One of the neat things about the Technical Note is that the solution to some of the complicated trig equations were found by an iteration method. The specific ideas for solving those equations are too advanced for kids, so I decided to show my son a different (and really simple) iteration method that converges to a well known number:

I and many others I know still communicate not digitally by text, but by voice on phone. I have made clear to all my kids for nearly 20 years in ALL your relationships you can communicate digitally by the text etc. but if you want to connect more deeply it is best not to rely on non-verbal communication. The text is not that entirely different from the telegraph in nature. There is nothing wrong with using technology to enhance learning, but it is likely that the majority or people will not learn better and faster by writing items down. You can look at the very top students, as they have more of a photographic memory in nature, which would lend to those few students having a more easy transition with technology. But looking at only the transition of the very top students o technology would create a large learning deficit with the masses. To move the needle best in learning you must always look at the center. The middle / average student. There you will have greatest effect. I wish you well.

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I performed a small study in my Pre-Algebra classes a few years ago to test whether forcing students to perform pencil-and-paper supporting work while doing on-line homework helped improve learning. Due to small sample size, I couldn't get a large effect size, but still the results were pretty convincing. The published article is here: -foundation.org/en/pencil-and-paper-in-math/ This summer I am hoping to recruit middle school teachers to run a similar experiment with a larger group. My hope is to show that while technology does have a role to play in modern math education (particularly, I think, in homework), students need to be encouraged to still perform complex mathematical tasks with pencil and paper.

Step 6: Provide Time, Materials, and Supervision for Self-Paced Learning

From this point on, students will begin the process of moving through the lessons on their own. Your job is to make sure they have the materials they need to do the work: If you are sending students to videos, make sure they have devices to access them (and earbuds to keep the audio to themselves). Make sure students know where to look for answer keys, and where they can access the mini-assessment when they are ready to take it. Check in with students regularly to make sure they are making good use of their time.

I teach Montessori at a public school and am trying something very similar to this with my students. It works really well for social studies topics that students need to research. Any bit of choice is exciting for students.

Hey, I love this idea! However, when you began to implement it did you have any push back from your administration or parents? I also have a limited amount of technology for students to watch videos and Be self paced. Are there any more ideas instead of videos?

That summer she had an opportunity to join a district Sheltered Instruction Observation Protocol (SIOP) cohort to receive professional development and support to meet the needs of ELLs in content classes. She learned about the importance of language acquisition, building background knowledge, increasing student language production, and explicitly teaching academic language. She began this school year with a new set of tools and a deeper understanding of the instructional scaffolding ELLs need in order to learn the content while also learning English. I am happy to report that while Hillary still feels challenged and is working very hard, this year has been much more successful for her and her students.

Hillary feels that she is providing them with the foundation they need not only to understand the mathematical concepts, but also to successfully interact within a math classroom in order to continue learning more advanced concepts.

This is a great site for teachers in the elementary levels, as it provides a list of keywords you can teach your ELLs to look for as they read word problems. Also included are useful ideas and tricks to better prepare students to understand written math problems.

Thanks so much for sharing your knowledge. This is one of the best articles I've read with ideas for teaching math to ELLs. We'll be putting these ideas into practice in our bilingual school in Mexico.

The study of secondary mathematics often begins by giving students the vocabulary first, along with definitions, before students have been able to explore the ideas. Preteaching definitions can actually hinder understanding rather than promoting exploration of important mathematical ideas, particularly for students bureaucratically designated as English Learners.

A microworld provides only the programming tools needed for a specific context. The Number Line microworld limits the programming blocks that children can access within Snap!; children have all, but only, the blocks they need. This limits cognitive distraction and provides a low threshold for entry into programming, while still giving children an authentic programming experience. The microworld also provides three sets of highly mathematical puzzles, increasing in sophistication, for children to solve. Children build scripts to solve these puzzles, which when run show the mathematical action on a stage, allowing the child to evaluate the results of their choices. In this way, the microworld acts as a math action technology (Dick & Hollenbrands, 2011; McCulloch et al., 2021), enabling children to explore mathematical concepts and relationships through action on mathematical objects.

Once you have created your question or determined your topic, prompt students to create a list of ideas and concepts related to the question. Novak refers to this as the parking lot. You may want to pre-create a list of concepts. Once students generate their parking lot list, you can either suggest any key terms that they missed or ask prompting questions to elicit them.

Concept maps are a simple but effective tool for helping students actively organize and consolidate their knowledge. They can be particularly effective in helping them literally see the cohesiveness of math. If you need more help to get started, check out the resources below:

At some point, teachers need to provide direct instruction to students that begins with manipulatives and conceptual knowledge, Too many teach algorithmic knowledge, so I get why the framework is swinging towards more varied strategies, but this is a swing way too far. The fact most teachers ignore the tech tools ( I teach teacher tech and elementary teacher math at Fresno State) that publishers now include with their series is something that needs to change and can be accomplished immediately with required trainings that were paid for but not used last adoption.

How do humans think about math at age 5, age 12, or age 18 and beyond? Students in this first-year seminar read, discuss, and write about mathematics teaching and learning. The course focuses on learning through a variety of methods, including hands-on crafts, open-ended class meetings, age-appropriate computer coding, and games ranging from very simple tech-free games to for-profit individualized-learning approaches. Each student reflects on their own pre-college experiences and thinks ahead about their anticipated courses and goals at Bates. No specific background in crafts, coding, games, or mathematics is expected, and everything students need to know will be taught as part of this course. Students of all backgrounds are welcome.

This course makes connections between the mathematics learned in math class and the mathematics used in several science courses. For example, how does the formula for the equation of a line relate to a set of data collected in physics, chemistry, biology, geology, or environmental studies? Students who wish to apply their mathematical knowledge to better understand scientific problems and students who want to strengthen their core mathematical skills are ideally suited to take this course. Not open to students who have received credit for MATH 106 or higher.

This course extends the ideas of Calculus I and II to deal with functions of more than one variable. While calculations make straightforward use of the techniques of single-variable calculus, more effort must be spent in developing a conceptual framework for understanding curves and surfaces in higher-dimensional spaces. Topics include partial derivatives, derivatives of vector-valued functions, vector fields, integration over regions in the plane and three-space, and integration on curves and surfaces. Prerequisite(s): MATH 106.

With varying subject matter, this writing-attentive seminar addresses both the oral and written communication of mathematics. The seminar focuses on understanding why rigor is necessary and what constitutes effective communication of mathematical ideas to different audiences. Students practice peer editing and peer reviewing, and learn how to write effective grant and thesis proposals. Prerequisite(s): MATH 221 or s21. 589ccfa754

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