Month: January 2023

Prioritizing Statistics over Algebra II

I have been reading “From reopen to reinventing” because I know the author promotes mastery learning and I came across a section that talked about the reluctance to consider changing many components of the curriculum. The discussion used Algebra II as an example. The section of the book argued that the math sequence – algebra, geometry, algebra II, and pre-calc has become possibly the most static part of the curriculum despite the discouraging experience it provides so many students. On one hand, there is the increasing K12 emphasis on STEM and on the other the low number of graduates who claim they so seldom have use for any mathematical knowledge/procedures past what they learned in Algebra I.

The book made reference to a Freakonomics podcast (America’s math curriculum doesn’t add up) which is probably over the top, but very interesting and well worth a listen. The podcast contains some of the stats on the long-term application of math that Horn uses in his book. For example, the Center for Education and the Workforce contend that only 11% of U.S. jobs require knowledge of concepts taught in Algebra II and 6% advanced operations. I suppose the argument “who actually ever uses this information” can be made for many content areas, but it is the combination of the number of math courses expected, the frustration so many students have with this discipline, and the limited number of courses students take that make this an important issue. BTW – if you do listen to the podcast take a look at the comment section which contains counterarguments from math teachers and math advocates. The argument which I recognize from one other area with many advocates (computational thinking developed through coding) suggests a different value for math beyond a direct application in a vocation. Such courses encourage the development of higher order thinking skills.

As I have argued in my comments on the “coding for all” position, there are many ways to develop the components of problem-solving in many other disciplines and the extent to which problem-solving as a higher-order skill transfers from one domain to another cannot be assumed. It is far easier to develop problem-solving skills in the domain to which they are to be applied. 

Horn makes a suggestion similar to the argument I have made several times in this blog. Statistics (I would argue it is more valuable to teach a course focused on both Statistics and Research Methods) as a math-oriented course teaching what I call data literacy. The use of data and the importance of interpreting and critiquing arguments made with data are so common it would seem familiarity with this topic is of greater value to more citizens and in more areas, than would be the case for advanced algebra concepts. Horn says the percentage of K12 students with some exposure to statistics is less than 20%.

So, I more and more see several of the math courses taught in K12 similar to the way I think about computer science courses in high school. These should be widely available as electives as both areas are essential for some students. Data literacy should be a topic widely integrated in multiple areas and statistics (and research methodology) should be as widely available as Algebra II.

Other resources: 

Just 1 in 4 high school students have taken statistics

My other posts on data literacy

Horn, M. B. (2022). From Reopen to Reinvent:(re) creating School for Every Child. John Wiley & Sons.

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Prepare students to make use of AI

Like so many educators I have been reading about and exploring ChatGPT. I recently read an article in the NYTimes that among other arguments made the point that all educators have a responsibility to prepare students for their future and AI will be an important factor in their future. So, while I was thinking about the role of educators and how they would deal with traditional issues such as student evaluation, I had not considered the broader goal of helping rather than preventing students from using AI.

I have not spent a great deal of time thinking through this new perspective, but it does seem important. Help students make use of ChatGPT rather than worrying about preventing the use of this tool.

For example, in their immediate circumstances, students might use ChatGPT to help themselves study. Note – I was originally trained as a biologist and to teach high school biology so I still often use that content area in my examples.

write 10 multiple choice questions about mitosis and meiosis and add an answer key at the end

1. What is the process of cell division that results in the formation of two genetically identical daughter cells?

a) Mitosis

b) Meiosis

c) Binary fission

d) Asexual reproduction

2. Which stage of mitosis do the chromosomes line up in the middle of the cell?

a) Prophase

b) Metaphase

c) Anaphase

d) Telophase

3. In which stage of mitosis do the sister chromatids separate?

a) Prophase

b) Metaphase

c) Anaphase

d) Telophase

4. How many cells are produced during mitosis?

a) 1

b) 2

c) 4

d) 8

5. In which stage of meiosis do homologous chromosomes pair up?

a) Prophase I

b) Metaphase I

c) Anaphase I

d) Telophase I

6. In which stage of meiosis do the cells divide?

a) Prophase I

b) Metaphase I

c) Anaphase I

d) Telophase I

7. How many cells are produced during meiosis?

a) 1

b) 2

c) 4

d) 8

8. Which of the following is a characteristic of meiosis?

a) The formation of genetically identical cells

b) The formation of genetically diverse cells

c) The formation of cells with half the number of chromosomes as the original cell

d) The formation of cells with twice the number of chromosomes as the original cell

