WO2015012764A1

WO2015012764A1 - A system and method for learning mathematics

Info

Publication number: WO2015012764A1
Application number: PCT/SG2014/000347
Authority: WO
Inventors: Meng Kian TAI
Original assignee: Tai Meng Kian
Priority date: 2013-07-23
Filing date: 2014-07-23
Publication date: 2015-01-29

Abstract

The present invention provides a system for teaching mathematics comprising: a database (132) configured to store student answers to previous questions and/or statistics in relation to the answers; a question selection module (130) to randomly generate a plurality of questions depending on the accurancy of the previous questions or the statistics; an answer module (130) configured to parse the students answer to each question, and to display a result, a dynamically generated graphic, any applicable explanation depending on the answer and/or a visula or vocal explanation.

Description

A System and Method for Learning Mathematics

Field

The present invention relates to a system and method for learning mathematics. Background

Traditional methods for learning mathematics are based on direct instruction (using textbooks focusing on standard arithmetic methods) where students are taught one standard method of performing a task, in a standard sequence. The task is however taught in isolation rather than as only a part of a more complex project, which may then result in the students being unable to fully grasp and master the necessary conceptual understanding.

In addition, there is a time gap between when the students have completed the homework exercises and when an instructor (i.e. teacher) is able to provide explanations for incorrectly answered questions in the exercises (which understandably can only be done after the teacher has finished marking). By then, the students may already have lost impression of the practise.

Moreover, mastery of important mathematical solving techniques typically requires repetitive practise over a period of time, which may eventually bore the students. Fading interest or lack of motivation may also result from using the route-based learning approach, or lack of variation should they wish to do more practising.

Summary

In general terms in a first aspect the invention proposes a website which teaches mathematical skills to students by generating questions related to a plurality of skills, where the questions are generated to focus on skills for which that student has a relatively lower success rate in previous attempts. The system may display a level of accuracy for each skill previously attempted, either for individual students, or overall for the teacher. The accuracy may be based off the most recent attempts, to provide a more timely measure of mastery for each skill. In a second aspect the invention proposes that an official video explaining a solution to particular problem skill may be provided on an external link and/or other users solutions to that skill. Other users can be followed, so that any new or unseen answer videos by those users can be identified. The user may be able to add each skill to a cart of questions, which may be done instantly or added to a homework assignment..

In a third aspect, the invention proposes that an add-to-cart function may be provided by providing multiple add-to-cart buttons on multiple pages, where each page allows a user to perform a different function e.g. select questions, review past performance etc. This allows the user to add questions relating to particular skills to a virtual cart while performing the different functions. The pages with "add-to-cart" buttons may include a Log page, a "Practice/Test" page, a "Skill Table" page, a Review page etc. Having this add-to-cart function facilitates the process of selecting questions for a practice or a homework as the user can add a question to the cart whenever he/she finds it necessary to do so while performing a certain function.

Although this invention proposes a website which teaches mathematical skills, the first, second and third aspects mentioned above may also be applicable to websites which teaches other academic skills.

According to a first expression of the invention, there is provided a system for teaching mathematics comprising:

a database configured to store student answers to previous questions and/or statistics in relation to the answers;

a question selection module to randomly generate a plurality of questions depending on the accuracy of the previous questions or the statistics;

an answer module configured to parse the students answer to each question, and to display a result, a dynamically generated graphic, any applicable explanation depending on the answer and/or a visual or vocal explanation

According to a second expression of the invention, there is provided a system for teaching mathematics comprising: a database configured to store a plurality of questions categorised by skills; a question module configured to display each question and provide an external link to an answer explanation video relating to each respective question.

According to a third expression of the invention, there is provided a system for teaching mathematics comprising:

a plurality of pages, each page configured to allow a user to perform a different function;

a database configured to store a plurality of questions categorised by skills;

a virtual cart comprising a number for each category wherein the number indicates a number of questions added by the user for the category to the virtual cart;

a plurality of add-to-cart buttons, each add-to-cart button configured to allow the user to add a question for a category to the virtual cart;

wherein the plurality of add-to-cart buttons are provided on multiple ones of the plurality of pages.

These and other embodiments will be apparent from and elucidated with reference to the drawings and description hereinafter.

