What are some appropriate and effective ways to use technology in the mathematics classroom? How can you ensure that students do not depend too heavily on technology to complete mathematics assignments?

On the second question, " do not depend too heavily..." is the issue. What does that mean?

Many schools, including the famous Chicago Math curriculum, have relegated the multiplication tables and fractions to calculator. So kids do not have to master 8 times 7, or 32 divided by 8 any longer....that is for the calculator. So kids never learn to estimate.
In that particular text, there are a few problems at the end of the chapter...that is the total extent of practice with that curriculum. Kids never get to master anything.
Enough preaching. But if math specialists cannot agree on what "too heavily" means, it is not possible to answer. As for myself, an Engineer by training, math is a language requiring fluency and detail.
So where does technology fit in? Not in 8 x 7. But it does have a use in 8.32 x 7.09
Computer graphing of complex equations. I remember in high school the hours I put in trying to graph manually.

y=Sinx + 1/2 sin3x + 1/5 sin 6x + 1/7 sin7x...The computer can do that easily, and should.

ok I do not understand that.

Using technology in the mathematics classroom can greatly enhance student learning and engagement. Here are some appropriate and effective ways to incorporate technology:

1. Interactive whiteboards: Utilize interactive whiteboards to display visual representations, solve problems step-by-step, and demonstrate concepts to the whole class.

2. Online math resources: Introduce students to online platforms and educational websites that offer interactive math activities, tutorials, and practice exercises. These resources provide personalized feedback and allow for independent practice.

3. Graphing calculators and math software: Encourage students to use graphing calculators and math software to visualize graphs, solve complex equations, and explore mathematical patterns.

4. Online collaboration tools: Foster collaborative learning by using online tools, such as shared documents, discussion forums, and video conferencing, to facilitate group problem-solving and peer feedback.

5. Mobile apps: Utilize math-related apps that provide additional practice, games, and real-world problem-solving scenarios to reinforce concepts and engage students.

To ensure students do not become overly dependent on technology, here are some strategies:

1. Set clear guidelines: Establish guidelines for when and how technology should be used in the classroom. Encourage students to solve problems manually before using technology.

2. Gradual integration: Instead of immediately introducing technology for all tasks, gradually integrate it into lessons and assignments, allowing students to build strong foundational skills first.

3. Provide alternatives: Offer a balance of technology-based and non-technology-based activities. For instance, some assignments can be done using traditional pen and paper methods or manipulatives.

4. Encourage critical thinking: Emphasize the importance of thought processes and problem-solving strategies over relying solely on technology. Assign tasks that require higher-order thinking skills.

5. Regular assessment: Regularly assess student understanding through quizzes, tests, or projects that require manual calculations or problem-solving without the use of technology.

By incorporating technology thoughtfully and purposefully, while also maintaining a balanced approach to math instruction, students can benefit from its advantages without becoming overly reliant on it.