Tuesday, March 28, 2023

8 Effective Practices that Improve Student Engagement and Learning

 As a teacher, it is important to be aware of high-leverage teaching practices that can increase student learning and engagement in the classroom. These practices are evidence-based and have been shown to be effective in a wide range of educational settings. There are many high-leverage teaching practices that can be used to ensure that students are learning and engaged. Here are some examples:

  1. Checking for understanding: Regularly check for student understanding to ensure that they are grasping the material. This can be done through informal questioning, exit tickets, or quizzes. My students love participating in a Quizziz, GimKit, Kahoot, or Blooket! These digital tools can give you valuable feedback about where students are in their progression of learning.

2. Active engagement:
Don't be a sage on the stage, be sure your students are actively engaged in the learning process. Get your students up and moving by having them rotate around the room and answer questions as well as check what other students think through a gallery walk. Use whiteboards to have students respond to questions and gamify learning through Jeopardy Labs or other online learning programs that give instant feedback. In addition, provide opportunities for students to participate in group work, problem-solving, and hands-on activities.

3. Clear learning objectives:
Be clear about what students are expected to learn and communicate this to them in a way that is easy to understand. Post your agenda on the whiteboard or use a Google Slide Deck to share the agenda and learning outcomes.

4. Effective feedback: Be sure to provide timely and effective feedback that is specific and actionable. This can be done through written feedback, verbal feedback, or peer feedback. Using Rubrics can also be an effective means of providing specific and measurable feedback as well as setting clear expectations for their work. Here is a rubric I created for our project on Area and Measurement.

5. Differentiated instruction:
Always differentiate instruction to meet the diverse learning needs of their students (including gifted and talented). This can be done by providing different levels of support, modifying assignments, or providing accommodations and challenges. One of my favorite ways to differentiate instruction is with games and open-ended tasks. Students can play a game and I can easily differentiate the cognitive demand so that students are working in their zone of proximal development.

6. Scaffolding: Teachers should provide support to students as they learn new skills and concepts. Explicit direct instruction is important to guide students and provide guidance in chunking and understanding the concepts and skills. This can be done by breaking down complex tasks into smaller, manageable steps and providing tools and resources for students to be able to work through the task independently.

7. Technology integration: Teachers should integrate technology into their instruction to enhance student engagement and learning. This can be done through the use of educational apps, online resources, or interactive whiteboards. Instead of having students look at maps to locate places, have them explore these places in real-time with Google Tours. You can have students create a virtual tour of historic events and narrate the significance of these places in a recorded tour that can be shared with other students, and parents too!

8. Classroom management: Teachers should have effective classroom management strategies in place to create a positive and productive learning environment. This can be done by establishing clear expectations, providing routines and procedures, and using positive reinforcement. My favorite way to set the stage for strong and positive classroom management practices is to greet students at the door and reinforce positive behavior throughout instruction.

Overall, these high-leverage practices have been shown to improve student learning outcomes across a wide range of subject areas and grade levels, and they are essential tools for effective teaching and learning.

So don't forget to plan to include these 8 Critical Practices for Effective Instruction. Leave a comment and let me know what is working in your class and be sure to subscribe for more fun posts and ideas that you can bring into your practice!

Thursday, February 23, 2023

7 Ways to Support Students Understanding of Place Value

Hey Teachers, did you know that a key foundation in students' mathematical learning is place value? Without a strong understanding, students will have difficulty in many other mathematical concepts and skills such as adding and subtracting multi-digit numbers. In addition, regrouping and decomposing numbers. (all based on place value) are critical to moving students toward fact fluency. Multiplication and division strategies also become too complex when students lack the foundation of place value to support their understanding of concepts and skills such as using the area model.

The decimal system, which is based on place value, is used in a wide range of mathematical concepts, including fractions, decimals, and percents.
Using manipulatives to support conceptual understanding of decimals builds a foundation for visualizing each place value. In this video Dr. D demonstrates how you can go from the concrete to the representational to the abstract (CRA Model) and build fluency with decimals through the process of building, speaking, writing, and representing decimal values. In addition, consider using virtual manipulatives for the exploration of decimals as shown here with the Math Learning Center.

Here are several reasons why students may struggle with place value:

  1. Conceptual understanding: Place value is a complex concept that requires a deep understanding of the relationships between digits and their place in a number. Students may have difficulty understanding the role that each digit plays in a number and how the position of a digit affects its value.