Brief Description of the Drawings

One or more embodiments will be disclosed with reference to the accompanying drawings, in which:

Figure 1 a is a screenshot of a student's home webpage;

Figure 1 b is a screenshot of a teacher's home webpage;

Figure 2a is a flow diagram illustrating a method of learning mathematics;

Figure 2b is a block diagram of the software modules;

Figure 3 shows an exemplary categorisation of questions stored in a database. Figure 4a shows the generation of parallel questions within a skill;

Figure 4b shows the output data structure for a pair of question and solution generated set within a skill;

Figure 5 shows two pairs of parallel question and solution set generated within a skill (data samples); Figure 6 shows an assessment analysis page where analytical homework creator may be used;

Figures 7 to 9 show screen shots of a Practice/Test page for a custom practice routine;

Figures 10 to 13 show screen shots of a quick pick routine;

Figure 4 show screen shots of a create scheduled homework routine;

Figure 15 show screen shots of a peer quiz routine;

Figures 16 to 18 show screen shots of a teach tweak routine;

Figures 19 to 23 show screen shots of an accuracy bar and tabulated results; Figure 24 is a screen shot of a results page for Students in relation to a test;

Figure 25 is a screen shot of a skill table including an accuracy report for a student;

Figure 26a is a screen shot of a different skill table;

Figure 26b is a screen shot of a log page;

Figure 27 is a screen shot of an accuracy report for a teacher;

Figure 28a is a screen shot of a skill page showing a YouTube link to an explanation video;

Figure 28b is a screen shot of a YouTube explanation video;

Figure 29 is a screen shot of a skill page showing a YouTube link to other user's explanation videos;

Figure 30 is a screen shot of a cart page;

Figure 31 is a screen shot of a different cart page;

Figure 32 is a screen shot of a different Practice/Test page;

Figures 33 to 35 are screen shots of further different log pages;

Figure 36 is a screen shot of a review page;

Figures 37 to 38 are screen shots of Analysis pages; and

Figure 39 is a screen shot of a followers page.

Detailed Description

A website for learning mathematics will now be described according to an example embodiment. The website uses sophisticated logic to generate a large number of permutations of questions and automatically generates easily understandable answers and explanations. Users of this website may be students, teachers or parents. The answers and explanations are provided in text, shown graphically and gradually explained by an avatar. The website allows a separate login facility for students and teachers.

Web Server

The website is hosted on a web server 120 as shown in Figure 2b. It is running a range of software modules and interfaces with other servers, including an avatar 122 and an accounting server 124. The accounting server 124 may limit availability of different features, or access to data depending on the time of the day and/or account level of the user who logs in. The web server 120 may include a MySQL database. The scripting language may be Hypertext Preprocessor (PHP).

Any of the modules, systems and/or methods disclosed below may alternatively be implemented on a private network, or as a standalone application.

Student module 126

Figure a is a screenshot of a student's home page. Under the "My" tab 202 the student may edit personal information, select a wall paper, customise the avatar, monitor any achievements and keep a log of past exercises done.

Under the "Work" tab 204 the student has a choice of a 8pm race, a practice/test or homework. For each option different questions are raised depending on the age/school level of the student. Submitted answers will be automatically marked by the website and a full set of solution is available for each question so that the students are able to get immediate feedback after attempting the questions. Explanation is provided in detail in both graphical as well as vocal form, by the avatar.

Under the "Fame" tab 206 the student can see the results for the 8pm race, interclass competition, the overall results compared to students at the same school level, and the monthly results for students at the same school level.

Under the "Play" tab 208 there is a game called Math Facts Power (MFP). This keeps a weekly high score of whoever is the best at answering as many questions as possible in each of four categories for a time period. The categories are addition, subtraction, multiplication and division and the time period is one minute each. There are also a range of other mathematics related games that the student can use to refresh mental stamina levels when getting bored.

Under the "Set HW" tab 210 the student or parent can set a homework exercise using selection criteria as shown in Figure 3. This will be described in more detail under the heading of "Homework automation" and "Analytical homework creator". As such, parents will be able to supervise and monitor their child's learning with ease by setting homework for their child. Student's correct attempts will contribute to their scores and the record may be tracked and maintained for a period of time to monitor their progress. Students with high scores may be displayed in "hall of fame" under a "Fame" tab 206 to stimulate their interest in learning and reinforce regular practice.. Races (under "Work" tab 204) may also be conducted on a regular basis via the online system to allow participants to have interactions and virtual competition with each other.

Teacher Module 128

Figure 1 b shows a screenshot of a teacher's home page. Under the "Tweak" tab 212, the teacher is able to get as many examples of each skill as he or she wants for classroom teaching. With the help of this function, the teacher may easily choose more questions from a particular skill for students to focus on.

The teacher may choose to refer to the text and answer solution in describing this to the students, or may utilise the avatar and graphical explanation by displaying the webpage to the class.

The "Worksheet" tab 214 is similar to the "Set HW" tab 210 for students (shown in Figure 3), in that it can be used to generate a set of questions for use during class. Various parameters can be set to determine how much working room, formatting options and ordering.

Under the "Homework" tab 216, the teacher can set and monitor homework. Similar to the generation of a worksheet, the homework can be set using the selection criteria shown in Figure 3. The results are shown in a table format showing the solution and how many students got each right. Homework groups can also be set, to select particular students for different homework allocations.