9. What is the process called when homologous chromosomes exchange segments of DNA?

a) Mitosis

b) Meiosis

c) Crossing over

d) Chromosome segregation

10. What is the purpose of meiosis?

a) The formation of new cells

b) The formation of genetically identical cells

c) The formation of genetically diverse cells

d) The formation of haploid cells for reproduction.

Answer key:

1. a) Mitosis

2. b) Metaphase

3. c) Anaphase

4. b) 2

5. a) Prophase I

6. b) Metaphase I

7. c) 4

8. b) The formation of genetically diverse cells

9. c) Crossing over

10. d) The formation of haploid cells for reproduction

Or, maybe I am getting ahead of myself here. Maybe the first step would be to generate a quick review.

Explain mitosis and meiosis to a 9th grade student

Mitosis is the process of cell division that results in the formation of two genetically identical daughter cells. During mitosis, the cell duplicates its chromosomes, which are the structures that carry the cell’s genetic information. The duplicated chromosomes are called sister chromatids, and they are held together by a structure called a centromere. After the chromosomes are duplicated, the cell goes through several stages of mitosis: prophase, metaphase, anaphase, and telophase. In prophase, the chromosomes condense and become visible under a microscope. In metaphase, the chromosomes line up in the middle of the cell. In anaphase, the sister chromatids separate and are pulled to opposite ends of the cell. In telophase, the cell divides and two identical daughter cells are formed.

Meiosis is a type of cell division that occurs in the reproductive cells of organisms, such as sperm and eggs. During meiosis, the cell goes through two rounds of division, resulting in the formation of four genetically diverse daughter cells. In the first round of meiosis, called meiosis I, the cell duplicates its chromosomes, just like in mitosis. However, during meiosis I, the homologous chromosomes, which are pairs of chromosomes that carry the same type of genetic information, pair up and exchange segments of DNA. This process is called crossing over and it results in the formation of genetically diverse chromosomes. After crossing over, the cell goes through the stages of meiosis I: prophase I, metaphase I, anaphase I, and telophase I. In meiosis II, the cell divides again, resulting in the formation of four genetically diverse daughter cells.

So, to sum up Mitosis is the process of cell division that results in the formation of two genetically identical daughter cells, while Meiosis is a type of cell division that occurs in the reproductive cells of organisms, such as sperm and eggs and results in the formation of four genetically diverse daughter cells.

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My personal interests are in instructional design and student study behavior, but I think creating suggestions for preparing students to use AI is an important perspective for some curriculum person to take. Here is an Edutopia article with some ideas and resources for introducing AI concepts to students.

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Counting birds – Data literacy

Data literacy is one of the categories of posts I continue to develop. My initial exposure to data literacy came from a journal for school librarians. “Data literacy refers to the ability to understand, generate, and use data.” As schools continue to encounter recommendations for the development of skills students need to deal with the realities of the future (e.g., computational thinking), the case can be made that data literacy is as important as any other. The closest I can come to understanding what this means is based in my repeated exposure to statistics. It was an important part of my training as a psychologist, but working with data is common across so many areas and now with “big data” it seems the importance of thinking with data has only grown.

One of the interesting things about data is that it is so common and part of so many issues we encounter. The variety of situations in which understanding and using data is important offers both a challenge and an opportunity. The category of posts I have generated on data literacy offers what I hope are opportunities to encounter this variety. Here is another example that recently emerged from an unusual source.

A few months ago my wife finally received the complimentary sample of an IndieGoGo project she had invested in. The product was Bird Buddy. I like to describe it as a bird feeder with an embedded motion-activated digital camera. In other words, it takes photos of birds that visit the feeder and sends them to your phone. Pretty cool.

