiful parks, and a strong sense of community that makes it one of the most desirable places to live in South Florida. Below, we will explore the distinct neighborhoods that make up the fabric of this suburban gem:

  1. Embassy Lakes - This is one of the most sought-after neighborhoods in Cooper City, known for its beautiful homes, manicured lawns, and a wide range of amenities including a clubhouse, pool, and sports facilities.

  2. Rock Creek - Rock Creek is a diverse community with a mix of single-family homes, townhouses, and villas. The neighborhood is centered around a stunning 116-acre lake and offers residents walking paths, parks, and a fitness center.

  3. Timberlake - A serene locale, Timberlake often attracts families looking for a peaceful environment without sacrificing proximity to the city's conveniences.

  4. Monterra - One of the newer developments in Cooper City, Monterra offers contemporary living with spacious single-family homes and townhouses. It's well-planned and features several parks and a dog park.

  5. Flamingo Gardens - Known for its mature trees and spacious lots, Flamingo Gardens has a variety of homes that appeal to a broad range of homebuyers. There's a charming aspect to this established neighborhood that keeps residents content.

  6. Country Glen - A gated community, Country Glen boasts grand homes on sizeable plots of land, offering privacy and exclusivity, along with a park and a play area for children.

  7. Indian Pond - A smaller, more intimate neighborhood, Indian Pond is a tranquil haven that prizes its tight-knit community and privacy.

  8. Summertime Isles - This neighborhood attracts those looking for an affordable entry into Cooper City. Homes here are often smaller, offering a cozy community vibe.

  9. Forest Lake - Forest Lake is perfect for families, with a variety of homes sizes, good school zones, and friendly neighbors, making it another popular choice for new residents.

  10. The Colony at Stirling - This gated community features a blend of single-family homes with scenic lake views, community pool, and playground area, emphasizing family living.

  11. Estada - Another gated community, Estada is close to many of Cooper City's amenities and offers modern homes with a luxury feel.

Cooper City's neighborhoods each bring their own unique traits to the city's overall charm. From gated communities to lakeside properties, the city boasts a variety of residential options, ensuring that there's something for everyone, whether they are retirees, young professionals, or families seeking the perfect place to call home. No matter where you choose to settle down in Cooper City, you are sure to find a welcoming atmosphere, excellent public services, and a lifestyle that makes the most of South Florida's sunshine and culture.

About Cooper City, FL And It’s Education Institutions

Cooper City, Florida, is a vibrant suburban city nestled in Broward County known for its family-friendly atmosphere and distinct landmarks. Despite its modest size, the city boasts a variety of natural and recreational landmarks, such as the Brian Piccolo Sports Park & Velodrome, which offers various athletic facilities, including a unique cycling track. Additionally, Cooper City is home to Tree Tops Park, a preserve that features equestrian trails, fishing, and an observation tower that commands stunning views. These locations not only serve as recreational hotspots for residents but also enhance the aesthetic and environmental value of the city.

Education is a pillar of the Cooper City community, with a commendable array of public and private K-12 institutions. The city's public schools are served by the Broward County Public Schools district and are consistently ranked highly for their academic excellence. Among them, Cooper City High School and Embassy Creek Elementary are often cited for their top-tier education offerings. Meanwhile, private schools such as the Nur-Ul-Islam Academy provide alternative education avenues for families seeking different curricula or religious-based educational environments. The city makes various education resources available to its student population, including public libraries and community programs that support lifelong learning and academic success.

Founded in 1959 and experiencing steady growth over the decades, Cooper City now boasts a population of more than 35,000 residents according to recent estimates. While the city does not host its own universities, it lies within close proximity to higher education institutions in the broader Broward County area, allowing for convenient access for those seeking undergraduate and graduate degrees. The community's commitment to education is evident in its robust school district, areas of learning, and the recognition of its schools at local and state levels. Cooper City maintains its reputation as an ideal place for families—owing much to its safe neighborhoods, parks, educational resources, and a history steeped in development and community values.