  2. Lack of practice: Practice is key when it comes to mastering place value. Students need repeated opportunities to work with numbers and see the relationship between the digits and their place in the number.

  3. Lack of visualization: Place value can be difficult to visualize, especially for students who struggle with spatial reasoning. Some students may have trouble visualizing what the numbers look like and how they change based on their place value.

  4. Memorization-based approach: If students rely solely on memorization to understand place value, they may struggle when they encounter new and more complex problems.

  5. Misconceptions: Students may develop misconceptions about place value due to their prior experiences or misunderstandings. For example, they may think that a number like "7" is the same as "70."

  6. Limited experience with larger numbers: Students who have limited experience with larger numbers may struggle with the concept of place value and the relative sizes of numbers.

Overall, place value is a complex concept that requires a deep understanding, repeated practice, and a clear visualization of the relationships between digits and their place in a number. Teachers can support students in their understanding of place value by providing opportunities for hands-on learning, visual aids, and direct instruction that addresses common misconceptions.

Here are 7 Ways to improve students' understanding of place value:

  1. Hands-on Activities: Provide students with hands-on activities that help them understand the concept of place value. For example, students can use base-10 blocks to build numbers and understand the relationship between the blocks and the digits in the numbers.

  2. Visual Representations: Use visual representations, such as place value charts and number lines, to help students see the relationship between the digits in a number and their place value.

  3. Real-world Applications: Connect the concept of place value to real-world situations, such as money and measurements, to help students see the relevance and importance of understanding place value.

  4. Practice and Repetition: Regular practice and repetition are essential for students to internalize the concept of place value. Provide students with a variety of problems and activities to work on and encourage them to self-check their work.

  5. Emphasize patterns: Show students how patterns can help them identify place values, such as noticing that the place value of a digit increases as you move from right to left.

  6. Use estimation strategies: Encouraging students to use estimation strategies, such as rounding numbers to the nearest ten or hundred, can help them understand the relative size of numbers and place value. Additionally, by estimating, students can check their answers and avoid making careless mistakes.

  7. Technology Tools: Students can engage in problem-solving with virtual manipulatives to build a number and solve problems with digital tools. Using virtual number lines, base ten blocks, and recording tools can help you see where students' gaps are and how they are making sense of the concepts and skills you are teaching.

For more math ideas please be sure to like and subscribe to the channel! @teacherpreptech

Saturday, February 11, 2023

5 Ways to Increase Student Engagement in your Classroom!

Check out my video on 5 Ways to Re-engage learners!

There is no doubt that student engagement matters. In fact, it is considered to be one of the most important factors in promoting academic success and well-being. Research has shown that students who are engaged in their education are more likely to have positive outcomes, such as higher grades, improved attendance, and better social and emotional well-being.

In addition, engaged students are more likely to develop a strong sense of self-efficacy, which is the belief in one's ability to succeed in any situation. This in turn leads to increased motivation and persistence whenever faced with a challenge. Engagement not only makes students gritty and develop a growth mindset, but it also promotes critical thinking skills and helps students make connections between the material they are learning and the real world. 

Engagement in the classroom is students taking part in the learning experience.  In my class, I often tell my students "whoever does the most talking".. and they respond "does the most learning".  But students' talking alone is not enough to foster engagement.  Teachers often use strategies such as equity sticks, randomized name pickers, cold calls, etc... but nothing fosters student engagement more than how you design instruction.  

Here are my 5 Ways to Increase Student Engagement:

  1. Make lessons interactive: Encourage students to actively participate in class by asking open-ended questions, conducting group discussions, and incorporating hands-on activities. This helps students stay focused and engaged in the learning process.

  2. Personalize learning: Get to know your students' individual interests, strengths, and needs. Use this information to create lessons that are tailored to their unique learning styles and incorporate their interests.

  3. Encourage collaboration: Group work can be a highly effective way to increase student engagement. Encourage students to work together on projects, assignments, and class discussions. This helps build teamwork skills and helps students learn from one another.

  4. Use technology: Incorporate technology into your lessons to make them more interactive and engaging. This can include using online resources, interactive whiteboards, or educational apps.

  5. Offer choice: Giving students choices in the learning process can help increase their engagement. Offer different options for assignments, such as podcasts, ted talks, and Youtube videos; allow students to choose topics for research projects, and provide opportunities for students to take the lead on class discussions. When students feel a sense of ownership and control over their learning, they are more likely to be engaged and motivated.