My initial experiences with the Bird Buddy reminded me of a data literacy project I had imagined several years ago. I do feed birds and I do take pictures. I had a different setup for taking pictures of the birds that came to my feeders and I proposed science projects be based on data that could be generated from such setups. The idea was not original and related to citizen science projects I was aware of originating from the ornithology program at Cornell University. 

The Bird Buddy people seem to have similar ideas and have taken advantage of their technology for capturing images and sharing these images digitally. My description of their process left out a few details. In their process, they make use of AI to identify the birds photographed and return the proposed identification to users. I say proposed because image identification is tricky and when uncertainty is clearly present the system proposes an identification and asks what the feeder owner thinks. 

The key to the potential for data literacy projects here is that the data from thousands of these feeders gets routed through the company to take advantage of AI identification and the company has begun aggregating these data in a project they call the Heartbeat Project. Try this link. It shows confirmed identifications of birds on a map as submitted from all over the world. It is fun just to watch. 

The company has started to do some simple analyses of these data and the first venture involved graphing the time of day with the greatest frequency of feeder visits. Simple, but you can begin to see the potential here. The variables are endless – region of world (down to a few yards), type of bird, time of year, time of day, etc., etc., etc. The company promises to share data with interested parties every few months.

I am hoping the company takes advantage of their data in the near future to offer opportunities to classrooms. It would be a great authentic data literacy experience to share feeder data with other schools and to propose questions the data might answer. 

I encourage educators who see the potential here to keep an eye on this company and its product.

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Designing instructional content using layering services

What is layering?

The addition of elements to the content offered by another content creator without actually changing that content as accessed from its original location.

Why should educators and instructional designers be aware of layering services?

There seems an increasing interest in moving beyond commercial materials (e.g., Ditch the Textbook) to meet educational goals and in some situations control costs. It can also be argued that most of us once out of formal school settings continue learning from sources not typically prepared as educational resources. Layering services allow those focused on education to use the content available online and improve this material to make it more productive for learning.

What elements can be added by layering?

The elements that can be added vary with the service. The total list I am aware of from my review of multiple services includes highlights, annotations or notes, questions, and discussion prompts. I use notes broadly to include the addition of multiple elements such as text, video, images, and links. Services differ in whether all participants can add all of the elements that a service makes available or whether some elements are limited to the educator/designer.

What makes the idea of layering distinct from activities such as highlighting a pdf or some other document I have downloaded?

Layering offers a way to respect content creator copyrights (see following segment), deliver learning experiences via the Internet, and transform informative online content into learning resources. The principles that make layering helpful to learners can certainly be applied to content a teacher or learner can access without the Internet.

Why should I worry about changing a document I have downloaded and want to share the new creation with students?

It depends on the situation. When a content creator places a video or multimedia content online, that content creator is not necessarily giving you permission to make that content your own or make changes to it and share it with others. However, this is often what an educator would really prefer to do for practical reasons such as changing the content to make it more useful as a learning resource and to provide the resource in the changed form to students. Such actions ignore the copyright expectations of the content creator which may intend the content to be offered complete with ads or even to generate download data financially benefitting the content creator. 

How does this situation change with layering?

With a layering service, the content a learner encounters is a combination of the content from the content creator and additions layered on this content. The service sends this combination to the learner and this does not change the original document and still downloads the original from the server each time the combination of original and layered content is requested by a user. Ads still appear and the content server still records the download to give the creator credit. 

My personal interest in promoting layering services is intended to encourage the use of services that meet the expectations of content creators and allow educators, educational content designers, and learners to work with this content to provide more effective learning resources and more generative learning experiences. 

The services I categorize as layering services vary along several dimensions. They differ in the elements that can be added and they differ in whether they are limited to adding layered elements to the composite served to learners or include other capabilities such as the management of assignments and the collection of learner performance data. Some services are free and some are provided to teachers and schools as subscription services.

A few years ago I generated some simple videos that offer examples of layering services suited to modifying online video and web content. These videos are available at no cost. I have also written an inexpensive Kindle book that provides an explanation of the value of the most common layered elements and takes users through adding these elements with several of the most popular layering services. I encourage you to at least take a look at the videos if what I have written here piques your interest. Layering services are also identified as a separate category on the blog and this content can be viewed by selecting the layering category option from drop-down category menu in the side column.

