After adding student or staff if you found there is no email is snding by system then thre may be email configuration issue on your server / Smart School.

In Smart School we have used phpmailer https://github.com/PHPMailer/PHPMailer library which is used by many popular php application like WordPress, Drupal, SugarCRM, Yii, Joomla etc.

By default SendMail is set as Email Engine in General Settings > Email Setting. SendMail can only work and send emails if you cpanel hosting supports it. If SendMail not sending email then contact to your hosting provider. Since SendMail is easiest but less reliable so check email recepient account Spam folder because sometimes SendMail sent emails detected as spams (if using SendMail). Another and best option is to use SMTP as email engine. You can use Gmail or any other free SMTP service provider to use SMTP email engine.
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If you are using your hosting smtp or any other provider smtp service then check their documentation for smtp settings.

You can use gmail smtp account for this go to Smart School admin panel System Settings > Email Setting then select SMTP then enter following details -

SMTP Username = your gmail email id
SMTP Password = your gmail email account password
SMTP Server = smtp.gmail.com
SMTP Port = 587
SMTP Security = tls

Now save this SMTP setting. After this login to your Gmail account then visit: https://www.google.com/settings/security/lesssecureapps then toggle on.

If you are using godaddy.com hosting then contact to godaddy because on some godaddy hosting smtp ports are disabled.

Note: After configuring email setting please check you have enabled email notification settings from System Settings > Notification Setting