Under the "Report" tab 218, the school can generate reports at different levels, such as by teacher, by class, by level etc. Assessment results may be analysed automatically to provide information of students' performance. For example, the system provides homework analysis by question in real-time with percentage of wrong answers among those who completed the homework. An example is shown in Figure 6.

Question & Answer Module 130

For example when a student selects the practice/test option under the "Work" tab 204, he or she is presented with a range of skills, topics and levels that can be selected as questions for a practice question session. Each skill for each topic at each level is represented by a star. When the student hovers over a star a box appears with an example of the type of question.

When the student clicks on a star the question answer module operates according to the method 100 as shown in Figure 2a. A student may select a skill/skills to practice in step 102. The number of questions that the student wishes to practice for each skill may be also indicated at this step. The selection of questions for a practice question session using the stars will be elaborated in greater detail later on with reference to the skill table shown in Figures 7 - 9. In response to the student's selection, the web server 120 will retrieve a question at the selected skill in step 104.

The questions are presented to the student in step 106 via a webpage. Additionally the . student may request an online avatar 122 to also read out the questions.

In step 108, the student enters an answer (either by entering text, number, radio buttons or clicking on icons) and submitting the answer to the system. The data entry is then validated for format using automarker in step 1 10. The student entered answers are then matched against stored answers to determine whether the answers are correct or incorrect in step 1 10. After attempting one question, the student has the choice to retry a similar question, move on to the next skill or access a detailed solution. The detailed solution may include a text solution statement, an answer statement, unit of answer, solution graphic attributes and explanation script, as shown in Figure 4b. The solution statement consists of .step-by-step detail workings towards the solution to the question. Solution graphics attributes contain information such as the file location of a picture or programming attributes for a flash graphic or a picture to be generated. Solution graphic attributes may contain variables that may be determined by the flash object whether the drawing is a table or sets of models. For tables, the variables provide information for the table layout, heading and cell contents. For the set of models, the variables provide information for the number of sets of models, layout, heading, and models content including wordings, colour and length of model. The explanation script is designed for vocalisation by a character animation or avatar 122, if the student clicks on listen.

Upon completion of the current question, the user has an option to use/attempt another question of the same skill based on a previously presented or attempted question via functions such as tweak 134, homework automation and analytical homework creator. In particular, when the system is used in "student module" 126, a student may use the "tweak" function 134 to practice another question of the same skill as the previously attempted question. Similarly, parents may use "homework automation" to automatically generate a new set of homework comprising questions of the same skill as that of previously wrongly answered questions. Based on the result analysis of completed homework, teachers may create new homework directly on the analysis page by choosing questions from the skill for which the most students answered wrongly.

Avatar 122

The system is also provided with an online avatar 122 which is capable of reading questions and solutions to give the student a real human-teaching experience. There is an external engine that performs Text-to-Speech function which allows the avatar 122 to speak any text dynamically, in real time with accurate lip-synching through real human voices. The appearance of the avatar 122 may be customized in terms of facial features (for example, hair color/style, eye color, mouth, nose, etc), body features (clothing, body size, etc) and even voice and tone of speech.

The avatar 122, a flash object, is loaded on pages where voice performances are applicable. Each LISTEN/EXPLAIN button is linked to a javascript command to generate the text for the avatar 122. When a user clicks on button LISTEN/EXPLAIN, the pre-stored question/explanation script is sent to the text- to-speech engine to return a voice file to the user's browser. The pre-stored script consists of text to be spoken, volume, users stored avatar preferences and speed commands to control the pace and grammar of the speech. For some mathematic expressions it is necessary to pre-parse this script, for example, to convert fractions or units etc into a compatible text string for vocalisation.

Question generation

The system stores questions categorised by skills (either in the form of logic/question frameworks or actual questions). In particular, the questions may be dynamically generated using a logic framework, or every permutation may be stored in a database 132 and randomly selected. In either case, the logic will use a certain question and answer format for each skill type at each level.

In the worksheet shown in Figure 3 there are 6 levels (Primary 1 to Primary 6) of questions and each level comprises four chapters with each chapter including five skills. The skills (Skill 1 -5) progress in terms of difficulty levels over each chapter.

In order to generate the respective questions for each skill a question framework 302 may be provided as shown in Figure 4a. This may generate parallel questions that are variations of the same type of question. The variation results because variables such as names, objects, quantities, etc are part of the template logic and are randomly selected every time the question is iterated.

Thus the question framework 302 can either be iterated in real-time every time a question is requested or a large database can store the result of a large number of such iterations. In either case a different framework is used for each level, chapter and skill level to which the question belongs. For example, a question code P6raa155 corresponds to the 55 parallel question in the level Primary 6 chapter Ratio A skill 1 .