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Exposure to AI

There is so much attention to AI with the release of ChatGPT I know most educators have wondered what the future holds. I propose a simple step that offers some insights into the capabilities of AI as a way to test the waters.

There is a Chrome extension that generates side-by-side Google search results and ChatGPT replies to the same request. Adding an extension is not that difficult. The site makes the install fairly easy. You do need to create a ChatGPT account (you will be prompted) and this has been challenging because the service has been overwhelmed and persistence is required. After using this extension, you can move beyond this experience to submitting requests directly to ChapGPT.

Here are some examples I generated based on questions I happened to have at that moment. The Google results appear to the left and the ChatGPT response to the right.

Q. When is raking snow off your roof necessary?

Q. 2 – Why is renting in Hawaii so expensive?

Q. 3 – What are some examples of mastery learning strategies? (the third column was generated by MEMEX which is a note-taking tool I use and that offers any notes I happen to have that seem relevant).

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Mem Note Taking

I don’t know if the time has come for specialized note-taking tools for students, but some of the emerging capabilities used in these tools (e.g., AI) point to important future opportunities. My comments on these services in other posts have mostly focused on the long-term advantages of developing a large store of information that can be repeatedly examined to address immediate needs. There is no reason that this capability could not be an opportunity for students of any age, but younger students tend to be more focused on the next assessment challenge. So the adoption of the type of capability I describe here will likely move over time from grad students to college students to secondary students.

The impetus for this post came from a post I read on the Mem site. This post explained how Mem could be used as a note-taking tool for college students. I have been a Mem user for some time and thought I would create a post on this same topic. A couple of points first. I use the Mem X version which costs me $8 a month for the annual plan. I made this investment because I was interested in exploring the AI capabilities. There is a free version without this capability and reduced prices for students. It makes sense to start with the free version before going all in.

It occurred to me that students may be hesitant to trust an online service that is unfamiliar for their notes. I think it far more likely students would lose a notebook than lose access to their online notes. Students who take notes using a more familiar application can easily continue to do so and then copy and paste their notes into Mem. Mem does offer input and export capabilities so there is no permanent commitment if having your notes locked into a system outside your own computer is a concern.

I have tried to decide how to explain the note-taking method that makes sense for this service in an efficient manner. I am ignoring a description of downloading Mem and an overview of the service and will begin with what to do with a blank note (the create a note button appears in the upper right-hand corner of the following image).

Mem does not rely on a hierarchical storage approach which most tech users might imagine as a hierarchical system of folders. Because the notes taken for a given course needs some efficient way to differentiate the notes for that course, the mechanism I describe in Mem takes advantage of tags. Mem uses what is called markdown to add capabilities to raw text (like the tags in HTML). For tags, the markdown symbol is #. My example is set up for IDT 540 which is a course I teach, so I am using #IDT 540 – 2022 as my tag for the notes for this course. One nice feature of Mem is that it begins to offer suggestions as soon as it can guess what tag you may be entering (this is what you see below). You can enter tags at any location on a Mem “note”. Mem also treats the first text on a note as a label or title so I don’t want the tag at the very top. At the top I enter a title that is appropriate for the notes from a specific date. There is no reason only one note could be generated for a date. It might be more effective to focus on topics covered and differentiate the notes taken on a given day with some addition to the title text.

Here is the other adaptation it is useful to make to a Mem note. A learner will eventually want to “page” through their notes for study. The easiest way to do this is to link notes from adjacent classes. Notes can be found in other ways using search, but this is a handy technique that does not depend on search. Internal links in Mem use + as the markdown indicator for a link. Enter the + and begin entering the title for the preceding or following day’s note and the dates of notes will appear (again this is the anticipation text entry feature) and select the appropriate target or enter the entire title if none appears.

One more markdown technique that may be useful. For external links, the format is [text](URL). So, to link to the online syllabus for this course, I use the Syllabus for the text and the URL for the Google Site for my syllabus.