Student engagement not only leads to higher cognitive achievement but can positively impact students' mental health and reduce stress levels. When students are actively engaged in their learning and feel a sense of connection to their school and classmates, they are more likely to feel a sense of belonging and a positive school climate.

Overall, the research highlights the importance of student engagement in promoting academic success, personal growth, and well-being. By prioritizing engagement in the classroom, teachers can create a positive and supportive learning environment that encourages students to reach their full potential.

Tuesday, January 31, 2023

Teacher's Beware: Chat GPT is Coming to a Classroom Near You!

Have you heard of Chat GPT? More importantly, have your students used ChatGPT?  If you've never heard of CHAT GPT you should be aware that you might be reading a student's paper that was written by a chatbot.   Proponents of Chat GPT may sing the praises of its potential for classroom learning such as instant access to information,  answers to any questions, and saving time for tasks.  But if students are not writing papers and teachers are grading a paper written by a chatbot, then education has turned into a bunch of hoops to skip through and ChatGPT holds a much bigger potential for loss of learning than the pandemic.   ChatGPT is free and the papers are well-written so there is nothing holding your students back from using it.  As teachers, we can either embrace the tool or harness the power or warn our students about the repercussions of turning in a ChatGPT paper    

Want to see how it works check out my video below: 

And now without further ado, a blog post about ChatGPT written by ChatGPT: 

ChatGPT is a cutting-edge artificial intelligence (AI) technology that has transformed the way we communicate with computers. Developed by OpenAI, this language model is capable of generating human-like responses to a wide range of questions, making it an excellent tool for customer support, online tutoring, and much more. In this blog post, we'll explore the basics of ChatGPT, its applications, and why it's considered to be a major milestone in the field of AI.

What is ChatGPT?

ChatGPT is a deep learning language model that uses state-of-the-art neural networks to understand and generate natural language. It's trained on a massive amount of text data, allowing it to generate coherent and meaningful responses to any input. The model can be fine-tuned to handle specific tasks, such as answering questions about a particular subject, providing customer support, or engaging in small talk.

Applications of ChatGPT

ChatGPT has a wide range of applications, ranging from customer support to content generation. Here are a few of the most popular use cases:

  1. Customer Support: ChatGPT can be integrated into websites and apps to provide 24/7 customer support. Its ability to understand and generate natural language makes it an excellent choice for handling customer inquiries and resolving their issues.

  2. Online Tutoring: ChatGPT can be used to answer student's questions and provide explanations in real-time. It can also be used to generate practice problems and provide feedback on student's work.

  3. Content Generation: ChatGPT can be used to generate articles, blog posts, and even social media content. Its ability to understand and generate natural language makes it an excellent tool for content creation.

Why ChatGPT is a Major Milestone in AI

ChatGPT is considered to be a major milestone in the field of AI for several reasons:

  1. Natural Language Understanding: ChatGPT's ability to understand and generate natural language is a significant step forward in the field of AI. Its training on massive amounts of text data allows it to understand the nuances of language and respond in a way that is coherent and meaningful.

  2. Ease of Use: ChatGPT is incredibly easy to use. All you need to do is provide it with an input, and it will generate a response. This makes it an excellent tool for a wide range of applications.

  3. Cost-Effective: ChatGPT is significantly more cost-effective than hiring human customer support or content creation teams. It's available 24/7 and can handle an unlimited number of queries simultaneously, making it an excellent choice for businesses looking to save on labor costs.

In conclusion, ChatGPT is a major milestone in the field of AI that has revolutionized the way we communicate with computers. Its ability to understand and generate natural language, ease of use, and cost-effectiveness make it an excellent tool for a wide range of applications, including customer support, online tutoring, and content generation. As AI continues to evolve, it's likely that ChatGPT will play an even more significant role in our daily lives, making it an exciting time to be a part of the AI community.

Thursday, August 4, 2022

5 Ways to Build Mathematical Representations with Virtual Manipulatives

5 Mathematical Representations of physical, visual, symbolic, contextual, and verbal,  (NCTM, 2014) highlights the importance of strengthening students' ability to move between and among representations. Virtual manipulatives have the power to support students in seeing these connections and strengthening their flexibility between different representations.    Research across the grade span shows the use of virtual manipulatives across math concepts including geometry, algebra, fractions, and integers not only leads to greater time on task, but gain in academic achievement and conceptual understanding (Bolyard & Moyer-Packenham, 2012; Jones, Uribe-Fiorez, & Wilkens, 2011) 

Let’s take a look at 5 Ways to build Mathematical Representations with Virtual Manipulatives 