To facilitate students' self-learning ability, user entered answers are marked automatically and detailed solution set is also automatically generated using a similar framework to the question framework. The answer framework also includes logic for automatically generating scripts for graphic generation, and text string to be validated to parsing to the avatar 122. Similarly the answer framework can either be iterated in real-time every time an answer is provided or a large database can store the result of a large number of such iterations.

For example, if 99 pairs of parallel questions and solution are generated by a Macro for a skill P6raa1 (Primary 6 Ratio A skill 1 ), each pair will then be assigned a non-overlapping question code from P6raa101 -P6raa 99, respectively. The above described frameworks may be implemented with software such as Microsoft Excel or visual basic or may be integrated into the webserver software. An example of the parallel questions and solutions is as shown in Figure 5.

Homework automation

Teachers, parents or students can select a set of skills to practice using the selection criteria shown in Figure 3. Based on this, the website randomly generates the selected number of questions. For example, parents and teacher may set homework for the students, and teachers may also conduct test and print worksheets based on generated questions.

When parents set homework using the homework automation function, for any questions that were wrongly answered, the website may regenerate another similar question until the student gets it right. A parallel question from the same skill to that of each of the wrongly answered questions is randomly selected and presented for the student to solve. This process may be repeated until the student manages to correctly answer the questions that were answered wrongly in previous assessment. This function helps the student identify their weak points and actively reinforce their skills in those aspects by practicing the questions of the same kind. Analytical homework creator

As mentioned above the teacher is able to analyse students' test/homework assessment results statistically in terms of percentages of wrongly answered students for each individual questions in text, as well as graphically, using graphs or charts.

Based on the analysis derived from existing homework, the teacher may set new homework by focussing on the skills which students find difficulty. As shown in Figure 6, the assessment results 602 show that 95% of the students answered wrongly for Question number 20 relating to P5 Number B Skill 5 and 84% of the students answered wrongly for Question number 18 relating to P5 Number B Skill 4. Then the teacher can select those skills to generate parallel questions to create new homework. As described above, the web server 120 is then configured to randomly select questions from those skills and present the questions to the student.

8 pm race

Online races may be conducted on a regular basis for each level of students. Each race may comprise a pre-defined number of questions randomly selected from the database 132, and the selected questions are made available to the participants at a stipulated time. In a preferred embodiment, each race is catered for a group of participants of the same level (one race for each of Primary 1 to Primary 6). The web server 120 is configured to present a list of pre-stored questions of the same level for each race. The web server 120 analyses and ranks the results of accuracy and time of submission. The winner is the one who answers the most questions correctly the soonest after the race starts.

Custom Practice

An example method of customising a practice question session when a student selects the practice/test option under the "Work" tab is shown by way of a skill table in Figures 7 to 9. When the student selects the practice/test option under the "Work" tab 204, he or she is presented with a "Practice/Test" page showing a range of skills, topics and levels that can be selected as questions for the practice question session. In Figure 7 the student has clicked the level P6 700, representing their current year of study. Again the stars 702 show the number of questions under the skill/level that have already been correctly answered.

For each new practice, the system obtains new questions. The student may manually click the "+" button 704 to add a question from a particular skill for that practise. For example, in Figure 7, the student has selected two questions relating to Skill 4 of Topic Algebra A, one question relating to Skill 5 of Topic Algebra A, one question relating to Skill 3 of Topic Algebra B and one question relating to Skill 2 of Topic Algebra B as shown by the stars 706. As shown in Figure 7, these stars 706 (indicating the chosen questions) differ from the stars 702 (indicating the number of questions that have been correctly answered) in that the former are faded whereas the latter are filled. Once the desired number of questions has been selected (the number of faded stars next to the "Do now" 712 corresponds to the number of questions selected), the student selects a number of stars (for example, two stars 710 as shown in Figure 7) to represent a target number of correct answers for this practise. The student then clicks "Do now" 712 to start practice.

The actual questions may be dynamically generated using a logic framework, or randomly selected from permutations stored in the database 132, as described previously. For each skill a random question text is selected to generate the question.

Figure 8 shows the generated questions 800, and the student entering answers 801. The student has the option to save 802 the practice for later or to submit 804 for marking now. The users answers may be stored in real-time on web server 120, or may be temporarily stored locally if connectivity to the web server 120 is not online.

Figure 9 shows for each question, whether the question has been answered correctly 900 after submitting 804 for marking, and the corrected answer 902 for the wrong answers. The student has option to do another practice on similar set of skills by clicking on the "Tweak All 6" button 904 or to do another practice on questions that he got wrong by clicking on the "Tweak 4 wrongs" button 906. Quick Pick System

According to another alternative embodiment, instead of manually selecting skills, Figure 10 shows a "Quick Pick" option (which can be activated using the "Pick 10" button 1000) which uses a weighted selection algorithm to automatically pick 10 questions from the database 132 for the current level of student, (eg: Primary 6_. skills for Primary 6 student). Initially the user may manually select skills they want to include, as shown in Figure 12. This is done using the same method as explained above with reference to Figures 7 - 9. In particular, in Figure 12, the user has manually selected two questions relating to Skill 4 of Topic Algebra A and one question relating to Skill 5 of Topic Algebra A as represented by the faded stars 1202. The user may then click on the "Pick 7" button 1204 to "quick pick" the remaining questions to make up the 10 questions as shown in Figure 13. In particular, the faded stars 1302 in Figure 13 represent the 7 questions that have been "quick picked".