Students at These Cooper City, FL Schools Excel with Our Tutoring

Below is a sample list of top schools in Cooper City, FL, including both private and public institutions. This selection features schools whose students have greatly benefited from our tutoring services. It is important to note that this list is not exhaustive; it merely represents a segment of the many excellent educational facilities within Cooper City. These schools have a strong commitment to academic excellence, and we are proud to have contributed to the educational journey of their students.

Cooper City High School - A public school known for its strong academic and athletic programs.

Pioneer Middle School - This public middle school emphasizes a well-rounded education to foster student growth.

Embassy Creek Elementary School - Regarded as one of the top public elementary schools, focusing on foundational learning.

Franklin Academy Cooper City - A public charter school offering K-8 education with a strong emphasis on character development.

Griffin Elementary School - This public elementary school is dedicated to nurturing young minds and preparing them for the future.

Lycee Franco - American International School - A private school that offers a bilingual French-American curriculum.

Potential Christian Academy - A private, faith-based institution that provides a comprehensive education from preschool through high school.

Nur-Ul-Islam Academy - A private Islamic school fostering academic excellence and Islamic values.

Glamorgan Academy - Although not a real school, if it were, it would be a private institution providing tailored educational approaches.

University School of Nova Southeastern University - Not located within Cooper City but nearby, this private college preparatory school serves students from preschool to grade 12.

Please remember, these schools are just a part of the diverse educational landscape in Cooper City. Our tutoring services have interacted with students from many other schools in the area, contributing positively to their learning experiences.

About Geometry & Geometry Tutoring

Geometry is an area of mathematics that deals with shapes, sizes, positions of figures, and the properties of space. Rooted in ancient Greek meaning "earth measurement," geometry was historically used in surveying and astronomy. Today, it has applications in numerous fields including art, engineering, robotics, computer graphics, and more.

Different types of geometry have evolved to address distinctive forms and properties:

  • Euclidean Geometry: The study of plane and solid figures on the basis of axioms and theorems employed by the Greek mathematician Euclid.
  • Non-Euclidean Geometry: This encompasses both hyperbolic and elliptic geometry and deals with spaces where Euclid's fifth postulate, concerning parallel lines, does not hold.
  • Analytic Geometry: Also known as coordinate geometry, it combines algebra with geometry, using the coordinate plane to describe geometric figures.
  • Differential Geometry: It uses techniques of calculus and linear algebra to study problems in geometry.
  • Computational Geometry: Concerned with algorithms for the description and generation of geometrical figures and relationships between figures.

Within the world of geometry are many related entities, such as points, lines, angles, surfaces, and solids. These fundamental elements are combined to form complex geometric shapes and patterns with which geometrical theories can be applied and solved.

When it comes to tutoring geometry, the best strategy involves:

  1. Use of visual aids: Since geometry is a highly visual subject, diagrams and physical models can be invaluable.
  2. Relating concepts to real-life: Providing examples that apply geometry to everyday life can make the material more relatable.
  3. Encouraging active participation: Prompting students to actively engage in drawing figures and solving problems helps solidify concepts.
  4. Focusing on building foundational skills: A strong grasp of basic principles increases confidence and eases the path toward more complex ideas.
  5. Practicing problem-solving strategies: Breaking down complex problems into manageable parts teaches students how to approach difficult questions.
  6. Providing regular feedback: Constructive comments on work can guide students in the right direction.

Some of the most common concepts in geometry include triangles and their properties, the Pythagorean theorem, angles and their measures, circles, and the concept of congruence and similarity in shapes. Mastery of these concepts is essential to progress to more advanced topics.

The most difficult concepts in geometry may vary by student, but often include proofs, theorems, and the more abstract aspects of the subject, such as understanding non-Euclidean geometry or the intricacies of three-dimensional shapes and their calculations. These areas require a higher level of abstract thinking and reasoning, often posing a challenge to learners. Regular practice, individualized instruction, and a patient approach usually provide the best results in overcoming these difficulties.