These three techniques should take care of the basics of taking notes. The screen view while taking notes is shown below. You should be able to identify the title, the link to the syllabus, and the internal link to the other existing note at the end. Other features on the screen include the button to control the sharing of notes and similar notes Mem has found among those I have stored (the system is using information in the present note to find related information in other notes).

The share feature could be useful if the teacher or student peers wanted to share notes. The previous image identified the share button that brings up the following window. Once you have identified other users or teams of users you share by entering the identity of the user or the team. You can also identify a share target using their email address. There are lots of interesting applications for sharing notes and Mem makes sharing easy among users.

This is the Mem home screen. I include it as a reminder that Mem has been designed as a location for all your notes over an extended period of time (i.e., years). Using Mem or a single course during that course would just scratch the surface of the power of this service. A couple of things to note from this image. The tags are displayed in the left-hand column. Most popular tags are visible and there is a link to all tags. The new note button appears in the upper right-hand corner.

Taking notes in this system is easy and requires only a couple of new techniques. The free version is the way to get started. Copying text from another existing note-taking approach (word processing document) would allow students to easily transition to using Mem “live” in their classes.

The link in the first couple of paragraphs to the Mem blog provides some other suggestions.

One more thing. Taking notes often benefits from including images or sketches. Mem note can include images. If the instructor provides access to her lecture slides, you can screen capture the parts of a slide you think would be helpful and then drag the image file onto a Mem note.

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Generative Hierarchy

I happened on this Medium post describing what the author called the Explanation Effect. The article itself was about strategies we can apply to learn and understand and the explanation effect sounded very similar to what I have previously described as Teaching to Learn. Teaching and even preparing to teach are great generative learning activities as most teachers will tell you. You must understand something to teach it well. The explanation effect implies more than the one-way act of teaching others and might be more accurately described as an educated discussion in which the parties involved share and perhaps even argue about something. Hence there is an exchange of information, accurate or not, about something. The Medium post argued this type of experience is one of the best ways to learn.

Generative learning activities have always been a personal fascination and the explanation effect would be an example. It is an example of an activity in which engagement in an external activity provides a likely way to manipulate important cognitive behaviors involved in retention and understanding. Many of the behaviors learners engage in as study activities are intended as generative activities.

To understand why engaging in tutoring (as a learner) or peer teaching (both parties are really learners) is proposed as a superior generative activity, it might be helpful to consider a hierarchical framework of generative activities proposed by Chi (citation included at end of this post). In this hierarchical framework, higher-level activities integrate lower-level activities and as one advances through the hierarchy it is proposed that activities at that level are more productive. In the following image, I have identified the stages of this framework and added an example of each level I assume would be familiar to most educators.

Smart notes require that a learner summarize and extend an input with personal insights or examples. So, a student might highlight a concept in a textbook (active) and then construct a note that summarizes what was highlighted as the learner understands it based on existing knowledge and perhaps include an example. Hence, additional cognitive activities would be included in the construction of a note. It is important to recognize that an activity (e.g., creating a note) may or may not involve productive cognitive behaviors (e.g., copying the text into a notebook) or may involve other cognitive activities leading to even more enhanced understanding and application. As an educational device, external activities are assigned with the expectation that the use of the activity will be productive, but the cognitive connections are always under the control of the learner.

I like to describe interactive activities as involving secondary inputs. If students discuss or argue about concepts from a book, the information in the book is the original input, but the comments from a peer or a tutor are a second input. The second input may add something new for the learner to add to an existing understanding or challenge the understanding the student has originally generated and now force a reconsideration and possible modification.

Chi and others have engaged in research to justify the proposed advantages I have described here. When researchers offer insights that hopefully will influence practice, the impact tends to depend on how practitioners translate general recommendations and how practical it seems it would be to come up with activities matched to these insights. I think educators understand practices such as guided discussion or issue debates and I hope the way in which I have explained the benefits of seeking activities at the constructive and interactive levels of Chi’s framework is persuasive

Chi, M. T. (2009). Active?constructive?interactive: A conceptual framework for differentiating learning activities. Topics in cognitive science, 1(1), 73-105.

Chi, M. T., & Wylie, R. (2014). The ICAP framework: Linking cognitive engagement to active learning outcomes. Educational psychologist, 49(4), 219-243.

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