The web server 120 picks questions based on the progress through the school year, and the number of correctly answered questions in each category. For example in the month of January, only questions from the first 10 skills are eligible eg: Algebra A 1002 and Algebra B 1004. In February the first 20 skills, so Ratio A and Ratio B are added. This is intended to roughly follow the lessons on the same topics during the school year. If there are 90 skills, then by September the full set of skills are eligible. The web server 120 starts from the beginning to scan for skills with no earned (previously correctly answered) stars or selected star/skill within the given skill zone. Each selection of a skill results in one question for that skill.

If after a first round of scanning the skill zone, not all 10 questions are allocated, the web server 120 proceeds to scan for skills with 1 earned/selected star within the skill zone, and so on for 2, 3 etc stars until all required selections are made. Each automatic selection counts as a selected star (represented by a faded star). Figure 1 1 shows the "Quick Pick" process after the "Pick 10" button in Figure 10 is clicked without first manually selecting questions and when the skill zone includes only Algebra A and Algebra B. As shown in Figure 11 the process was partially through the 3rd star iteration 1 100 when 10 stars had been selected. In particular, in the first iteration, three questions were selected and these related to Skill 2 of Topic Algebra B, Skill 4 of Topic Algebra B and Skill 5 of Topic Algebra B as there were no filled or faded stars for these skills. In the second iteration, four questions were selected and these related to Skill 4 of Topic Algebra A, Skill 2 of Topic Algebra B, Skill 4 of Topic Algebra B and Skill 5 of Topic Algebra B as there was one star (either faded or filled) for each of these skills. In the third iteration, three questions were selected and these related to Skill 4 of Topic Algebra A, Skill 2 of Topic Algebra B and Skill 3 of Topic Algebra B as there were two stars (either faded or filled) for each of these skills. After selecting the 10 questions using the "Quick Pick" process, the student can then select "Do Now" 1 102 to generate the questions.

If after scanning for 9 earned/selected stars within the skill zone not all questions are allocated, the same process extends outside of the skill zone. If the entire 90 questions have been exhausted then it will select questions from the next level of student eg: P5->P6. If the maximum level is already reached, the process begins again as if there are no stars in the current level.

Scheduled Homework

According to a further alternative embodiment, the student can set scheduled homework as shown in Figure 14. The selections include frequency 1400 (Daily, Mondays, Tuesdays, Wednesdays, Thursdays, Fridays, Saturdays or Sundays), + and - buttons 1402 for the number of questions, a target 1403 number of correct answers, whether the homework automation feature(system automatically generates another homework from the wrongly answered question(s) of the scheduled homework done) 1404 is enabled and whether there is a reward 1405. Once the attributes are selected the student clicks "add" 1406 to save that schedule. Existing scheduled homework can be removed by selecting "delete" 1408 beside that line.

Peers Quiz System

According to a still further alternative embodiment, the student can create a quiz as shown in Figure 15. The student selects the number of questions 1500, closing date for the quiz 1502, and friends 1504 to include (class mates or students with the same star status). Once the student clicks on "create" 1506 the same generated quiz questions will appear in each contestant's menu. The quiz will be instantaneously marked (like practices) but the result will only be shown either after the deadline or after all contestants have completed the quiz, whichever is earlier. The quiz ranking is then determined based on most correct answers followed by shortest time taken to complete the quiz. The rankings are displayed to each contestant.

Teach-Tweak-Set Panel

As shown in Figure 16 the Teacher clicks Teach button 1600 under a given skill 1602, and as shown in Figure 17 a sample question 1700 for that skill is shown. The Teacher can click on the solution button 1702 to display an accompanying solution to teach. If necessary, the Teacher can click the Tweak button 1800 shown in Figure 18, that generates a similar question 1802 for the same skill, to reinforce teaching.

The Teacher can also click on Set 1804 to add questions to be set as homework for the students. Similarly the "Quick Pick" button 1806 is also available to set homework for the students.

Accuracy Bar

Figure 19 shows in Students' Practice/Set Homework pages the bar 1900 above each box of stars. The bar 1900 above the stars for each skill indicates the accuracy of that student's attempts on the skill (from all activities including practices, tests, quizzes, homework and race). A fuller bar indicates good performances (fully shaded bar means 100% accuracy).

In Figure 20, in the Teacher screen, the bar 2000 for each skill shows the accuracy of all of the students' attempts at the skill.