  1. Encourage Exploration with Virtual Manipulatives.  Our class would spend hours making fraction kits and too often those kits would only last a brief time.  While physically constructing manipulatives provides a sense of ownership and an opportunity for rich discussion, virtual manipulatives provide an efficient way for students to make sense of a math concept and attend to precision in their representation.  Using the Math Learning Center Fraction App students who may struggle to cut and physically distribute paper fractions, can easily create, and color. label and compare virtual fractions.  Students' representations can be shared visually to showcase a variety of representations using tools like Padlet or Google Slides. Encourage students to use virtual manipulatives when solving a rich CGI (Cognitively Guided Instruction) math problem or creating their own problem to share with the class. Display students' representation while they explain their thinking as a way to create a visual cue for recall.  

How to use Math Learning Center Fraction App:

How to use Pattern Blocks for dividing fractions:

  1. Build a virtual manipulative toolbox with Google Slides.  Students will need access to virtual manipulatives at their digital fingertips.  Using multiple forms of representations allows students to make sense of concepts and be flexible in mathematics.  Providing a virtual toolbox for students to use allows students to decide which virtual manipulatives to use to make sense of the problem and encourages students to extend their thinking with other representations.  As teachers, by focusing our attention on the task, students can have the authority to make a choice of which virtual manipulative works best.  Consider a problem such as 36 + 25 students can use base ten blocks, unifex cubes, an abacus, or counters to model their thinking and justify their reasoning.  Having students talk about and display their representation allows other students to see strategies that may be more efficient as well as connect visual representations with symbolic form.  You can make a copy of my Virtual Manipulative Toolbox to share with your students.  

Google Slide Manipulative Deck: https://bit.ly/3A21css

  1. Use Virtual Manipulatives Across Math Domains.  Whether physical or digital in order for manipulatives to be effective they must be used consistently over time (Sowell, 1989). Repeated exposure to the same manipulatives across math domains and concepts helps students activate prior knowledge, identify patterns, make the connection and see relationships across math domains.  In addition, this repeated exposure helps students understand the symbolic relationship and can lead to “concreteness fading” where students who receive consistent and effective use of manipulatives are more likely to transfer problems correctly as compared to children who do not receive instruction with only symbolic equations (Fyfe & McNeil, 2009). Thus it is important for teachers to not only use manipulatives consistently but build on manipulative use across grade spans.  Knowing that a kinder teacher used an abacus to teach counting, the first-grade teacher can extend using this tool into adding and subtraction, and the third-grade teacher can build on this skill by using an abacus to teach multiplication and division.  Teachers should plan strategically with their colleagues on using virtual manipulatives across grade spans.  The more experiences students have with the same manipulatives the greater they can extend their thinking with that tool.   

Check out my video on how to use an abacus across early math concepts:


  1. Be explicit in Making Math Connections.  As teachers, we often need to explicitly tell the relationship between the manipulatives and the math concept.  In fact, research has found that explicit statements about how the manipulative represents the concept or procedure direct children’s attention and allows students to focus on mathematics rather than trying to understand the relationship (Kirschner, Sweller & Clark, 2006). Repetition and practice of the skill are necessary for fluency to happen and certainly when students are allowed to construct understanding with digital tools mistakes are visible and reasoning can happen.  Too often in math students only see the product represented in symbolic form.  With virtual manipulatives, students can be guided visually throughout the process and see their product, while self-correcting where needed.  

6th grade Student Video Adding Integers with Digital Counters:



  1. Show what you Know with Virtual Manipulatives.  What appears on a test might not always represent what students understand and can do independently.  Providing students with an opportunity to explain their thinking is paramount in the process of learning and highlights the 5 Math Representations.  When students create products of learning with digital tools they can construct their understanding visually.  This will allow you to pinpoint student's misconceptions and provide just-in-time support. But more often than not, I have found this process has led to students’ self-correcting and deepening their understanding.  To build upon this process, you can have students record themselves explaining their representation using a tool such as Screencastify, Loom, or Flip Grid.  Student explanations are best supported with visual models, but visual models might not always transfer exactly how students would like them to be.  For example, I had a student with Dysgraphia who was unable to illustrate a net, however with  Virtual graph paper (http://print-graph-paper.com/) the student was able to attend to precision and demonstrate with confidence his understanding.