In Figure 21 when a student clicks on the accuracy bar, more details are shown:

(1 ) User accuracy information (You, 36%, 10/28) 2100 indicating the percentage of questions the student has answered correctly in all of his or her attempts from all activities for that skill;

(2) Everyone accuracy information (Everyone, 27%, 14/52) 2102 indicating the percentage of questions all the users (including the student) have answered correctly in all their attempts from all activities for that skill (3) (For students only) History of users' 28 attempts in graphic forms of ticks and crosses 2104 with each tick or cross 2104 indicating whether the student has answered a question correctly or wrongly.

When the student clicks on one of the ticks or crosses 2104, as shown in Figure 22, that particular attempt will be displayed with

(1 ) Attempt information (indicating details of the particular attempt including Date, Activity Type, User answer, Correct answer) 2200

(2) Question 2202

(3) Solution 2204

Figure 23 shows an alternative Teachers' Homework List Panel, where a fuller bar 2300 indicates good performances (fully shaded bar means all attempts were correct). When the bar is clicked, detailed information will be shown:

(1 )Number of wrong answers 2302

(2)Name of student and their wrong answers 2304

Figure 24 shows the results screen for Students in relation to a test. When the student clicks on the accuracy bar 2401 for tests, more details are shown:

(1 ) User test average (Your test average,2%) 2400 indicating the average level of accuracy for the student for that skill (e.g. Skill 5 in Figure 24) in the test;

(2) Everyone (Everyone, 2%) 2402 indicating the average level of accuracy for everyone for that skill (e.g. Skill 5 in Figure 24) in the test;

(3) History of user's 13 test attempts 2404 indicating the number of questions answered correctly for each attempt.

Accuracy report

In a further embodiment at the skill table (under practice for students, and under set homework for students and teachers), an ACCURACY button 2500 can be clicked to indicate the accuracy of attempts for each skill. In Figure 25, the number on the ACCURACY button 2500 indicates the number of attempts that will be considered when calculating the accuracy. The most recent 5 attempts usually reflect a user's current proficiency on that particular skill but this number on the ACCURACY button 2500 can be changed according to the user's preferences. Figure 25 shows that for the student, upon clicking the ACCURACY button 2500, the success or failure of all the attempts are shown by a series of ticks or crosses, and the most 5 (since the number on the ACCURACY button 2500 is 5) recent attempts are highlighted 2506. The percentage of the answers the user answered correctly in the most 5 recent attempts is what is shown in other views. In particular, these other views include the percentage of answers the user answered correctly in the last 5 attempts (see "ME" in Figure 24) and the percentage of answers everyone (including the user) answered correctly in attempts similar to the user's last 5 attempts.

The T button 2502 is the Tweak button referred to previously, when clicked once, a sample question will be shown. Repeated clicks will generate parallel questions. The + button 2504 allow selection to be made on that skill (much like the "add-to-cart concept in online shopping), for practices or homework.

Figure 26a shows a skill table in another embodiment. In this embodiment, the skill table also includes multiple buttons for each skill, one of which is the "add- to-cart" + button 2602 which allows the user to add a further question relating to the skill. The number in the square 2604 indicates the number of questions which have been added to the virtual cart (in Figure 26a, this number is 1 for Skill 1 of Topic Numbers to 10). The user can click on this square 2604 to remove a question related to the skill from the cart. The user can also click on the button 2606 to play a related Youtube video. The star button 2608 beside the + button 2602 indicates the number of correct attempts made for this skill (this number ranges from 0 to 10). When the user clicks on the star button 2608, a log page is brought up showing a log of the attempts made for this skill. This log page is shown in Figure 26b where there are also "add-to-cart" + buttons 2610 which allows the user to add questions to the virtual cart while reviewing his/her past attempts at the skill. In particular, each + button 2610 is associated with a particular question and when the user clicks on a + button 2610, a question parallel to the associated question will be added to the cart.

The "add-to-cart" function will be described in more detail later on.

Figure 27 shows for teachers, the ACCURACY button 2700 indicates the accuracy percentage for all her students' attempts. For example, in Figure 27, the number 96 in the ACCURACY button 2700 indicates an accuracy percentage of 96%.

Upon clicking on the ACCURACY button 2700, additional accuracy information is presented. These include "My class" 2702 which indicates the percentage of correctly answered questions in the most recent 100 attempts by students of the teacher's class and Everyone 2704 which indicates the percentage of correctly answered questions in the most recent 100 attempts by every user (including the teacher's students).

When user clicks on "Pick 10 Least Accurate" button 2508, the system scans for the least accurately (based on the ACCURACY button indicators) answered skills, and selects them for either practice (students) or homework (students or teachers). Once the skill categories are determined, then the subsequent steps of generating questions, asking the questions, and feedback, occurs as described previously.

Solution videos

As shown in Figure 28a, an alternative way of explaining the solution is providing users with a video link button 2802 for each of the 540 skills. The link eg: https://www.youtube.com/watch?v=U-ytoUsSVmQ will trigger a related explanation video like the screen shot shown in Figure 28b.

This will include an avatar explaining the solution as before, but it will include

(1 ) background music

(2) speech synchronized highlighted cursor movement

(3) speech synchronized progressive display of the solution statement.

User uploaded videos

Students and teachers can upload their own recorded solution video to their own youtube account, using tag "Learnlogy p5fra2" (for questions from the website) or "Learnlogy p5others" (for questions not from the website). For the former, as shown in Figure 29, video links appear under the respective skill's video link 2902. For the latter, videos are listed under a "other videos" page. Users can LIKE 2904 a video and FOLLOW 2906 their favourite uploaders. Users can record their own solutions using their preferred means (smart phones, cameras, webcam, screen capture etc). The web server 120 includes an automated algorithm or webcrawler to periodically scan for new YouTube clips with tag "Learnlogy". The clips are then vetted for clarity and accuracy before approval to be used as links in the website.

Add to cart system

The embodiments with the "add-to-cart" function include a Cart Page that can be accessed by the user (student or the teacher). Figure 30 shows an example of this Cart Page. In particular, the Cart Page shows a virtual cart that contains questions selected by the user. For example, in Figure 30, the virtual cart contains 2 questions for the (P6) Ratio A Skill 2, 1 question for the (P5) Fraction B Skill 5, 2 questions for the (P4) High Challenge A Skill 4 and 1 question for the (P4) High Challenge D Skill 1. Each time the user clicks on the add-to-cart + button 3002 (or the - button 3003) associated with a skill, the number of questions for the skill increases (or decreases) by 1. Figure 31 shows a variation of the virtual cart of Figure 30.

The number of questions for each skill in the virtual cart may be increased at pages other than the Cart Page. In particular, the user can add questions using add-to-cart buttons at other pages when reviewing performance for previously attempted questions. The user may be a student and the performance may indicate how he/she did for previously attempted questions or the user may be a teacher and the performance may indicate how his/her students did for previously attempted questions. Some of these other pages are elaborated below.

As mentioned above, the Skill Tables as shown in Figures 25 and 26 each includes add-to-cart + buttons 2504, 2602. In particular, there is an add-to-cart button for each skill of each topic. This allows the user to add a question for each skill based on his/her or his/her students' competency in the skill.

Figure 32 shows a "Practice/Test" page in an embodiment having the "add-to- cart" function. This "Practice/Test" page in Figure 32 differs from the "Practice/Test" page in Figure 7 in that instead of a "Do Now" button, an "add-to- cart" button 3202 in the form of a cart is provided. In this embodiment, the user selects the questions using the "+" buttons 3204 in the same manner as described with reference to Figure 7. However, in this embodiment, every time the user clicks on a "+" button 3204 associated with a particular skill, a question related to the skill is added to the virtual cart. After the user is done with the selection of the questions, the user then clicks on the "add-to-cart" button 3202 which brings the user to the Cart Page. At the Cart Page, the user can then decide whether to immediately do a practice with the cart items (which may include not only the selected questions from the "Practice/Test" page but also questions from other pages) or set a homework with the cart items.

The user can also add questions at the Log page. Figure 33 illustrates an example of a Log page which shows a history of the questions attempted by a student. The Log page includes a "+" button 3302 beside each attempted question so the student can click on the "+" button to add a question parallel to the attempted question to the virtual cart. Hence, the user may add more questions parallel to the attempted questions that he/she or his/her students got wrong. Figure 34 illustrates a variation of the example of the Log page in Figure 33. In this variation, instead of having the "+" button, the Log page includes buttons 3402 in the form of a cart. Each button 3402 corresponds to an attempted question and when the button 3402 is clicked, a question parallel to the attempted question is added to the virtual cart. Figure 35 illustrates another Log page whereby instead of showing a history of the questions attempted by the student, it shows a history of the activities performed by the student. This Log page also includes buttons 3502 in the form of a cart. Each button 3502 is associated with an activity such as Practice or Homework of the student. When the button 3502 is clicked, a question parallel to one of the questions that the student has gotten incorrect in the associated activity is added to the virtual cart. In particular, if the student has gotten more than one question wrong in the associated activity, one of these "wrong" questions is chosen (by a random selection) and a question parallel to the chosen "wrong" question is added to the virtual cart. If the student has not gotten any question wrong in the associated activity, then one of the questions in the activity is chosen (again by random selection) and a question parallel to this chosen question is added to the virtual cart.