Teacher-created scaffolds for digital products lay the foundation for student success and can remove barriers to learning.  Take for example a student with ADD who has a hard time recalling the steps to solve two-digit multiplication with the area model.  With a digital template, the student can move step-by-step with support, while working independently.  https://youtu.be/gMFDqdNm2T0

Jamboard for reuse: https://bit.ly/35OzWA4

Whether you are teaching online, onsite or hybrid, virtual manipulatives are robust tools that can provide students with a pathway to make meaning out of abstract concepts. This is critical for all learners across the K-12 grade span as visual representations can cue students to make connections to previously learned concepts and lower the language barrier that teachers may not consider when it comes to teaching and learning math.  Virtual math manipulatives are defined as an “interactive web-based visual representation of a dynamic object that presents opportunities for constructing mathematical knowledge (Moyer, et al., 2002, p.373).  These web-based tools might not be how you experienced learning mathematics, but they certainly will pave the way for students who are entering a technology-rich workforce where digital skills are in high demand.  

Virtual manipulatives hold much promise for supporting students in developing  mathematical skills and conceptual understandings, and they certainly align with what students are doing outside the classroom and how they engage with friends in digital worlds such as Mindcraft and Roblox.  As teachers we know that capturing our students attention is paramount to learning and that our students are already coming into the classroom using digital tools to create, explore and have fun.  Why not extend your teaching of math concepts with virtual manipulatives, and let students show you what they know with virtual representations?


Bolyard, J., & Moyer-Packenham, P. (2012). Making sense of integer arithmetic: The effect of using virtual manipulatives on students’ representational fluency. Journal of Computers in Mathematics and Science Teaching, 31(2), 93-113.

Dickenson, Patricia (September 10, 2021) Virtual Math Manipulatives. Google Slides  https://docs.google.com/presentation/d/1JVpVH0zWzqF-QqdqZxGIs2Zc1p6aDiJk7rl3RMW3kYU/edit?usp=sharing

Dickenson, Patricia (ND) Area Model Multiplcation. Google Jamboard. https://bit.ly/35OzWA4

Fyfe, E. R., & McNeil, N. M. (2009). Benefits of “concreteness fading” for children with low knowledge of mathematical equivalence. Poster presented at the Cognitive Development Society, San Antonio, TX.

Huinker, D., McLeod, K., Hertzog, H., Gold, N. O. R. J., Zeitlin, J., & McCrory, R. Mathematics for Elementary School Teaching: What Is It and How Do Teachers Learn It?.

Jones, B. D., Uribe-Florez, L. J., & Wilkins, J. L. M. (2011). Motivating mathematics students with manipulatives: Using self-determination theory to intrinsically motivate students. Yearbook (National Council of Teachers of Mathematics), 73, 215-227.

Kirschner, P., Sweller, J., & Clark, R. E. (2006). Why unguided learning does not work: An analysis of the failure of discovery learning, problem-based learning, experiential learning and inquiry-based learning. Educational Psychologist, 41(2), 75-86.

Math Apps. The Math Learning Center (2005-2022). https://www.mathlearningcenter.org/apps 

Moyer, P. S., Bolyard, J. J., & Spikell, M. A. (2002). What are virtual manipulatives? Teaching Children Mathematics, 8(6), 372–377.

NCTM 2014 Executive summary principles and standards for school mathematics Natl. Counc. Teach. Math. 1–6

Sowell, E. J. (1989). Effects of manipulative materials in mathematics instruction. Journal for research in mathematics education, 20(5), 498-505.

Teacher Prep Tech (2021, Sept. 12). Virtual Manipulatives: Teachers K-8 Blended Learning [Video]. Youtube. https://youtu.be/uuqtq9oR53o

Teacher Prep Tech (2021, March 18). Dividing Fractions Using Pattern Blocks: Math Models with Virtual Manipulatives [Video]. Youtube. https://youtu.be/07DbIlbVtHM

Teacher Prep Tech (2021, March 18). How to use Virtual Manipulatives for Modeling: Addition Subtraction, Multiplication and Division [Video]. Youtube.https://youtu.be/ZqJ7ZKZtKZw

Teacher Prep Tech (2021, January 26). How to Add and Subtract Integers With Counters Using Google Jamboard Math For Kids By Kids

[Video]. Youtube.https://youtu.be/Kd7yjdoa88c

Teacher Prep Tech (2021, January 6). How to Use Google Jamboard for Math Area Model 2 Digit Multiplication for Kids by Kids [Video]. Youtube https://youtu.be/gMFDqdNm2T0

Virtual Online Graph Paper (2022). Print-Graph-Paper.com  http://print-graph-paper.com/virtual-graph-paper