Figure 36 shows an example of a Review page of a student. This page shows the questions attempted by the student and whether the student has answered the questions correctly.. On this page, as the student is reviewing his/her answers to the questions, he/she can click on the "+" button 3602 beside an attempted question to add a question parallel to this attempted question to the virtual cart.

Figures 37 and 38 respectively show example Analysis pages for teachers. In particular, the Analysis page in Figure 37 shows a table whereby each column with a "+" button 3702 represents a question, each row with a student's name represents a student and a tick or cross at the intersection of a row and a column indicates that the student represented by the row has answered the question represented by the column correctly or wrongly. When the teacher clicks on a "+" button 3702 of a column, a question parallel to the question represented by the column is added to the virtual cart. The Analysis page in Figure 38 shows a number of rows, each representing a question. Each question is associated with an accuracy level indicated in the rightmost "Accuracy" column. For example, in the first row representing a first question, 8 students have gotten the question wrong as shown in the "Accuracy" column. A "+" button 3802 is associated with each attempted question and similarly, when the teacher clicks on the "+" button 3802, a question parallel to the attempted question is added to the virtual cart.

Referring to Figures 30 and 31 , the Cart page shows the number of questions which have been added by the user either at the Cart Page or at other pages as discussed above. Users can make modifications (add or delete questions for each skill) and proceed to either do a practise based on the cart items instantly 3004, 3104 (for students only) or set a homework with the items in the cart 3006, 3106 (for students and teachers).

Similar to the embodiment in which the user clicks on the "Do Now" button in the Practice/Test page as discussed with reference to Figures 7 - 9, after the user clicks on the "Do Now" button or the "Set as Homework" button in the virtual cart, the actual questions may be dynamically generated using a logic framework, or randomly selected from permutations stored in the database 132. For each skill a random question text is selected to generate the question.

Followers

Under FOLLOWED page shown in Figure 39, users see all their favourite uploaders' videos, with the un-seen ones in bold 3902. Users can choose to "add to cart" 3904 the skills relating to the video.

While the invention has been illustrated and described in detail in the drawings and foregoing description, such illustration and description are to be considered illustrative or exemplary, and not restrictive; the invention is not limited to the disclosed embodiments. Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practising the claimed invention.

Claims

1. A system for teaching mathematics comprising:

an answer module configured to parse the students answer to each question, and to display a result, a dynamically generated graphic, any applicable explanation depending on the answer and/or a visual or vocal explanation.

2. The system in claim 1 wherein the database is further configured to store questions divided into sub-subject or skill categories, and the statistics include for each category, an accuracy figure indicating the accuracy at a most recent predetermined number of attempts at questions in the category.

3. The system in claim 2 further comprising a report module, the report module displaying one or more aspects determined from the student answers and/or the statistics.

4. The system in claim 3 wherein a first aspect is a teacher report configured to display the accuracy percentage for all her students' attempts for each category.

5. The system in claim 3 wherein a second aspect is a student report configured to display the accuracy for the most recent 5 attempts for each category.

6. The system in any one of claims 2 - 5 wherein the generated plurality of questions are first picked from the stored questions in the categories with the lowest accuracy figures.

7. The system in any of claims 3 to 6 wherein the one or more aspects include a visual representation of whether the sequence of answers were correct or not, and a summary of the accuracy of everyone on the system.

8. A system for teaching mathematics comprising:

a database configured to store a plurality of questions categorised by skills;

a question module configured to display each question and provide an external link to an answer explanation video relating to each respective question.

9. The system in claim 8 wherein a user can upload a video of an answer to the respective question.

10. The system in claim 9 wherein another user can follow or like the user's video.

1 1. The system in claim 10 wherein any newly uploaded videos from a followed user are highlighted.

12. The system in any of claims 8 to 1 1 further comprising a virtual cart to which users can add questions relating to the skills.

13. The system in claim 12 wherein the cart can be used to generate an instant series of questions or to provide a homework exercise.

14. A system for teaching mathematics comprising:

a database configured to store a plurality of questions categorised by skills;

a plurality of add-to-cart buttons, each add-to-cart button configured to allow the user to add a question for a category to the virtual cart; wherein the plurality of add-to-cart buttons are provided on multiple ones of the plurality of pages.

15. The system in claim 14, wherein the user can add questions to the virtual cart using the add-to-cart buttons when reviewing performance for previously attempted questions.

16. The system in claim 14 or 15, wherein the system comprises a skill table showing different skills of each of a plurality of topics and wherein the skill table comprises an add-to-cart button for each skill of each topic. 7. The system in any one of claims 14 - 16 , wherein another user can upload a video of an answer to an attempted question and wherein the add-to-cart buttons comprise a button provided with the video to allow the user to add to the virtual cart a question relating to a same skill as the attempted question in the video.

18. The system in any one of claims 14 - 17, wherein the virtual cart can be used to generate an instant series of questions or to provide a homework exercise based on the number of questions added to the virtual cart by the user for each category.